Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.2% → 99.6%

Time: 8.6s

Alternatives: 11

Speedup: 0.2×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ t_2 := t_1 \cdot x\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-248}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-219}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))) (t_2 (* t_1 x)))
   (if (<= t_1 (- INFINITY))
     (/ y (/ z x))
     (if (<= t_1 -2e-248)
       t_2
       (if (<= t_1 2e-219)
         (* (/ x z) (+ y t))
         (if (<= t_1 5e+307) t_2 (/ (* y x) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / (z / x);
	} else if (t_1 <= -2e-248) {
		tmp = t_2;
	} else if (t_1 <= 2e-219) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double t_2 = t_1 * x;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (z / x);
	} else if (t_1 <= -2e-248) {
		tmp = t_2;
	} else if (t_1 <= 2e-219) {
		tmp = (x / z) * (y + t);
	} else if (t_1 <= 5e+307) {
		tmp = t_2;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	t_2 = t_1 * x
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y / (z / x)
	elif t_1 <= -2e-248:
		tmp = t_2
	elif t_1 <= 2e-219:
		tmp = (x / z) * (y + t)
	elif t_1 <= 5e+307:
		tmp = t_2
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	t_2 = Float64(t_1 * x)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(z / x));
	elseif (t_1 <= -2e-248)
		tmp = t_2;
	elseif (t_1 <= 2e-219)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (t_1 <= 5e+307)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	t_2 = t_1 * x;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y / (z / x);
	elseif (t_1 <= -2e-248)
		tmp = t_2;
	elseif (t_1 <= 2e-219)
		tmp = (x / z) * (y + t);
	elseif (t_1 <= 5e+307)
		tmp = t_2;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * x), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-248], t$95$2, If[LessEqual[t$95$1, 2e-219], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+307], t$95$2, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} + t \cdot \left(-1 - z\right)\right)\\ \mathbf{if}\;z \leq -0.76:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;z \leq -4.65 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-256}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (/ y z) (* t (- -1.0 z))))))
   (if (<= z -0.76)
     (* (/ x z) (+ y t))
     (if (<= z -4.65e-212)
       t_1
       (if (<= z 1.26e-256)
         (/ y (/ z x))
         (if (<= z 2.2e-8) t_1 (* x (/ (+ y t) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) + (t * (-1.0 - z)));
	double tmp;
	if (z <= -0.76) {
		tmp = (x / z) * (y + t);
	} else if (z <= -4.65e-212) {
		tmp = t_1;
	} else if (z <= 1.26e-256) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) + (t * ((-1.0d0) - z)))
    if (z <= (-0.76d0)) then
        tmp = (x / z) * (y + t)
    else if (z <= (-4.65d-212)) then
        tmp = t_1
    else if (z <= 1.26d-256) then
        tmp = y / (z / x)
    else if (z <= 2.2d-8) then
        tmp = t_1
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) + (t * (-1.0 - z)));
	double tmp;
	if (z <= -0.76) {
		tmp = (x / z) * (y + t);
	} else if (z <= -4.65e-212) {
		tmp = t_1;
	} else if (z <= 1.26e-256) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) + (t * (-1.0 - z)))
	tmp = 0
	if z <= -0.76:
		tmp = (x / z) * (y + t)
	elif z <= -4.65e-212:
		tmp = t_1
	elif z <= 1.26e-256:
		tmp = y / (z / x)
	elif z <= 2.2e-8:
		tmp = t_1
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) + Float64(t * Float64(-1.0 - z))))
	tmp = 0.0
	if (z <= -0.76)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (z <= -4.65e-212)
		tmp = t_1;
	elseif (z <= 1.26e-256)
		tmp = Float64(y / Float64(z / x));
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) + (t * (-1.0 - z)));
	tmp = 0.0;
	if (z <= -0.76)
		tmp = (x / z) * (y + t);
	elseif (z <= -4.65e-212)
		tmp = t_1;
	elseif (z <= 1.26e-256)
		tmp = y / (z / x);
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] + N[(t * N[(-1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.76], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.65e-212], t$95$1, If[LessEqual[z, 1.26e-256], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-8], t$95$1, N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-96}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= y -9e-96)
     (/ (* y x) z)
     (if (<= y -1.75e-245)
       t_1
       (if (<= y 1.6e-296)
         (/ (* t x) z)
         (if (<= y 3.35e-164) t_1 (* y (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (y <= -9e-96) {
		tmp = (y * x) / z;
	} else if (y <= -1.75e-245) {
		tmp = t_1;
	} else if (y <= 1.6e-296) {
		tmp = (t * x) / z;
	} else if (y <= 3.35e-164) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (y <= (-9d-96)) then
        tmp = (y * x) / z
    else if (y <= (-1.75d-245)) then
        tmp = t_1
    else if (y <= 1.6d-296) then
        tmp = (t * x) / z
    else if (y <= 3.35d-164) then
        tmp = t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (y <= -9e-96) {
		tmp = (y * x) / z;
	} else if (y <= -1.75e-245) {
		tmp = t_1;
	} else if (y <= 1.6e-296) {
		tmp = (t * x) / z;
	} else if (y <= 3.35e-164) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if y <= -9e-96:
		tmp = (y * x) / z
	elif y <= -1.75e-245:
		tmp = t_1
	elif y <= 1.6e-296:
		tmp = (t * x) / z
	elif y <= 3.35e-164:
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (y <= -9e-96)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= -1.75e-245)
		tmp = t_1;
	elseif (y <= 1.6e-296)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 3.35e-164)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (y <= -9e-96)
		tmp = (y * x) / z;
	elseif (y <= -1.75e-245)
		tmp = t_1;
	elseif (y <= 1.6e-296)
		tmp = (t * x) / z;
	elseif (y <= 3.35e-164)
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-96], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.75e-245], t$95$1, If[LessEqual[y, 1.6e-296], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3.35e-164], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* x (/ (+ y t) z))))
   (if (<= z -1.0)
     t_2
     (if (<= z -3.8e-212)
       t_1
       (if (<= z 1.45e-256) (/ y (/ z x)) (if (<= z 2.2e-8) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_2;
	} else if (z <= -3.8e-212) {
		tmp = t_1;
	} else if (z <= 1.45e-256) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    t_2 = x * ((y + t) / z)
    if (z <= (-1.0d0)) then
        tmp = t_2
    else if (z <= (-3.8d-212)) then
        tmp = t_1
    else if (z <= 1.45d-256) then
        tmp = y / (z / x)
    else if (z <= 2.2d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_2;
	} else if (z <= -3.8e-212) {
		tmp = t_1;
	} else if (z <= 1.45e-256) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = x * ((y + t) / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_2
	elif z <= -3.8e-212:
		tmp = t_1
	elif z <= 1.45e-256:
		tmp = y / (z / x)
	elif z <= 2.2e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_2;
	elseif (z <= -3.8e-212)
		tmp = t_1;
	elseif (z <= 1.45e-256)
		tmp = Float64(y / Float64(z / x));
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_2;
	elseif (z <= -3.8e-212)
		tmp = t_1;
	elseif (z <= 1.45e-256)
		tmp = y / (z / x);
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$2, If[LessEqual[z, -3.8e-212], t$95$1, If[LessEqual[z, 1.45e-256], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-8], t$95$1, t$95$2]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -1.06:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-257}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -1.06)
     (* (/ x z) (+ y t))
     (if (<= z -2.7e-212)
       t_1
       (if (<= z 6.4e-257)
         (/ y (/ z x))
         (if (<= z 2.2e-8) t_1 (* x (/ (+ y t) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -1.06) {
		tmp = (x / z) * (y + t);
	} else if (z <= -2.7e-212) {
		tmp = t_1;
	} else if (z <= 6.4e-257) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (z <= (-1.06d0)) then
        tmp = (x / z) * (y + t)
    else if (z <= (-2.7d-212)) then
        tmp = t_1
    else if (z <= 6.4d-257) then
        tmp = y / (z / x)
    else if (z <= 2.2d-8) then
        tmp = t_1
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -1.06) {
		tmp = (x / z) * (y + t);
	} else if (z <= -2.7e-212) {
		tmp = t_1;
	} else if (z <= 6.4e-257) {
		tmp = y / (z / x);
	} else if (z <= 2.2e-8) {
		tmp = t_1;
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -1.06:
		tmp = (x / z) * (y + t)
	elif z <= -2.7e-212:
		tmp = t_1
	elif z <= 6.4e-257:
		tmp = y / (z / x)
	elif z <= 2.2e-8:
		tmp = t_1
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -1.06)
		tmp = Float64(Float64(x / z) * Float64(y + t));
	elseif (z <= -2.7e-212)
		tmp = t_1;
	elseif (z <= 6.4e-257)
		tmp = Float64(y / Float64(z / x));
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -1.06)
		tmp = (x / z) * (y + t);
	elseif (z <= -2.7e-212)
		tmp = t_1;
	elseif (z <= 6.4e-257)
		tmp = y / (z / x);
	elseif (z <= 2.2e-8)
		tmp = t_1;
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.06], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-212], t$95$1, If[LessEqual[z, 6.4e-257], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-8], t$95$1, N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 64.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+53}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.3e+144)
     t_1
     (if (<= t -1.65e+53)
       (/ (* y x) z)
       (if (<= t -5.8e+36) t_1 (* y (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.3e+144) {
		tmp = t_1;
	} else if (t <= -1.65e+53) {
		tmp = (y * x) / z;
	} else if (t <= -5.8e+36) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-2.3d+144)) then
        tmp = t_1
    else if (t <= (-1.65d+53)) then
        tmp = (y * x) / z
    else if (t <= (-5.8d+36)) then
        tmp = t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.3e+144) {
		tmp = t_1;
	} else if (t <= -1.65e+53) {
		tmp = (y * x) / z;
	} else if (t <= -5.8e+36) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.3e+144:
		tmp = t_1
	elif t <= -1.65e+53:
		tmp = (y * x) / z
	elif t <= -5.8e+36:
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -2.3e+144)
		tmp = t_1;
	elseif (t <= -1.65e+53)
		tmp = Float64(Float64(y * x) / z);
	elseif (t <= -5.8e+36)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -2.3e+144)
		tmp = t_1;
	elseif (t <= -1.65e+53)
		tmp = (y * x) / z;
	elseif (t <= -5.8e+36)
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+144], t$95$1, If[LessEqual[t, -1.65e+53], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.8e+36], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-64)
   (/ (* y x) z)
   (if (<= y 3e-19) (* x (/ t (+ z -1.0))) (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-64) {
		tmp = (y * x) / z;
	} else if (y <= 3e-19) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5d-64)) then
        tmp = (y * x) / z
    else if (y <= 3d-19) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-64) {
		tmp = (y * x) / z;
	} else if (y <= 3e-19) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e-64:
		tmp = (y * x) / z
	elif y <= 3e-19:
		tmp = x * (t / (z + -1.0))
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-64)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 3e-19)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-64)
		tmp = (y * x) / z;
	elseif (y <= 3e-19)
		tmp = x * (t / (z + -1.0));
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e-64], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3e-19], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 65.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.3e+143) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e+143) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.3d+143)) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e+143) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.3e+143:
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.3e+143)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.3e+143)
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.3e+143], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 65.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.95e+146) (* x (/ t z)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e+146) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.95d+146)) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e+146) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.95e+146:
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.95e+146)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.95e+146)
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.95e+146], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 61.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \frac{y}{z} \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ y z) x))

C

double code(double x, double y, double z, double t) {
	return (y / z) * x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y / z) * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return (y / z) * x;
}

Python

def code(x, y, z, t):
	return (y / z) * x

Julia

function code(x, y, z, t)
	return Float64(Float64(y / z) * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (y / z) * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 22.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(-x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- x)))

C

double code(double x, double y, double z, double t) {
	return t * -x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * -x
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * -x;
}

Python

def code(x, y, z, t):
	return t * -x

Julia

function code(x, y, z, t)
	return Float64(t * Float64(-x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * -x;
end

Wolfram

code[x_, y_, z_, t_] := N[(t * (-x)), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

  (* x (- (/ y z) (/ t (- 1.0 z)))))