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

Percentage Accurate: 88.5% → 97.4%

Time: 13.3s

Alternatives: 21

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: 88.5% 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: 97.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (/ (pow (cbrt x) 2.0) (- y z)) (/ (cbrt x) (- t z))))

C

double code(double x, double y, double z, double t) {
	return (pow(cbrt(x), 2.0) / (y - z)) * (cbrt(x) / (t - z));
}

Java

public static double code(double x, double y, double z, double t) {
	return (Math.pow(Math.cbrt(x), 2.0) / (y - z)) * (Math.cbrt(x) / (t - z));
}

Julia

function code(x, y, z, t)
	return Float64(Float64((cbrt(x) ^ 2.0) / Float64(y - z)) * Float64(cbrt(x) / Float64(t - z)))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Power[N[Power[x, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Power[x, 1/3], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.7%

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

   1. add-cube-cbrt 88.9%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

4. Final simplification 98.1%

   \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -490000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ (- -1.0) z))))
   (if (<= y -2.7e+77)
     (/ (/ x (- t z)) y)
     (if (<= y -1.35e+36)
       t_1
       (if (<= y -490000.0)
         (/ (/ x y) (- t z))
         (if (<= y -6.5e-125)
           t_1
           (if (<= y -1.35e-160)
             (/ (/ x t) (- y z))
             (if (<= y -4.8e-292) t_1 (/ x (* (- y z) t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-(-1.0) / z);
	double tmp;
	if (y <= -2.7e+77) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.35e+36) {
		tmp = t_1;
	} else if (y <= -490000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6.5e-125) {
		tmp = t_1;
	} else if (y <= -1.35e-160) {
		tmp = (x / t) / (y - z);
	} else if (y <= -4.8e-292) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	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 / z) * (-(-1.0d0) / z)
    if (y <= (-2.7d+77)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.35d+36)) then
        tmp = t_1
    else if (y <= (-490000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-6.5d-125)) then
        tmp = t_1
    else if (y <= (-1.35d-160)) then
        tmp = (x / t) / (y - z)
    else if (y <= (-4.8d-292)) then
        tmp = t_1
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-(-1.0) / z);
	double tmp;
	if (y <= -2.7e+77) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.35e+36) {
		tmp = t_1;
	} else if (y <= -490000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -6.5e-125) {
		tmp = t_1;
	} else if (y <= -1.35e-160) {
		tmp = (x / t) / (y - z);
	} else if (y <= -4.8e-292) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (-(-1.0) / z)
	tmp = 0
	if y <= -2.7e+77:
		tmp = (x / (t - z)) / y
	elif y <= -1.35e+36:
		tmp = t_1
	elif y <= -490000.0:
		tmp = (x / y) / (t - z)
	elif y <= -6.5e-125:
		tmp = t_1
	elif y <= -1.35e-160:
		tmp = (x / t) / (y - z)
	elif y <= -4.8e-292:
		tmp = t_1
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(Float64(-(-1.0)) / z))
	tmp = 0.0
	if (y <= -2.7e+77)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.35e+36)
		tmp = t_1;
	elseif (y <= -490000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -6.5e-125)
		tmp = t_1;
	elseif (y <= -1.35e-160)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (y <= -4.8e-292)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (-(-1.0) / z);
	tmp = 0.0;
	if (y <= -2.7e+77)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.35e+36)
		tmp = t_1;
	elseif (y <= -490000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= -6.5e-125)
		tmp = t_1;
	elseif (y <= -1.35e-160)
		tmp = (x / t) / (y - z);
	elseif (y <= -4.8e-292)
		tmp = t_1;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[((--1.0) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e+77], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.35e+36], t$95$1, If[LessEqual[y, -490000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-125], t$95$1, If[LessEqual[y, -1.35e-160], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-292], t$95$1, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6999999999999998e77

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-/r* 94.3%

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

   4. Simplified 94.3%

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

   if -2.6999999999999998e77 < y < -1.35e36 or -4.9e5 < y < -6.4999999999999999e-125 or -1.35000000000000005e-160 < y < -4.8000000000000002e-292

   1. Initial program 87.6%

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

      1. clear-num 86.6%

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

      2. inv-pow 86.6%

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

      3. associate-/l* 95.1%

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

   3. Applied egg-rr 95.1%

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

      1. unpow-1 95.1%

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

      2. clear-num 96.9%

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

      3. div-inv 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in y around 0 74.1%

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

   7. Taylor expanded in t around 0 59.4%

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

      1. associate-*r/ 25.9%

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

      2. neg-mul-1 25.9%

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

   9. Simplified 59.4%

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

   if -1.35e36 < y < -4.9e5

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.1%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.3%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.3%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 86.8%

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

      1. associate-/r* 87.0%

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

   8. Simplified 87.0%

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

   if -6.4999999999999999e-125 < y < -1.35000000000000005e-160

   1. Initial program 82.6%

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

      1. add-cube-cbrt 82.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.0%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.0%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.8%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.1%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in t around inf 60.3%

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

      1. associate-/r* 66.0%

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

   8. Simplified 66.0%

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

   if -4.8000000000000002e-292 < y

   1. Initial program 93.4%

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

   2. Taylor expanded in t around inf 57.2%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{elif}\;y \leq -490000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 3: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(y - z\right)}\\ t_2 := \frac{\frac{-x}{z}}{t - z}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -750000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- y z)))) (t_2 (/ (/ (- x) z) (- t z))))
   (if (<= y -3.7e+80)
     (/ (/ x (- t z)) y)
     (if (<= y -2.75e+23)
       t_1
       (if (<= y -750000.0)
         (/ (/ x y) (- t z))
         (if (<= y -4.3e-79)
           t_2
           (if (<= y -2.55e-126)
             t_1
             (if (<= y 1.25e-203) t_2 (/ x (* (- y z) t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (y - z));
	double t_2 = (-x / z) / (t - z);
	double tmp;
	if (y <= -3.7e+80) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.75e+23) {
		tmp = t_1;
	} else if (y <= -750000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -4.3e-79) {
		tmp = t_2;
	} else if (y <= -2.55e-126) {
		tmp = t_1;
	} else if (y <= 1.25e-203) {
		tmp = t_2;
	} else {
		tmp = x / ((y - z) * t);
	}
	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 / (z * (y - z))
    t_2 = (-x / z) / (t - z)
    if (y <= (-3.7d+80)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.75d+23)) then
        tmp = t_1
    else if (y <= (-750000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-4.3d-79)) then
        tmp = t_2
    else if (y <= (-2.55d-126)) then
        tmp = t_1
    else if (y <= 1.25d-203) then
        tmp = t_2
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (y - z));
	double t_2 = (-x / z) / (t - z);
	double tmp;
	if (y <= -3.7e+80) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.75e+23) {
		tmp = t_1;
	} else if (y <= -750000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -4.3e-79) {
		tmp = t_2;
	} else if (y <= -2.55e-126) {
		tmp = t_1;
	} else if (y <= 1.25e-203) {
		tmp = t_2;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z * (y - z))
	t_2 = (-x / z) / (t - z)
	tmp = 0
	if y <= -3.7e+80:
		tmp = (x / (t - z)) / y
	elif y <= -2.75e+23:
		tmp = t_1
	elif y <= -750000.0:
		tmp = (x / y) / (t - z)
	elif y <= -4.3e-79:
		tmp = t_2
	elif y <= -2.55e-126:
		tmp = t_1
	elif y <= 1.25e-203:
		tmp = t_2
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(y - z)))
	t_2 = Float64(Float64(Float64(-x) / z) / Float64(t - z))
	tmp = 0.0
	if (y <= -3.7e+80)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.75e+23)
		tmp = t_1;
	elseif (y <= -750000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -4.3e-79)
		tmp = t_2;
	elseif (y <= -2.55e-126)
		tmp = t_1;
	elseif (y <= 1.25e-203)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (y - z));
	t_2 = (-x / z) / (t - z);
	tmp = 0.0;
	if (y <= -3.7e+80)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.75e+23)
		tmp = t_1;
	elseif (y <= -750000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= -4.3e-79)
		tmp = t_2;
	elseif (y <= -2.55e-126)
		tmp = t_1;
	elseif (y <= 1.25e-203)
		tmp = t_2;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+80], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.75e+23], t$95$1, If[LessEqual[y, -750000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.3e-79], t$95$2, If[LessEqual[y, -2.55e-126], t$95$1, If[LessEqual[y, 1.25e-203], t$95$2, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.69999999999999996e80

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/r* 94.0%

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

   4. Simplified 94.0%

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

   if -3.69999999999999996e80 < y < -2.75000000000000002e23 or -4.29999999999999982e-79 < y < -2.55000000000000001e-126

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 81.7%

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

      1. associate-*r/ 81.7%

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

      2. neg-mul-1 81.7%

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

   4. Simplified 81.7%

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

   if -2.75000000000000002e23 < y < -7.5e5

   1. Initial program 99.7%

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

      1. add-cube-cbrt 99.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.2%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.2%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 84.6%

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

      1. associate-/r* 84.8%

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

   8. Simplified 84.8%

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

   if -7.5e5 < y < -4.29999999999999982e-79 or -2.55000000000000001e-126 < y < 1.25e-203

   1. Initial program 85.0%

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

      1. add-cube-cbrt 84.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 98.6%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 98.6%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-/r* 86.5%

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

      3. distribute-neg-frac 86.5%

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

   8. Simplified 86.5%

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

   if 1.25e-203 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 55.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq -750000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-126}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 4: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -490000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- t z)))))
   (if (<= y -3.4e+77)
     (/ (/ x (- t z)) y)
     (if (<= y -1.4e+36)
       t_1
       (if (<= y -490000.0)
         (/ (/ x y) (- t z))
         (if (<= y -2.35e-60)
           (* (/ x z) (/ (- -1.0) z))
           (if (<= y 1.25e-203) t_1 (/ x (* (- y z) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.4e+36) {
		tmp = t_1;
	} else if (y <= -490000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.35e-60) {
		tmp = (x / z) * (-(-1.0) / z);
	} else if (y <= 1.25e-203) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	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 / (z * (t - z))
    if (y <= (-3.4d+77)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.4d+36)) then
        tmp = t_1
    else if (y <= (-490000.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-2.35d-60)) then
        tmp = (x / z) * (-(-1.0d0) / z)
    else if (y <= 1.25d-203) then
        tmp = t_1
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.4e+36) {
		tmp = t_1;
	} else if (y <= -490000.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= -2.35e-60) {
		tmp = (x / z) * (-(-1.0) / z);
	} else if (y <= 1.25e-203) {
		tmp = t_1;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z * (t - z))
	tmp = 0
	if y <= -3.4e+77:
		tmp = (x / (t - z)) / y
	elif y <= -1.4e+36:
		tmp = t_1
	elif y <= -490000.0:
		tmp = (x / y) / (t - z)
	elif y <= -2.35e-60:
		tmp = (x / z) * (-(-1.0) / z)
	elif y <= 1.25e-203:
		tmp = t_1
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(t - z)))
	tmp = 0.0
	if (y <= -3.4e+77)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.4e+36)
		tmp = t_1;
	elseif (y <= -490000.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -2.35e-60)
		tmp = Float64(Float64(x / z) * Float64(Float64(-(-1.0)) / z));
	elseif (y <= 1.25e-203)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (t - z));
	tmp = 0.0;
	if (y <= -3.4e+77)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.4e+36)
		tmp = t_1;
	elseif (y <= -490000.0)
		tmp = (x / y) / (t - z);
	elseif (y <= -2.35e-60)
		tmp = (x / z) * (-(-1.0) / z);
	elseif (y <= 1.25e-203)
		tmp = t_1;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+77], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.4e+36], t$95$1, If[LessEqual[y, -490000.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.35e-60], N[(N[(x / z), $MachinePrecision] * N[((--1.0) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-203], t$95$1, N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.39999999999999997e77

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-/r* 94.3%

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

   4. Simplified 94.3%

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

   if -3.39999999999999997e77 < y < -1.4e36 or -2.35e-60 < y < 1.25e-203

   1. Initial program 88.5%

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

   2. Taylor expanded in y around 0 76.4%

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

      1. associate-*r/ 76.4%

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

      2. neg-mul-1 76.4%

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

   4. Simplified 76.4%

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

   if -1.4e36 < y < -4.9e5

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.1%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.3%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.3%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 86.8%

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

      1. associate-/r* 87.0%

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

   8. Simplified 87.0%

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

   if -4.9e5 < y < -2.35e-60

   1. Initial program 87.6%

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

      1. clear-num 87.7%

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

      2. inv-pow 87.7%

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

      3. associate-/l* 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. unpow-1 99.6%

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

      2. clear-num 99.6%

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

      3. div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around 0 63.4%

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

   7. Taylor expanded in t around 0 51.3%

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

      1. associate-*r/ 22.1%

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

      2. neg-mul-1 22.1%

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

   9. Simplified 51.3%

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

   if 1.25e-203 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 55.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -490000:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{--1}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 5: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-126}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+79)
   (/ (/ x (- t z)) y)
   (if (<= y -2.55e-126)
     (/ (- x) (* z (- y z)))
     (if (<= y 1.25e-203) (/ (- x) (* z (- t z))) (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+79) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.55e-126) {
		tmp = -x / (z * (y - z));
	} else if (y <= 1.25e-203) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	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 <= (-5.2d+79)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.55d-126)) then
        tmp = -x / (z * (y - z))
    else if (y <= 1.25d-203) then
        tmp = -x / (z * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+79) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.55e-126) {
		tmp = -x / (z * (y - z));
	} else if (y <= 1.25e-203) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+79:
		tmp = (x / (t - z)) / y
	elif y <= -2.55e-126:
		tmp = -x / (z * (y - z))
	elif y <= 1.25e-203:
		tmp = -x / (z * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+79)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.55e-126)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (y <= 1.25e-203)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+79)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.55e-126)
		tmp = -x / (z * (y - z));
	elseif (y <= 1.25e-203)
		tmp = -x / (z * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+79], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.55e-126], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-203], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.20000000000000029e79

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/r* 94.0%

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

   4. Simplified 94.0%

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

   if -5.20000000000000029e79 < y < -2.55000000000000001e-126

   1. Initial program 95.9%

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

   2. Taylor expanded in t around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. neg-mul-1 70.6%

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

   4. Simplified 70.6%

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

   if -2.55000000000000001e-126 < y < 1.25e-203

   1. Initial program 84.1%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. associate-*r/ 79.5%

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

      2. neg-mul-1 79.5%

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

   4. Simplified 79.5%

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

   if 1.25e-203 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 55.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-126}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 6: 69.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= y -5.2e+79)
     (/ (/ x (- t z)) y)
     (if (<= y -2.9e-127)
       (/ t_1 (- y z))
       (if (<= y 1.25e-203) (/ t_1 (- t z)) (/ x (* (- y z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -5.2e+79) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.9e-127) {
		tmp = t_1 / (y - z);
	} else if (y <= 1.25e-203) {
		tmp = t_1 / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	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 / z
    if (y <= (-5.2d+79)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.9d-127)) then
        tmp = t_1 / (y - z)
    else if (y <= 1.25d-203) then
        tmp = t_1 / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -5.2e+79) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.9e-127) {
		tmp = t_1 / (y - z);
	} else if (y <= 1.25e-203) {
		tmp = t_1 / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if y <= -5.2e+79:
		tmp = (x / (t - z)) / y
	elif y <= -2.9e-127:
		tmp = t_1 / (y - z)
	elif y <= 1.25e-203:
		tmp = t_1 / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (y <= -5.2e+79)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.9e-127)
		tmp = Float64(t_1 / Float64(y - z));
	elseif (y <= 1.25e-203)
		tmp = Float64(t_1 / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (y <= -5.2e+79)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.9e-127)
		tmp = t_1 / (y - z);
	elseif (y <= 1.25e-203)
		tmp = t_1 / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[y, -5.2e+79], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.9e-127], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-203], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.20000000000000029e79

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/r* 94.0%

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

   4. Simplified 94.0%

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

   if -5.20000000000000029e79 < y < -2.9e-127

   1. Initial program 96.0%

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

      1. add-cube-cbrt 94.9%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   4. Taylor expanded in t around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. associate-/r* 71.1%

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

      3. distribute-neg-frac 71.1%

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

      4. distribute-frac-neg 71.1%

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

   6. Simplified 71.1%

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

   if -2.9e-127 < y < 1.25e-203

   1. Initial program 83.9%

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

      1. add-cube-cbrt 83.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 98.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 98.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.7%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 98.7%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 98.7%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. associate-/r* 93.6%

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

      3. distribute-neg-frac 93.6%

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

   8. Simplified 93.6%

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

   if 1.25e-203 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 55.2%

      \[\leadsto \color{blue}{\frac{x}{t \cdot \left(y - z\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7: 47.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -300000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-50} \lor \neg \left(z \leq 5.2 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -300000.0)
   (/ (- x) (* z t))
   (if (or (<= z -2.5e-50) (not (<= z 5.2e-67)))
     (/ (- x) (* y z))
     (/ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -300000.0) {
		tmp = -x / (z * t);
	} else if ((z <= -2.5e-50) || !(z <= 5.2e-67)) {
		tmp = -x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	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 (z <= (-300000.0d0)) then
        tmp = -x / (z * t)
    else if ((z <= (-2.5d-50)) .or. (.not. (z <= 5.2d-67))) then
        tmp = -x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -300000.0) {
		tmp = -x / (z * t);
	} else if ((z <= -2.5e-50) || !(z <= 5.2e-67)) {
		tmp = -x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -300000.0:
		tmp = -x / (z * t)
	elif (z <= -2.5e-50) or not (z <= 5.2e-67):
		tmp = -x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -300000.0)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif ((z <= -2.5e-50) || !(z <= 5.2e-67))
		tmp = Float64(Float64(-x) / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -300000.0)
		tmp = -x / (z * t);
	elseif ((z <= -2.5e-50) || ~((z <= 5.2e-67)))
		tmp = -x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -300000.0], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.5e-50], N[Not[LessEqual[z, 5.2e-67]], $MachinePrecision]], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e5

   1. Initial program 90.2%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.4%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.4%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.4%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around inf 47.1%

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

      1. associate-/r* 45.8%

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

   8. Simplified 45.8%

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

   9. Taylor expanded in y around 0 45.0%

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

       1. associate-*r/ 45.0%

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

       2. neg-mul-1 45.0%

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

       3. *-commutative 45.0%

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

   11. Simplified 45.0%

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

   if -3e5 < z < -2.49999999999999984e-50 or 5.1999999999999998e-67 < z

   1. Initial program 86.6%

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

   2. Taylor expanded in y around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-/r* 49.8%

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

   4. Simplified 49.8%

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

   5. Taylor expanded in t around 0 37.8%

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

      1. associate-*r/ 37.8%

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

      2. neg-mul-1 37.8%

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

      3. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if -2.49999999999999984e-50 < z < 5.1999999999999998e-67

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 65.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -300000:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-50} \lor \neg \left(z \leq 5.2 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 8: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-131} \lor \neg \left(t \leq 1.05 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e-131) (not (<= t 1.05e-167)))
   (/ x (* (- y z) t))
   (/ (/ (- x) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e-131) || !(t <= 1.05e-167)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-x / z) / y;
	}
	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 <= (-1.05d-131)) .or. (.not. (t <= 1.05d-167))) then
        tmp = x / ((y - z) * t)
    else
        tmp = (-x / z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e-131) || !(t <= 1.05e-167)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (-x / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e-131) or not (t <= 1.05e-167):
		tmp = x / ((y - z) * t)
	else:
		tmp = (-x / z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e-131) || !(t <= 1.05e-167))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(Float64(-x) / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e-131) || ~((t <= 1.05e-167)))
		tmp = x / ((y - z) * t);
	else
		tmp = (-x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e-131], N[Not[LessEqual[t, 1.05e-167]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999999e-131 or 1.05000000000000009e-167 < t

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 67.9%

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

   if -1.04999999999999999e-131 < t < 1.05000000000000009e-167

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-/r* 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in t around 0 59.6%

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

      1. associate-*r/ 59.6%

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

      2. neg-mul-1 59.6%

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

   7. Simplified 59.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-131} \lor \neg \left(t \leq 1.05 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \end{array} \]

Alternative 9: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e-130)
   (/ x (* y t))
   (if (<= t 2.9e+67) (/ (/ (- x) z) y) (* (/ -1.0 z) (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e-130) {
		tmp = x / (y * t);
	} else if (t <= 2.9e+67) {
		tmp = (-x / z) / y;
	} else {
		tmp = (-1.0 / z) * (x / t);
	}
	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 <= (-5d-130)) then
        tmp = x / (y * t)
    else if (t <= 2.9d+67) then
        tmp = (-x / z) / y
    else
        tmp = ((-1.0d0) / z) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e-130) {
		tmp = x / (y * t);
	} else if (t <= 2.9e+67) {
		tmp = (-x / z) / y;
	} else {
		tmp = (-1.0 / z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e-130:
		tmp = x / (y * t)
	elif t <= 2.9e+67:
		tmp = (-x / z) / y
	else:
		tmp = (-1.0 / z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e-130)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 2.9e+67)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5e-130)
		tmp = x / (y * t);
	elseif (t <= 2.9e+67)
		tmp = (-x / z) / y;
	else
		tmp = (-1.0 / z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e-130], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+67], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.9999999999999996e-130

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 43.5%

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

   if -4.9999999999999996e-130 < t < 2.90000000000000023e67

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-/r* 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in t around 0 49.8%

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

      1. associate-*r/ 49.8%

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

      2. neg-mul-1 49.8%

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

   7. Simplified 49.8%

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

   if 2.90000000000000023e67 < t

   1. Initial program 82.6%

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

      1. clear-num 81.8%

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

      2. inv-pow 81.8%

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

      3. associate-/l* 89.7%

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

   3. Applied egg-rr 89.7%

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

      1. unpow-1 89.7%

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

      2. clear-num 92.3%

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

      3. div-inv 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in y around 0 63.8%

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

   7. Taylor expanded in t around inf 58.2%

      \[\leadsto \color{blue}{\frac{x}{t}} \cdot \frac{-1}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \]

Alternative 10: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.36 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.36e-167)
   (/ x (* y (- t z)))
   (if (<= t 2.3e+215) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.36e-167) {
		tmp = x / (y * (t - z));
	} else if (t <= 2.3e+215) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - 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 <= 1.36d-167) then
        tmp = x / (y * (t - z))
    else if (t <= 2.3d+215) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.36e-167) {
		tmp = x / (y * (t - z));
	} else if (t <= 2.3e+215) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.36e-167:
		tmp = x / (y * (t - z))
	elif t <= 2.3e+215:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.36e-167)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 2.3e+215)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.36e-167)
		tmp = x / (y * (t - z));
	elseif (t <= 2.3e+215)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.36e-167], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+215], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.36000000000000009e-167

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   if 1.36000000000000009e-167 < t < 2.3000000000000001e215

   1. Initial program 86.3%

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

   2. Taylor expanded in t around inf 64.7%

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

   if 2.3000000000000001e215 < t

   1. Initial program 84.4%

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

      1. add-cube-cbrt 84.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.6%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.6%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 84.4%

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

      1. associate-/r* 95.0%

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

   8. Simplified 95.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.36 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.6e-71)
   (/ (/ x (- t z)) y)
   (if (<= t 3e+215) (/ x (* (- y z) t)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.6e-71) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 3e+215) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - 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 <= 1.6d-71) then
        tmp = (x / (t - z)) / y
    else if (t <= 3d+215) then
        tmp = x / ((y - z) * t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.6e-71) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 3e+215) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.6e-71:
		tmp = (x / (t - z)) / y
	elif t <= 3e+215:
		tmp = x / ((y - z) * t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.6e-71)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 3e+215)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.6e-71)
		tmp = (x / (t - z)) / y;
	elseif (t <= 3e+215)
		tmp = x / ((y - z) * t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.6e-71], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 3e+215], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.5999999999999999e-71

   1. Initial program 92.0%

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

   2. Taylor expanded in y around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-/r* 61.8%

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

   4. Simplified 61.8%

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

   if 1.5999999999999999e-71 < t < 2.9999999999999999e215

   1. Initial program 84.8%

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

   2. Taylor expanded in t around inf 69.1%

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

   if 2.9999999999999999e215 < t

   1. Initial program 84.4%

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

      1. add-cube-cbrt 84.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.6%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.6%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 84.4%

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

      1. associate-/r* 95.0%

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

   8. Simplified 95.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.95 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.95e+185) (/ (/ x y) (- t z)) (/ x (* (- y z) (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.95e+185) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (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) :: tmp
    if (y <= (-4.95d+185)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.95e+185) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.95e+185:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.95e+185)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.95e+185)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.95e+185], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9499999999999999e185

   1. Initial program 79.2%

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

      1. add-cube-cbrt 78.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 96.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 96.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.1%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 96.2%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 96.2%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. associate-/r* 96.9%

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

   8. Simplified 96.9%

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

   if -4.9499999999999999e185 < y

   1. Initial program 91.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.95 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 13: 46.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6e-125)
   (/ x (* y t))
   (if (<= t 7e+66) (/ (/ (- x) z) y) (/ (- x) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-125) {
		tmp = x / (y * t);
	} else if (t <= 7e+66) {
		tmp = (-x / z) / y;
	} else {
		tmp = -x / (z * t);
	}
	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 <= (-6d-125)) then
        tmp = x / (y * t)
    else if (t <= 7d+66) then
        tmp = (-x / z) / y
    else
        tmp = -x / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6e-125) {
		tmp = x / (y * t);
	} else if (t <= 7e+66) {
		tmp = (-x / z) / y;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6e-125:
		tmp = x / (y * t)
	elif t <= 7e+66:
		tmp = (-x / z) / y
	else:
		tmp = -x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6e-125)
		tmp = Float64(x / Float64(y * t));
	elseif (t <= 7e+66)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6e-125)
		tmp = x / (y * t);
	elseif (t <= 7e+66)
		tmp = (-x / z) / y;
	else
		tmp = -x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6e-125], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+66], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999981e-125

   1. Initial program 89.9%

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

   2. Taylor expanded in z around 0 43.5%

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

   if -5.99999999999999981e-125 < t < 6.9999999999999994e66

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. associate-/r* 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in t around 0 49.8%

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

      1. associate-*r/ 49.8%

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

      2. neg-mul-1 49.8%

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

   7. Simplified 49.8%

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

   if 6.9999999999999994e66 < t

   1. Initial program 82.6%

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

      1. add-cube-cbrt 82.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.1%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around inf 82.5%

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

      1. associate-/r* 81.0%

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

   8. Simplified 81.0%

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

   9. Taylor expanded in y around 0 59.2%

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

       1. associate-*r/ 59.2%

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

       2. neg-mul-1 59.2%

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

       3. *-commutative 59.2%

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

   11. Simplified 59.2%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 14: 45.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -220000000 \lor \neg \left(z \leq 1.72 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -220000000.0) (not (<= z 1.72e+131)))
   (/ x (* y z))
   (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -220000000.0) || !(z <= 1.72e+131)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	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 ((z <= (-220000000.0d0)) .or. (.not. (z <= 1.72d+131))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -220000000.0) || !(z <= 1.72e+131)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -220000000.0) or not (z <= 1.72e+131):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -220000000.0) || !(z <= 1.72e+131))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -220000000.0) || ~((z <= 1.72e+131)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -220000000.0], N[Not[LessEqual[z, 1.72e+131]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e8 or 1.71999999999999994e131 < z

   1. Initial program 84.5%

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

   2. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. associate-/r* 57.3%

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

   4. Simplified 57.3%

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

   5. Taylor expanded in t around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

      1. expm1-log1p-u 52.9%

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

      2. expm1-udef 70.3%

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

      3. associate-/l/ 70.3%

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

      4. add-sqr-sqrt 28.9%

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

      5. sqrt-unprod 64.2%

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

      6. sqr-neg 64.2%

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

      7. sqrt-unprod 41.0%

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

      8. add-sqr-sqrt 69.9%

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

   9. Applied egg-rr 69.9%

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

       1. expm1-def 42.1%

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

       2. expm1-log1p 42.3%

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

       3. *-commutative 42.3%

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

   11. Simplified 42.3%

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

   if -2.2e8 < z < 1.71999999999999994e131

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 46.5%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -220000000 \lor \neg \left(z \leq 1.72 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 47.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+25} \lor \neg \left(z \leq 7.6 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e+25) (not (<= z 7.6e+132))) (/ x (* y z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+25) || !(z <= 7.6e+132)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	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 ((z <= (-7.6d+25)) .or. (.not. (z <= 7.6d+132))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e+25) || !(z <= 7.6e+132)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e+25) or not (z <= 7.6e+132):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e+25) || !(z <= 7.6e+132))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e+25) || ~((z <= 7.6e+132)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e+25], N[Not[LessEqual[z, 7.6e+132]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000001e25 or 7.60000000000000012e132 < z

   1. Initial program 84.2%

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

   2. Taylor expanded in y around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-/r* 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in t around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

      1. expm1-log1p-u 52.9%

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

      2. expm1-udef 70.1%

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

      3. associate-/l/ 70.1%

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

      4. add-sqr-sqrt 28.5%

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

      5. sqrt-unprod 64.5%

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

      6. sqr-neg 64.5%

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

      7. sqrt-unprod 41.8%

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

      8. add-sqr-sqrt 70.2%

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

   9. Applied egg-rr 70.2%

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

       1. expm1-def 42.8%

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

       2. expm1-log1p 43.1%

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

       3. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   if -7.6000000000000001e25 < z < 7.60000000000000012e132

   1. Initial program 93.5%

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

   2. Taylor expanded in y around inf 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-/r* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in t around inf 47.5%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+25} \lor \neg \left(z \leq 7.6 \cdot 10^{+132}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16: 48.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e-29)
   (/ (- x) (* z t))
   (if (<= z 6.8e+131) (/ (/ x t) y) (/ x (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e-29) {
		tmp = -x / (z * t);
	} else if (z <= 6.8e+131) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * 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 (z <= (-1.35d-29)) then
        tmp = -x / (z * t)
    else if (z <= 6.8d+131) then
        tmp = (x / t) / y
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e-29) {
		tmp = -x / (z * t);
	} else if (z <= 6.8e+131) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e-29:
		tmp = -x / (z * t)
	elif z <= 6.8e+131:
		tmp = (x / t) / y
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e-29)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 6.8e+131)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e-29)
		tmp = -x / (z * t);
	elseif (z <= 6.8e+131)
		tmp = (x / t) / y;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e-29], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+131], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000011e-29

   1. Initial program 91.6%

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

      1. add-cube-cbrt 91.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 99.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 99.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.2%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 99.2%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 99.2%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around inf 47.3%

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

      1. associate-/r* 46.1%

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

   8. Simplified 46.1%

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

   9. Taylor expanded in y around 0 43.1%

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

       1. associate-*r/ 43.1%

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

       2. neg-mul-1 43.1%

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

       3. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   if -1.35000000000000011e-29 < z < 6.79999999999999972e131

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/r* 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in t around inf 49.2%

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

   if 6.79999999999999972e131 < z

   1. Initial program 78.7%

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

   2. Taylor expanded in y around inf 47.0%

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

      1. *-commutative 47.0%

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

      2. associate-/r* 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around 0 54.8%

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

      1. associate-*r/ 54.8%

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

      2. neg-mul-1 54.8%

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

   7. Simplified 54.8%

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

      1. expm1-log1p-u 54.6%

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

      2. expm1-udef 70.4%

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

      3. associate-/l/ 70.4%

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

      4. add-sqr-sqrt 30.8%

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

      5. sqrt-unprod 60.5%

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

      6. sqr-neg 60.5%

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

      7. sqrt-unprod 39.6%

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

      8. add-sqr-sqrt 70.6%

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

   9. Applied egg-rr 70.6%

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

       1. expm1-def 46.8%

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

       2. expm1-log1p 46.8%

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

       3. *-commutative 46.8%

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

   11. Simplified 46.8%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-29}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]

Alternative 17: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.36 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.36e-167) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.36e-167) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	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 <= 1.36d-167) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.36e-167) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.36e-167:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.36e-167)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.36e-167)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.36e-167], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.36000000000000009e-167

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   if 1.36000000000000009e-167 < t

   1. Initial program 86.0%

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

   2. Taylor expanded in t around inf 68.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.36 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 18: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-94) (/ (/ x y) (- t z)) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-94) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	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 <= (-2.25d-94)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-94) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-94:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-94)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-94)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-94], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2500000000000001e-94

   1. Initial program 89.1%

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

      1. add-cube-cbrt 88.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. times-frac 96.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

      3. pow2 96.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

   3. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 95.6%

         \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

      2. associate-*l/ 95.7%

         \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

      3. unpow2 95.7%

         \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

      4. add-cube-cbrt 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 74.8%

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

      1. associate-/r* 79.1%

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

   8. Simplified 79.1%

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

   if -2.2500000000000001e-94 < y

   1. Initial program 90.0%

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

   2. Taylor expanded in t around inf 53.4%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 19: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

   1. add-cube-cbrt 88.9%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
4. Step-by-step derivation

   1. frac-times 88.9%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(y - z\right) \cdot \left(t - z\right)}} \]

   2. unpow2 88.9%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   3. add-cube-cbrt 89.7%

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

   4. associate-/l/ 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 20: 96.8% accurate, 1.0× speedup

Math

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

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(Float64(x / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.7%

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

   1. add-cube-cbrt 88.9%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. times-frac 98.1%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]

   3. pow2 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z} \]

3. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
4. Step-by-step derivation

   1. associate-*r/ 97.4%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \sqrt[3]{x}}{t - z}} \]

   2. associate-*l/ 97.4%

      \[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{y - z}}}{t - z} \]

   3. unpow2 97.4%

      \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{y - z}}{t - z} \]

   4. add-cube-cbrt 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 21: 38.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

2. Taylor expanded in z around 0 34.9%

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

3. Final simplification 34.9%

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

Developer target: 87.3% 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 2023310 
(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))))