import math

time: float = 0.0

# Initial assignments
P1 = time
P2 = abs(time)
P3 = abs(time)
P4 = math.acos(time)
P5 = math.acos(-time)
P6 = math.asin(time)
P7 = -math.asin(time)
P8 = math.atan(time)
P9 = -math.atan(time)
P10 = math.ceil(time)
P11 = math.ceil(-time)
P13 = math.cos(time)
P14 = math.cos(time)
P15 = math.exp(time)
P16 = math.exp(-time)
P18 = math.floor(time)
P19 = math.floor(-time)
P20 = math.log(time + 1)
P22 = math.log(time + 1) / math.log(10)
P24 = time**2
P25 = 2**time
P26 = time**time
P29 = math.sqrt(time)
P31 = math.sin(time)
P32 = -math.sin(time)
P34 = math.tan(time)
P35 = -math.tan(time)
P37 = time + 2
P38 = time - 2
P39 = (1 / 2) * time
P40 = 3 * time
P41 = time + 2
P42 = 2 - time
P43 = 2 / (time + 1)
P44 = 3 * time
y0 = []
variable_names = []


def model(time: float, variables: tuple[float, ...]) -> tuple[float, ...]:
    return


def derived(time: float, variables: tuple[float, ...]) -> dict[str, float]:
    P1: float = time
    P2: float = abs(time)
    P3: float = abs(time)
    P4: float = math.acos(time)
    P5: float = math.acos(-time)
    P6: float = math.asin(time)
    P7: float = -math.asin(time)
    P8: float = math.atan(time)
    P9: float = -math.atan(time)
    P10: float = math.ceil(time)
    P11: float = math.ceil(-time)
    P13: float = math.cos(time)
    P14: float = math.cos(time)
    P15: float = math.exp(time)
    P16: float = math.exp(-time)
    P18: float = math.floor(time)
    P19: float = math.floor(-time)
    P20: float = math.log(time + 1)
    P22: float = math.log(time + 1) / math.log(10)
    P24: float = time**2
    P25: float = 2**time
    P26: float = time**time
    P29: float = math.sqrt(time)
    P31: float = math.sin(time)
    P32: float = -math.sin(time)
    P34: float = math.tan(time)
    P35: float = -math.tan(time)
    P37: float = time + 2
    P38: float = time - 2
    P39: float = (1 / 2) * time
    P40: float = 3 * time
    P41: float = time + 2
    P42: float = 2 - time
    P43: float = 2 / (time + 1)
    P44: float = 3 * time
    return {
        "P1": P1,
        "P2": P2,
        "P3": P3,
        "P4": P4,
        "P5": P5,
        "P6": P6,
        "P7": P7,
        "P8": P8,
        "P9": P9,
        "P10": P10,
        "P11": P11,
        "P13": P13,
        "P14": P14,
        "P15": P15,
        "P16": P16,
        "P18": P18,
        "P19": P19,
        "P20": P20,
        "P22": P22,
        "P24": P24,
        "P25": P25,
        "P26": P26,
        "P29": P29,
        "P31": P31,
        "P32": P32,
        "P34": P34,
        "P35": P35,
        "P37": P37,
        "P38": P38,
        "P39": P39,
        "P40": P40,
        "P41": P41,
        "P42": P42,
        "P43": P43,
        "P44": P44,
    }
