Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 89.1% → 96.8%

Time: 10.2s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - 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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{y - z}}{t - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- y z)) (- t z)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return (x / (y - z)) / (t - z);
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 - z)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (y - z)) / (t - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(y - z)) / Float64(t - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) / (t - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.4%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. associate-/r* 98.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

3. Simplified 98.3%

   \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

4. Final simplification 98.3%

   \[\leadsto \frac{\frac{x}{y - z}}{t - z} \]

Alternative 2: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))) (t_2 (/ (/ x t) y)))
   (if (<= z -1.7e+20)
     t_1
     (if (<= z -7.5e-113)
       (/ (/ (- x) t) z)
       (if (<= z 2.8e-305)
         (/ x (* y t))
         (if (<= z 2.85e-188)
           t_2
           (if (<= z 3.1e-109)
             (/ x (* z (- t)))
             (if (<= z 0.58) t_2 t_1))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.7e+20) {
		tmp = t_1;
	} else if (z <= -7.5e-113) {
		tmp = (-x / t) / z;
	} else if (z <= 2.8e-305) {
		tmp = x / (y * t);
	} else if (z <= 2.85e-188) {
		tmp = t_2;
	} else if (z <= 3.1e-109) {
		tmp = x / (z * -t);
	} else if (z <= 0.58) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / z) * (1.0d0 / z)
    t_2 = (x / t) / y
    if (z <= (-1.7d+20)) then
        tmp = t_1
    else if (z <= (-7.5d-113)) then
        tmp = (-x / t) / z
    else if (z <= 2.8d-305) then
        tmp = x / (y * t)
    else if (z <= 2.85d-188) then
        tmp = t_2
    else if (z <= 3.1d-109) then
        tmp = x / (z * -t)
    else if (z <= 0.58d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -1.7e+20) {
		tmp = t_1;
	} else if (z <= -7.5e-113) {
		tmp = (-x / t) / z;
	} else if (z <= 2.8e-305) {
		tmp = x / (y * t);
	} else if (z <= 2.85e-188) {
		tmp = t_2;
	} else if (z <= 3.1e-109) {
		tmp = x / (z * -t);
	} else if (z <= 0.58) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	t_2 = (x / t) / y
	tmp = 0
	if z <= -1.7e+20:
		tmp = t_1
	elif z <= -7.5e-113:
		tmp = (-x / t) / z
	elif z <= 2.8e-305:
		tmp = x / (y * t)
	elif z <= 2.85e-188:
		tmp = t_2
	elif z <= 3.1e-109:
		tmp = x / (z * -t)
	elif z <= 0.58:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -1.7e+20)
		tmp = t_1;
	elseif (z <= -7.5e-113)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 2.8e-305)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 2.85e-188)
		tmp = t_2;
	elseif (z <= 3.1e-109)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 0.58)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -1.7e+20)
		tmp = t_1;
	elseif (z <= -7.5e-113)
		tmp = (-x / t) / z;
	elseif (z <= 2.8e-305)
		tmp = x / (y * t);
	elseif (z <= 2.85e-188)
		tmp = t_2;
	elseif (z <= 3.1e-109)
		tmp = x / (z * -t);
	elseif (z <= 0.58)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.7e+20], t$95$1, If[LessEqual[z, -7.5e-113], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.8e-305], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e-188], t$95$2, If[LessEqual[z, 3.1e-109], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7e20 or 0.57999999999999996 < z

   1. Initial program 86.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.1%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 72.1%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 79.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

      2. div-inv 79.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   6. Applied egg-rr 79.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   if -1.7e20 < z < -7.5000000000000002e-113

   1. Initial program 95.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 68.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 56.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 56.4%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 53.5%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac 53.5%

         \[\leadsto \color{blue}{\frac{-\frac{x}{t}}{z}} \]

      4. distribute-neg-frac 53.5%

         \[\leadsto \frac{\color{blue}{\frac{-x}{t}}}{z} \]

   5. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{\frac{-x}{t}}{z}} \]

   if -7.5000000000000002e-113 < z < 2.80000000000000014e-305

   1. Initial program 95.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 86.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if 2.80000000000000014e-305 < z < 2.85000000000000013e-188 or 3.1e-109 < z < 0.57999999999999996

   1. Initial program 90.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 65.9%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   3. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   4. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 2.85000000000000013e-188 < z < 3.1e-109

   1. Initial program 99.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 63.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 51.8%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \frac{x}{\color{blue}{-t \cdot z}} \]

      2. distribute-rgt-neg-out 51.8%

         \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]

   5. Simplified 51.8%

      \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 3: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ t_3 := \frac{x}{z \cdot \left(-t\right)}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.7:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))) (t_2 (/ (/ x t) y)) (t_3 (/ x (* z (- t)))))
   (if (<= z -1.55e+21)
     t_1
     (if (<= z -8.2e-113)
       t_3
       (if (<= z 2.2e-306)
         (/ x (* y t))
         (if (<= z 6.3e-198)
           t_2
           (if (<= z 7.5e-110) t_3 (if (<= z 3.7) t_2 t_1))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double t_3 = x / (z * -t);
	double tmp;
	if (z <= -1.55e+21) {
		tmp = t_1;
	} else if (z <= -8.2e-113) {
		tmp = t_3;
	} else if (z <= 2.2e-306) {
		tmp = x / (y * t);
	} else if (z <= 6.3e-198) {
		tmp = t_2;
	} else if (z <= 7.5e-110) {
		tmp = t_3;
	} else if (z <= 3.7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = x / (z * z)
    t_2 = (x / t) / y
    t_3 = x / (z * -t)
    if (z <= (-1.55d+21)) then
        tmp = t_1
    else if (z <= (-8.2d-113)) then
        tmp = t_3
    else if (z <= 2.2d-306) then
        tmp = x / (y * t)
    else if (z <= 6.3d-198) then
        tmp = t_2
    else if (z <= 7.5d-110) then
        tmp = t_3
    else if (z <= 3.7d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double t_3 = x / (z * -t);
	double tmp;
	if (z <= -1.55e+21) {
		tmp = t_1;
	} else if (z <= -8.2e-113) {
		tmp = t_3;
	} else if (z <= 2.2e-306) {
		tmp = x / (y * t);
	} else if (z <= 6.3e-198) {
		tmp = t_2;
	} else if (z <= 7.5e-110) {
		tmp = t_3;
	} else if (z <= 3.7) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = (x / t) / y
	t_3 = x / (z * -t)
	tmp = 0
	if z <= -1.55e+21:
		tmp = t_1
	elif z <= -8.2e-113:
		tmp = t_3
	elif z <= 2.2e-306:
		tmp = x / (y * t)
	elif z <= 6.3e-198:
		tmp = t_2
	elif z <= 7.5e-110:
		tmp = t_3
	elif z <= 3.7:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	t_2 = Float64(Float64(x / t) / y)
	t_3 = Float64(x / Float64(z * Float64(-t)))
	tmp = 0.0
	if (z <= -1.55e+21)
		tmp = t_1;
	elseif (z <= -8.2e-113)
		tmp = t_3;
	elseif (z <= 2.2e-306)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 6.3e-198)
		tmp = t_2;
	elseif (z <= 7.5e-110)
		tmp = t_3;
	elseif (z <= 3.7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	t_2 = (x / t) / y;
	t_3 = x / (z * -t);
	tmp = 0.0;
	if (z <= -1.55e+21)
		tmp = t_1;
	elseif (z <= -8.2e-113)
		tmp = t_3;
	elseif (z <= 2.2e-306)
		tmp = x / (y * t);
	elseif (z <= 6.3e-198)
		tmp = t_2;
	elseif (z <= 7.5e-110)
		tmp = t_3;
	elseif (z <= 3.7)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+21], t$95$1, If[LessEqual[z, -8.2e-113], t$95$3, If[LessEqual[z, 2.2e-306], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e-198], t$95$2, If[LessEqual[z, 7.5e-110], t$95$3, If[LessEqual[z, 3.7], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e21 or 3.7000000000000002 < z

   1. Initial program 86.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.1%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 72.1%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -1.55e21 < z < -8.1999999999999999e-113 or 6.30000000000000015e-198 < z < 7.50000000000000053e-110

   1. Initial program 97.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 66.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 54.7%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.7%

         \[\leadsto \frac{x}{\color{blue}{-t \cdot z}} \]

      2. distribute-rgt-neg-out 54.7%

         \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]

   5. Simplified 54.7%

      \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]

   if -8.1999999999999999e-113 < z < 2.20000000000000016e-306

   1. Initial program 95.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 86.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if 2.20000000000000016e-306 < z < 6.30000000000000015e-198 or 7.50000000000000053e-110 < z < 3.7000000000000002

   1. Initial program 90.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 65.9%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   3. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   4. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 3.7:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 4: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))) (t_2 (/ (/ x t) y)))
   (if (<= z -5e+20)
     t_1
     (if (<= z -3.3e-113)
       (/ (/ (- x) t) z)
       (if (<= z 2.3e-306)
         (/ x (* y t))
         (if (<= z 2.5e-188)
           t_2
           (if (<= z 9e-107)
             (/ x (* z (- t)))
             (if (<= z 3.8e-5) t_2 t_1))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -5e+20) {
		tmp = t_1;
	} else if (z <= -3.3e-113) {
		tmp = (-x / t) / z;
	} else if (z <= 2.3e-306) {
		tmp = x / (y * t);
	} else if (z <= 2.5e-188) {
		tmp = t_2;
	} else if (z <= 9e-107) {
		tmp = x / (z * -t);
	} else if (z <= 3.8e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / (z * z)
    t_2 = (x / t) / y
    if (z <= (-5d+20)) then
        tmp = t_1
    else if (z <= (-3.3d-113)) then
        tmp = (-x / t) / z
    else if (z <= 2.3d-306) then
        tmp = x / (y * t)
    else if (z <= 2.5d-188) then
        tmp = t_2
    else if (z <= 9d-107) then
        tmp = x / (z * -t)
    else if (z <= 3.8d-5) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -5e+20) {
		tmp = t_1;
	} else if (z <= -3.3e-113) {
		tmp = (-x / t) / z;
	} else if (z <= 2.3e-306) {
		tmp = x / (y * t);
	} else if (z <= 2.5e-188) {
		tmp = t_2;
	} else if (z <= 9e-107) {
		tmp = x / (z * -t);
	} else if (z <= 3.8e-5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = (x / t) / y
	tmp = 0
	if z <= -5e+20:
		tmp = t_1
	elif z <= -3.3e-113:
		tmp = (-x / t) / z
	elif z <= 2.3e-306:
		tmp = x / (y * t)
	elif z <= 2.5e-188:
		tmp = t_2
	elif z <= 9e-107:
		tmp = x / (z * -t)
	elif z <= 3.8e-5:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -5e+20)
		tmp = t_1;
	elseif (z <= -3.3e-113)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 2.3e-306)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 2.5e-188)
		tmp = t_2;
	elseif (z <= 9e-107)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (z <= 3.8e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -5e+20)
		tmp = t_1;
	elseif (z <= -3.3e-113)
		tmp = (-x / t) / z;
	elseif (z <= 2.3e-306)
		tmp = x / (y * t);
	elseif (z <= 2.5e-188)
		tmp = t_2;
	elseif (z <= 9e-107)
		tmp = x / (z * -t);
	elseif (z <= 3.8e-5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -5e+20], t$95$1, If[LessEqual[z, -3.3e-113], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.3e-306], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-188], t$95$2, If[LessEqual[z, 9e-107], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-5], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5e20 or 3.8000000000000002e-5 < z

   1. Initial program 86.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 72.1%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 72.1%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 72.1%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -5e20 < z < -3.3000000000000002e-113

   1. Initial program 95.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 68.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 56.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 56.4%

         \[\leadsto \color{blue}{-\frac{x}{t \cdot z}} \]

      2. associate-/r* 53.5%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

      3. distribute-neg-frac 53.5%

         \[\leadsto \color{blue}{\frac{-\frac{x}{t}}{z}} \]

      4. distribute-neg-frac 53.5%

         \[\leadsto \frac{\color{blue}{\frac{-x}{t}}}{z} \]

   5. Simplified 53.5%

      \[\leadsto \color{blue}{\frac{\frac{-x}{t}}{z}} \]

   if -3.3000000000000002e-113 < z < 2.29999999999999989e-306

   1. Initial program 95.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 86.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if 2.29999999999999989e-306 < z < 2.5e-188 or 9.00000000000000032e-107 < z < 3.8000000000000002e-5

   1. Initial program 90.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 65.9%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   3. Step-by-step derivation

      1. associate-/r* 75.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   4. Simplified 75.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   if 2.5e-188 < z < 9.00000000000000032e-107

   1. Initial program 99.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 63.7%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 51.8%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 51.8%

         \[\leadsto \frac{x}{\color{blue}{-t \cdot z}} \]

      2. distribute-rgt-neg-out 51.8%

         \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]

   5. Simplified 51.8%

      \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-188}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 5: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 5e+307) (/ x t_1) (/ (/ (- x) z) (- t z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 = (y - z) * (t - z)
    if (t_1 <= 5d+307) then
        tmp = x / t_1
    else
        tmp = (-x / z) / (t - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+307) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 5e+307:
		tmp = x / t_1
	else:
		tmp = (-x / z) / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+307)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+307)
		tmp = x / t_1;
	else
		tmp = (-x / z) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+307], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 5e307

   1. Initial program 95.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   if 5e307 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 77.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around 0 73.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 73.3%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(t - z\right)}} \]

      2. distribute-frac-neg 73.3%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]

      3. associate-/r* 90.2%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

   4. Simplified 90.2%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 6: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y - z}}{t}\\ t_2 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- y z)) t)) (t_2 (/ (/ x z) (- z y))))
   (if (<= z -2.2e-40)
     t_2
     (if (<= z 1.4e-81)
       t_1
       (if (<= z 2.2e-52) (/ (/ x y) (- t z)) (if (<= z 1.3e-23) t_1 t_2))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / (y - z)) / t;
	double t_2 = (x / z) / (z - y);
	double tmp;
	if (z <= -2.2e-40) {
		tmp = t_2;
	} else if (z <= 1.4e-81) {
		tmp = t_1;
	} else if (z <= 2.2e-52) {
		tmp = (x / y) / (t - z);
	} else if (z <= 1.3e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / z) / (z - y)
    if (z <= (-2.2d-40)) then
        tmp = t_2
    else if (z <= 1.4d-81) then
        tmp = t_1
    else if (z <= 2.2d-52) then
        tmp = (x / y) / (t - z)
    else if (z <= 1.3d-23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / (y - z)) / t;
	double t_2 = (x / z) / (z - y);
	double tmp;
	if (z <= -2.2e-40) {
		tmp = t_2;
	} else if (z <= 1.4e-81) {
		tmp = t_1;
	} else if (z <= 2.2e-52) {
		tmp = (x / y) / (t - z);
	} else if (z <= 1.3e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / (y - z)) / t
	t_2 = (x / z) / (z - y)
	tmp = 0
	if z <= -2.2e-40:
		tmp = t_2
	elif z <= 1.4e-81:
		tmp = t_1
	elif z <= 2.2e-52:
		tmp = (x / y) / (t - z)
	elif z <= 1.3e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(y - z)) / t)
	t_2 = Float64(Float64(x / z) / Float64(z - y))
	tmp = 0.0
	if (z <= -2.2e-40)
		tmp = t_2;
	elseif (z <= 1.4e-81)
		tmp = t_1;
	elseif (z <= 2.2e-52)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 1.3e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / (y - z)) / t;
	t_2 = (x / z) / (z - y);
	tmp = 0.0;
	if (z <= -2.2e-40)
		tmp = t_2;
	elseif (z <= 1.4e-81)
		tmp = t_1;
	elseif (z <= 2.2e-52)
		tmp = (x / y) / (t - z);
	elseif (z <= 1.3e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-40], t$95$2, If[LessEqual[z, 1.4e-81], t$95$1, If[LessEqual[z, 2.2e-52], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000009e-40 or 1.3e-23 < z

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 74.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 74.5%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(y - z\right)}} \]

      2. distribute-frac-neg 74.5%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

      3. associate-/r* 82.5%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]

   4. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]
   5. Step-by-step derivation

      1. frac-2neg 82.5%

         \[\leadsto \color{blue}{\frac{-\frac{-x}{z}}{-\left(y - z\right)}} \]

      2. div-inv 82.5%

         \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right) \cdot \frac{1}{-\left(y - z\right)}} \]

      3. distribute-frac-neg 82.5%

         \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{-\left(y - z\right)} \]

      4. remove-double-neg 82.5%

         \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{-\left(y - z\right)} \]

      5. sub-neg 82.5%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{-\color{blue}{\left(y + \left(-z\right)\right)}} \]

      6. distribute-neg-in 82.5%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\color{blue}{\left(-y\right) + \left(-\left(-z\right)\right)}} \]

      7. add-sqr-sqrt 46.4%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right)} \]

      8. sqrt-unprod 64.4%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)} \]

      9. sqr-neg 64.4%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\sqrt{\color{blue}{z \cdot z}}\right)} \]

      10. sqrt-prod 24.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{z} \cdot \sqrt{z}}\right)} \]

      11. add-sqr-sqrt 57.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{z}\right)} \]

      12. add-sqr-sqrt 32.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

      13. sqrt-unprod 65.3%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

      14. sqr-neg 65.3%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \sqrt{\color{blue}{z \cdot z}}} \]

      15. sqrt-prod 36.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

      16. add-sqr-sqrt 82.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{z}} \]

   6. Applied egg-rr 82.5%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{\left(-y\right) + z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 82.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{\left(-y\right) + z}} \]

      2. *-rgt-identity 82.5%

         \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\left(-y\right) + z} \]

      3. neg-mul-1 82.5%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{-1 \cdot y} + z} \]

      4. +-commutative 82.5%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + -1 \cdot y}} \]

      5. neg-mul-1 82.5%

         \[\leadsto \frac{\frac{x}{z}}{z + \color{blue}{\left(-y\right)}} \]

      6. unsub-neg 82.5%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - y}} \]

   8. Simplified 82.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - y}} \]

   if -2.20000000000000009e-40 < z < 1.3999999999999999e-81 or 2.20000000000000009e-52 < z < 1.3e-23

   1. Initial program 93.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 79.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 79.2%

         \[\leadsto \frac{x}{\color{blue}{\left(y - z\right) \cdot t}} \]

      2. associate-/r* 84.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t}} \]

   4. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t}} \]

   if 1.3999999999999999e-81 < z < 2.20000000000000009e-52

   1. Initial program 99.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 60.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. associate-/r* 60.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   4. Simplified 60.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]

Alternative 7: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.12e-40)
   (/ (/ x z) (- z y))
   (if (<= z 5e-81)
     (/ (/ x (- y z)) t)
     (if (<= z 2.85e-5) (/ (/ x y) (- t z)) (/ (/ (- x) z) (- t z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e-40) {
		tmp = (x / z) / (z - y);
	} else if (z <= 5e-81) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 2.85e-5) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 (z <= (-1.12d-40)) then
        tmp = (x / z) / (z - y)
    else if (z <= 5d-81) then
        tmp = (x / (y - z)) / t
    else if (z <= 2.85d-5) then
        tmp = (x / y) / (t - z)
    else
        tmp = (-x / z) / (t - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e-40) {
		tmp = (x / z) / (z - y);
	} else if (z <= 5e-81) {
		tmp = (x / (y - z)) / t;
	} else if (z <= 2.85e-5) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.12e-40:
		tmp = (x / z) / (z - y)
	elif z <= 5e-81:
		tmp = (x / (y - z)) / t
	elif z <= 2.85e-5:
		tmp = (x / y) / (t - z)
	else:
		tmp = (-x / z) / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.12e-40)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 5e-81)
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (z <= 2.85e-5)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.12e-40)
		tmp = (x / z) / (z - y);
	elseif (z <= 5e-81)
		tmp = (x / (y - z)) / t;
	elseif (z <= 2.85e-5)
		tmp = (x / y) / (t - z);
	else
		tmp = (-x / z) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.12e-40], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-81], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.85e-5], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1200000000000001e-40

   1. Initial program 83.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 72.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 72.1%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(y - z\right)}} \]

      2. distribute-frac-neg 72.1%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

      3. associate-/r* 84.1%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]

   4. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]
   5. Step-by-step derivation

      1. frac-2neg 84.1%

         \[\leadsto \color{blue}{\frac{-\frac{-x}{z}}{-\left(y - z\right)}} \]

      2. div-inv 84.1%

         \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right) \cdot \frac{1}{-\left(y - z\right)}} \]

      3. distribute-frac-neg 84.1%

         \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{-\left(y - z\right)} \]

      4. remove-double-neg 84.1%

         \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{-\left(y - z\right)} \]

      5. sub-neg 84.1%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{-\color{blue}{\left(y + \left(-z\right)\right)}} \]

      6. distribute-neg-in 84.1%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\color{blue}{\left(-y\right) + \left(-\left(-z\right)\right)}} \]

      7. add-sqr-sqrt 84.0%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right)} \]

      8. sqrt-unprod 72.0%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)} \]

      9. sqr-neg 72.0%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\sqrt{\color{blue}{z \cdot z}}\right)} \]

      10. sqrt-prod 0.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{z} \cdot \sqrt{z}}\right)} \]

      11. add-sqr-sqrt 58.8%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{z}\right)} \]

      12. add-sqr-sqrt 58.8%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

      13. sqrt-unprod 56.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

      14. sqr-neg 56.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \sqrt{\color{blue}{z \cdot z}}} \]

      15. sqrt-prod 0.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

      16. add-sqr-sqrt 84.1%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{z}} \]

   6. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{\left(-y\right) + z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 84.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{\left(-y\right) + z}} \]

      2. *-rgt-identity 84.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\left(-y\right) + z} \]

      3. neg-mul-1 84.1%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{-1 \cdot y} + z} \]

      4. +-commutative 84.1%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + -1 \cdot y}} \]

      5. neg-mul-1 84.1%

         \[\leadsto \frac{\frac{x}{z}}{z + \color{blue}{\left(-y\right)}} \]

      6. unsub-neg 84.1%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - y}} \]

   8. Simplified 84.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - y}} \]

   if -1.1200000000000001e-40 < z < 4.99999999999999981e-81

   1. Initial program 94.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 80.8%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 80.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y - z\right) \cdot t}} \]

      2. associate-/r* 84.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t}} \]

   4. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t}} \]

   if 4.99999999999999981e-81 < z < 2.8500000000000002e-5

   1. Initial program 93.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 51.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. associate-/r* 57.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   4. Simplified 57.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if 2.8500000000000002e-5 < z

   1. Initial program 92.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 80.3%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(t - z\right)}} \]

      2. distribute-frac-neg 80.3%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(t - z\right)}} \]

      3. associate-/r* 85.1%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

   4. Simplified 85.1%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 8: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= z -2.6e+21)
     t_1
     (if (<= z 4.4e-81)
       (/ x (* (- y z) t))
       (if (<= z 6.1e+66) (/ x (* y (- t z))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -2.6e+21) {
		tmp = t_1;
	} else if (z <= 4.4e-81) {
		tmp = x / ((y - z) * t);
	} else if (z <= 6.1e+66) {
		tmp = x / (y * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / z) * (1.0d0 / z)
    if (z <= (-2.6d+21)) then
        tmp = t_1
    else if (z <= 4.4d-81) then
        tmp = x / ((y - z) * t)
    else if (z <= 6.1d+66) then
        tmp = x / (y * (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -2.6e+21) {
		tmp = t_1;
	} else if (z <= 4.4e-81) {
		tmp = x / ((y - z) * t);
	} else if (z <= 6.1e+66) {
		tmp = x / (y * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -2.6e+21:
		tmp = t_1
	elif z <= 4.4e-81:
		tmp = x / ((y - z) * t)
	elif z <= 6.1e+66:
		tmp = x / (y * (t - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -2.6e+21)
		tmp = t_1;
	elseif (z <= 4.4e-81)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 6.1e+66)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -2.6e+21)
		tmp = t_1;
	elseif (z <= 4.4e-81)
		tmp = x / ((y - z) * t);
	elseif (z <= 6.1e+66)
		tmp = x / (y * (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+21], t$95$1, If[LessEqual[z, 4.4e-81], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e+66], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e21 or 6.10000000000000021e66 < z

   1. Initial program 84.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 77.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 77.0%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 86.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

      2. div-inv 86.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   6. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   if -2.6e21 < z < 4.3999999999999998e-81

   1. Initial program 94.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 79.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 4.3999999999999998e-81 < z < 6.10000000000000021e66

   1. Initial program 96.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 48.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto \frac{x}{\color{blue}{\left(t - z\right) \cdot y}} \]

   4. Simplified 48.1%

      \[\leadsto \color{blue}{\frac{x}{\left(t - z\right) \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 9: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= z -3.2e+21)
     t_1
     (if (<= z 2.25e-82)
       (/ x (* (- y z) t))
       (if (<= z 5e+66) (/ (/ x y) (- t z)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -3.2e+21) {
		tmp = t_1;
	} else if (z <= 2.25e-82) {
		tmp = x / ((y - z) * t);
	} else if (z <= 5e+66) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / z) * (1.0d0 / z)
    if (z <= (-3.2d+21)) then
        tmp = t_1
    else if (z <= 2.25d-82) then
        tmp = x / ((y - z) * t)
    else if (z <= 5d+66) then
        tmp = (x / y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -3.2e+21) {
		tmp = t_1;
	} else if (z <= 2.25e-82) {
		tmp = x / ((y - z) * t);
	} else if (z <= 5e+66) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -3.2e+21:
		tmp = t_1
	elif z <= 2.25e-82:
		tmp = x / ((y - z) * t)
	elif z <= 5e+66:
		tmp = (x / y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -3.2e+21)
		tmp = t_1;
	elseif (z <= 2.25e-82)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 5e+66)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -3.2e+21)
		tmp = t_1;
	elseif (z <= 2.25e-82)
		tmp = x / ((y - z) * t);
	elseif (z <= 5e+66)
		tmp = (x / y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+21], t$95$1, If[LessEqual[z, 2.25e-82], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+66], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e21 or 4.99999999999999991e66 < z

   1. Initial program 84.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 77.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 77.0%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 86.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

      2. div-inv 86.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   6. Applied egg-rr 86.0%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   if -3.2e21 < z < 2.2499999999999999e-82

   1. Initial program 94.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 79.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   if 2.2499999999999999e-82 < z < 4.99999999999999991e66

   1. Initial program 96.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in y around inf 48.1%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(t - z\right)}} \]
   3. Step-by-step derivation

      1. associate-/r* 51.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   4. Simplified 51.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 10: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 3.6 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.14e+21) (not (<= z 3.6e-37)))
   (* (/ x z) (/ 1.0 z))
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.14e+21) || !(z <= 3.6e-37)) {
		tmp = (x / z) * (1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 ((z <= (-1.14d+21)) .or. (.not. (z <= 3.6d-37))) then
        tmp = (x / z) * (1.0d0 / z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.14e+21) || !(z <= 3.6e-37)) {
		tmp = (x / z) * (1.0 / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.14e+21) or not (z <= 3.6e-37):
		tmp = (x / z) * (1.0 / z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.14e+21) || !(z <= 3.6e-37))
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.14e+21) || ~((z <= 3.6e-37)))
		tmp = (x / z) * (1.0 / z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.14e+21], N[Not[LessEqual[z, 3.6e-37]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14e21 or 3.60000000000000007e-37 < z

   1. Initial program 86.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.3%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 71.3%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 78.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z}} \]

      2. div-inv 78.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   6. Applied egg-rr 78.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]

   if -1.14e21 < z < 3.60000000000000007e-37

   1. Initial program 94.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 80.1%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+21} \lor \neg \left(z \leq 3.6 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 46.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+43} \lor \neg \left(z \leq 4.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+43) (not (<= z 4.5e+66))) (/ x (* z t)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+43) || !(z <= 4.5e+66)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 ((z <= (-6.2d+43)) .or. (.not. (z <= 4.5d+66))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+43) || !(z <= 4.5e+66)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+43) or not (z <= 4.5e+66):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+43) || !(z <= 4.5e+66))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+43) || ~((z <= 4.5e+66)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+43], N[Not[LessEqual[z, 4.5e+66]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e43 or 4.4999999999999998e66 < z

   1. Initial program 84.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 42.3%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]

   3. Taylor expanded in y around 0 42.2%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \frac{x}{\color{blue}{-t \cdot z}} \]

      2. distribute-rgt-neg-out 42.2%

         \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]

   5. Simplified 42.2%

      \[\leadsto \frac{x}{\color{blue}{t \cdot \left(-z\right)}} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 41.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot \left(-z\right)}\right)\right)} \]

      2. expm1-udef 63.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t \cdot \left(-z\right)}\right)} - 1} \]

      3. frac-2neg 63.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{-t \cdot \left(-z\right)}}\right)} - 1 \]

      4. add-sqr-sqrt 33.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-t \cdot \left(-z\right)}\right)} - 1 \]

      5. sqrt-unprod 59.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{-t \cdot \left(-z\right)}\right)} - 1 \]

      6. sqr-neg 59.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{-t \cdot \left(-z\right)}\right)} - 1 \]

      7. sqrt-unprod 28.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-t \cdot \left(-z\right)}\right)} - 1 \]

      8. add-sqr-sqrt 62.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{-t \cdot \left(-z\right)}\right)} - 1 \]

      9. distribute-rgt-neg-out 62.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{-\color{blue}{\left(-t \cdot z\right)}}\right)} - 1 \]

      10. remove-double-neg 62.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{\color{blue}{t \cdot z}}\right)} - 1 \]

   7. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 39.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t \cdot z}\right)\right)} \]

      2. expm1-log1p 39.6%

         \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

   9. Simplified 39.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

   if -6.2000000000000003e43 < z < 4.4999999999999998e66

   1. Initial program 95.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 55.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+43} \lor \neg \left(z \leq 4.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 12: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.45 \cdot 10^{-72} \lor \neg \left(z \leq 3 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.45e-72) (not (<= z 3e-41))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.45e-72) || !(z <= 3e-41)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 ((z <= (-4.45d-72)) .or. (.not. (z <= 3d-41))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.45e-72) || !(z <= 3e-41)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4.45e-72) or not (z <= 3e-41):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.45e-72) || !(z <= 3e-41))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.45e-72) || ~((z <= 3e-41)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.45e-72], N[Not[LessEqual[z, 3e-41]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4499999999999999e-72 or 2.99999999999999989e-41 < z

   1. Initial program 87.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 67.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 67.0%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 67.0%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -4.4499999999999999e-72 < z < 2.99999999999999989e-41

   1. Initial program 94.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 68.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.45 \cdot 10^{-72} \lor \neg \left(z \leq 3 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 0.0165\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e+18) (not (<= z 0.0165))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+18) || !(z <= 0.0165)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 ((z <= (-1.6d+18)) .or. (.not. (z <= 0.0165d0))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e+18) || !(z <= 0.0165)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e+18) or not (z <= 0.0165):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e+18) || !(z <= 0.0165))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e+18) || ~((z <= 0.0165)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e+18], N[Not[LessEqual[z, 0.0165]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e18 or 0.016500000000000001 < z

   1. Initial program 87.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around inf 71.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 71.6%

         \[\leadsto \frac{x}{\color{blue}{z \cdot z}} \]

   4. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]

   if -1.6e18 < z < 0.016500000000000001

   1. Initial program 94.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0 61.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   3. Step-by-step derivation

      1. associate-/r* 65.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]

   4. Simplified 65.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18} \lor \neg \left(z \leq 0.0165\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 14: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.05e-65) (/ (/ x z) (- z y)) (/ (/ x t) (- y z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.05e-65) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 <= 1.05d-65) then
        tmp = (x / z) / (z - y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.05e-65) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.05e-65:
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.05e-65)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.05e-65)
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.05e-65], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.05000000000000001e-65

   1. Initial program 91.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around 0 57.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. mul-1-neg 57.6%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot \left(y - z\right)}} \]

      2. distribute-frac-neg 57.6%

         \[\leadsto \color{blue}{\frac{-x}{z \cdot \left(y - z\right)}} \]

      3. associate-/r* 64.4%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]

   4. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{y - z}} \]
   5. Step-by-step derivation

      1. frac-2neg 64.4%

         \[\leadsto \color{blue}{\frac{-\frac{-x}{z}}{-\left(y - z\right)}} \]

      2. div-inv 64.4%

         \[\leadsto \color{blue}{\left(-\frac{-x}{z}\right) \cdot \frac{1}{-\left(y - z\right)}} \]

      3. distribute-frac-neg 64.4%

         \[\leadsto \left(-\color{blue}{\left(-\frac{x}{z}\right)}\right) \cdot \frac{1}{-\left(y - z\right)} \]

      4. remove-double-neg 64.4%

         \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{1}{-\left(y - z\right)} \]

      5. sub-neg 64.4%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{-\color{blue}{\left(y + \left(-z\right)\right)}} \]

      6. distribute-neg-in 64.4%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\color{blue}{\left(-y\right) + \left(-\left(-z\right)\right)}} \]

      7. add-sqr-sqrt 35.9%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}\right)} \]

      8. sqrt-unprod 48.3%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)} \]

      9. sqr-neg 48.3%

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\sqrt{\color{blue}{z \cdot z}}\right)} \]

      10. sqrt-prod 18.7%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{\sqrt{z} \cdot \sqrt{z}}\right)} \]

      11. add-sqr-sqrt 41.5%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \left(-\color{blue}{z}\right)} \]

      12. add-sqr-sqrt 22.8%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

      13. sqrt-unprod 49.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} \]

      14. sqr-neg 49.0%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \sqrt{\color{blue}{z \cdot z}}} \]

      15. sqrt-prod 28.4%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

      16. add-sqr-sqrt 64.4%

          \[\leadsto \frac{x}{z} \cdot \frac{1}{\left(-y\right) + \color{blue}{z}} \]

   6. Applied egg-rr 64.4%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{\left(-y\right) + z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 64.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{\left(-y\right) + z}} \]

      2. *-rgt-identity 64.4%

         \[\leadsto \frac{\color{blue}{\frac{x}{z}}}{\left(-y\right) + z} \]

      3. neg-mul-1 64.4%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{-1 \cdot y} + z} \]

      4. +-commutative 64.4%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z + -1 \cdot y}} \]

      5. neg-mul-1 64.4%

         \[\leadsto \frac{\frac{x}{z}}{z + \color{blue}{\left(-y\right)}} \]

      6. unsub-neg 64.4%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - y}} \]

   8. Simplified 64.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - y}} \]

   if 1.05000000000000001e-65 < t

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in t around inf 77.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
   3. Step-by-step derivation

      1. associate-/r* 84.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y - z}} \]

   4. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 / (t - z)) / (y - z)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.4%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. associate-/r* 98.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}} \]

   2. div-inv 98.2%

      \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]

3. Applied egg-rr 98.2%

   \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}} \]
4. Step-by-step derivation

   1. associate-*l/ 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{t - z}}{y - z}} \]

   2. un-div-inv 96.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{t - z}}}{y - z} \]

5. Applied egg-rr 96.6%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

6. Final simplification 96.6%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]

Alternative 16: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{x}{y \cdot t} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* y t)))

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
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 * t)
end function

Java

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

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return x / (y * t)

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(x / Float64(y * t))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y * t);
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.4%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

2. Taylor expanded in z around 0 39.5%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

3. Final simplification 39.5%

   \[\leadsto \frac{x}{y \cdot t} \]

Developer target: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / 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) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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