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

Percentage Accurate: 89.2% → 97.7%

Time: 13.4s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% 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: 97.7% accurate, 0.0× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (* (/ (pow (cbrt x) 2.0) (- y z)) (/ (cbrt x) (- t z))))

C

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

Java

assert x < y && y < z && z < t;
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

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

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 87.5%

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

   1. add-cube-cbrt 86.7%

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

   2. times-frac 97.4%

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

   3. pow2 97.4%

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

4. Applied egg-rr 97.4%

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

5. Final simplification 97.4%

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

Alternative 2: 80.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+204)
   (/ (/ x (- t z)) y)
   (if (<= y -4.1e-63)
     (/ x (* y (- t z)))
     (if (<= y 1.3e-126) (/ (- x) (* z (- t z))) (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -4.1e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.3e-126) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d+204)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-4.1d-63)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.3d-126) then
        tmp = -x / (z * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -4.1e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.3e-126) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+204:
		tmp = (x / (t - z)) / y
	elif y <= -4.1e-63:
		tmp = x / (y * (t - z))
	elif y <= 1.3e-126:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+204)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -4.1e-63)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.3e-126)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e+204)
		tmp = (x / (t - z)) / y;
	elseif (y <= -4.1e-63)
		tmp = x / (y * (t - z));
	elseif (y <= 1.3e-126)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+204], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -4.1e-63], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-126], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.4999999999999998e204

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 95.1%

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

   5. Simplified 95.1%

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

   if -7.4999999999999998e204 < y < -4.0999999999999998e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -4.0999999999999998e-63 < y < 1.3e-126

   1. Initial program 89.4%

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

   3. Taylor expanded in y around 0 75.9%

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

      1. associate-*r/ 75.9%

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

      2. neg-mul-1 75.9%

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

   5. Simplified 75.9%

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

   if 1.3e-126 < y

   1. Initial program 86.8%

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

      1. add-cube-cbrt 86.0%

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

      2. times-frac 97.9%

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

      3. pow2 97.9%

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

   4. Applied egg-rr 97.9%

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

      1. frac-times 86.0%

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

      2. unpow2 86.0%

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

      3. add-cube-cbrt 86.8%

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

      4. *-commutative 86.8%

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

      5. associate-/r* 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in t around inf 64.8%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-126}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+204)
   (/ (/ x (- t z)) y)
   (if (<= y -4.7e-63)
     (/ x (* y (- t z)))
     (if (<= y 1.9e-126) (/ (- (/ x z)) (- t z)) (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -4.7e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.9e-126) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d+204)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-4.7d-63)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.9d-126) then
        tmp = -(x / z) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -4.7e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.9e-126) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+204:
		tmp = (x / (t - z)) / y
	elif y <= -4.7e-63:
		tmp = x / (y * (t - z))
	elif y <= 1.9e-126:
		tmp = -(x / z) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+204)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -4.7e-63)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.9e-126)
		tmp = Float64(Float64(-Float64(x / z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+204)
		tmp = (x / (t - z)) / y;
	elseif (y <= -4.7e-63)
		tmp = x / (y * (t - z));
	elseif (y <= 1.9e-126)
		tmp = -(x / z) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+204], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -4.7e-63], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-126], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000002e204

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 95.1%

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

   5. Simplified 95.1%

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

   if -5.2000000000000002e204 < y < -4.7000000000000001e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -4.7000000000000001e-63 < y < 1.8999999999999999e-126

   1. Initial program 89.4%

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

      1. add-cube-cbrt 88.4%

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

      2. times-frac 95.2%

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

      3. pow2 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. associate-/r* 82.9%

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

      3. distribute-neg-frac 82.9%

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

      4. distribute-frac-neg 82.9%

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

   7. Simplified 82.9%

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

   if 1.8999999999999999e-126 < y

   1. Initial program 86.8%

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

      1. add-cube-cbrt 86.0%

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

      2. times-frac 97.9%

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

      3. pow2 97.9%

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

   4. Applied egg-rr 97.9%

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

      1. frac-times 86.0%

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

      2. unpow2 86.0%

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

      3. add-cube-cbrt 86.8%

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

      4. *-commutative 86.8%

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

      5. associate-/r* 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in t around inf 64.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-126}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-207}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+204)
   (/ (/ x (- t z)) y)
   (if (<= y -1.3e-63)
     (/ x (* y (- t z)))
     (if (<= y -1.9e-207) (* (/ 1.0 z) (/ x z)) (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.3e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.9e-207) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d+204)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-1.3d-63)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.9d-207)) then
        tmp = (1.0d0 / z) * (x / z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+204) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -1.3e-63) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.9e-207) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+204:
		tmp = (x / (t - z)) / y
	elif y <= -1.3e-63:
		tmp = x / (y * (t - z))
	elif y <= -1.9e-207:
		tmp = (1.0 / z) * (x / z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+204)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -1.3e-63)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.9e-207)
		tmp = Float64(Float64(1.0 / z) * Float64(x / z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+204)
		tmp = (x / (t - z)) / y;
	elseif (y <= -1.3e-63)
		tmp = x / (y * (t - z));
	elseif (y <= -1.9e-207)
		tmp = (1.0 / z) * (x / z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+204], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1.3e-63], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-207], N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000002e204

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 95.1%

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

   5. Simplified 95.1%

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

   if -5.2000000000000002e204 < y < -1.3000000000000001e-63

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -1.3000000000000001e-63 < y < -1.9e-207

   1. Initial program 91.6%

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

      1. add-cube-cbrt 90.5%

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

      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%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in t around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. associate-/r* 61.9%

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

      3. distribute-neg-frac 61.9%

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

      4. distribute-frac-neg 61.9%

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

   7. Simplified 61.9%

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

      1. associate-/l/ 57.7%

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

      2. neg-mul-1 57.7%

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

      3. times-frac 61.8%

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

   9. Applied egg-rr 61.8%

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

   10. Taylor expanded in y around 0 53.6%

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

   if -1.9e-207 < y

   1. Initial program 87.4%

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

      1. add-cube-cbrt 86.6%

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

      2. times-frac 96.5%

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

      3. pow2 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. frac-times 86.6%

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

      2. unpow2 86.6%

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

      3. add-cube-cbrt 87.4%

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

      4. *-commutative 87.4%

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

      5. associate-/r* 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in t around inf 63.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-207}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-\frac{x}{z}}{y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ x z)) y)))
   (if (<= z -4.8e+118)
     t_1
     (if (<= z -2.4e-87)
       (/ (/ (- x) t) z)
       (if (<= z 5.8e+65) (/ (/ x t) y) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(x / z) / y;
	double tmp;
	if (z <= -4.8e+118) {
		tmp = t_1;
	} else if (z <= -2.4e-87) {
		tmp = (-x / t) / z;
	} else if (z <= 5.8e+65) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(x / z) / y
    if (z <= (-4.8d+118)) then
        tmp = t_1
    else if (z <= (-2.4d-87)) then
        tmp = (-x / t) / z
    else if (z <= 5.8d+65) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -(x / z) / y;
	double tmp;
	if (z <= -4.8e+118) {
		tmp = t_1;
	} else if (z <= -2.4e-87) {
		tmp = (-x / t) / z;
	} else if (z <= 5.8e+65) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -(x / z) / y
	tmp = 0
	if z <= -4.8e+118:
		tmp = t_1
	elif z <= -2.4e-87:
		tmp = (-x / t) / z
	elif z <= 5.8e+65:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-Float64(x / z)) / y)
	tmp = 0.0
	if (z <= -4.8e+118)
		tmp = t_1;
	elseif (z <= -2.4e-87)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 5.8e+65)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -(x / z) / y;
	tmp = 0.0;
	if (z <= -4.8e+118)
		tmp = t_1;
	elseif (z <= -2.4e-87)
		tmp = (-x / t) / z;
	elseif (z <= 5.8e+65)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-N[(x / z), $MachinePrecision]) / y), $MachinePrecision]}, If[LessEqual[z, -4.8e+118], t$95$1, If[LessEqual[z, -2.4e-87], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.8e+65], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e118 or 5.8000000000000001e65 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 42.5%

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

      1. *-commutative 42.5%

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

      2. associate-/r* 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around 0 52.7%

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

      1. associate-*r/ 52.7%

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

      2. neg-mul-1 52.7%

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

   8. Simplified 52.7%

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

   if -4.8e118 < z < -2.4e-87

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 41.0%

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

   4. Taylor expanded in y around 0 32.2%

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

      1. associate-*r/ 32.2%

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

      2. associate-/r* 36.3%

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

      3. neg-mul-1 36.3%

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

   6. Simplified 36.3%

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

   if -2.4e-87 < z < 5.8000000000000001e65

   1. Initial program 92.1%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/r* 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around inf 66.8%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e+120)
   (* (/ x z) (/ -1.0 y))
   (if (<= z -1.5e-93)
     (/ (/ (- x) t) z)
     (if (<= z 3.4e+62) (/ (/ x t) y) (/ (- (/ x z)) y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+120) {
		tmp = (x / z) * (-1.0 / y);
	} else if (z <= -1.5e-93) {
		tmp = (-x / t) / z;
	} else if (z <= 3.4e+62) {
		tmp = (x / t) / y;
	} else {
		tmp = -(x / z) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.2d+120)) then
        tmp = (x / z) * ((-1.0d0) / y)
    else if (z <= (-1.5d-93)) then
        tmp = (-x / t) / z
    else if (z <= 3.4d+62) then
        tmp = (x / t) / y
    else
        tmp = -(x / z) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+120) {
		tmp = (x / z) * (-1.0 / y);
	} else if (z <= -1.5e-93) {
		tmp = (-x / t) / z;
	} else if (z <= 3.4e+62) {
		tmp = (x / t) / y;
	} else {
		tmp = -(x / z) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e+120:
		tmp = (x / z) * (-1.0 / y)
	elif z <= -1.5e-93:
		tmp = (-x / t) / z
	elif z <= 3.4e+62:
		tmp = (x / t) / y
	else:
		tmp = -(x / z) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e+120)
		tmp = Float64(Float64(x / z) * Float64(-1.0 / y));
	elseif (z <= -1.5e-93)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 3.4e+62)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-Float64(x / z)) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e+120)
		tmp = (x / z) * (-1.0 / y);
	elseif (z <= -1.5e-93)
		tmp = (-x / t) / z;
	elseif (z <= 3.4e+62)
		tmp = (x / t) / y;
	else
		tmp = -(x / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e+120], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-93], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.4e+62], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[((-N[(x / z), $MachinePrecision]) / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.19999999999999947e120

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-/r* 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   8. Simplified 51.6%

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

      1. associate-/l/ 42.2%

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

      2. neg-mul-1 42.2%

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

      3. times-frac 51.6%

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

   10. Applied egg-rr 51.6%

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

   if -6.19999999999999947e120 < z < -1.5000000000000001e-93

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 41.0%

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

   4. Taylor expanded in y around 0 32.2%

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

      1. associate-*r/ 32.2%

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

      2. associate-/r* 36.3%

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

      3. neg-mul-1 36.3%

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

   6. Simplified 36.3%

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

   if -1.5000000000000001e-93 < z < 3.40000000000000014e62

   1. Initial program 92.1%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/r* 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around inf 66.8%

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

   if 3.40000000000000014e62 < z

   1. Initial program 79.1%

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

   3. Taylor expanded in y around inf 42.8%

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

      1. *-commutative 42.8%

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

      2. associate-/r* 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. neg-mul-1 53.5%

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

   8. Simplified 53.5%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-10} \lor \neg \left(z \leq 7 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-10) (not (<= z 7e+19)))
   (* (/ 1.0 z) (/ x z))
   (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-10) || !(z <= 7e+19)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-10)) .or. (.not. (z <= 7d+19))) then
        tmp = (1.0d0 / z) * (x / z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-10) || !(z <= 7e+19)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-10) or not (z <= 7e+19):
		tmp = (1.0 / z) * (x / z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-10) || !(z <= 7e+19))
		tmp = Float64(Float64(1.0 / z) * Float64(x / z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-10) || ~((z <= 7e+19)))
		tmp = (1.0 / z) * (x / z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-10], N[Not[LessEqual[z, 7e+19]], $MachinePrecision]], N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e-10 or 7e19 < z

   1. Initial program 82.5%

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

      1. add-cube-cbrt 82.0%

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

      2. times-frac 99.0%

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

      3. pow2 99.0%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/r* 83.2%

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

      3. distribute-neg-frac 83.2%

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

      4. distribute-frac-neg 83.2%

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

   7. Simplified 83.2%

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

      1. associate-/l/ 71.9%

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

      2. neg-mul-1 71.9%

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

      3. times-frac 83.1%

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

   9. Applied egg-rr 83.1%

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

   10. Taylor expanded in y around 0 74.2%

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

   if -1.5999999999999999e-10 < z < 7e19

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-/r* 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around inf 67.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-10} \lor \neg \left(z \leq 7 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -70000 \lor \neg \left(z \leq 2.05 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -70000.0) (not (<= z 2.05e+56)))
   (* (/ 1.0 z) (/ x z))
   (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -70000.0) || !(z <= 2.05e+56)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-70000.0d0)) .or. (.not. (z <= 2.05d+56))) then
        tmp = (1.0d0 / z) * (x / z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -70000.0) || !(z <= 2.05e+56)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -70000.0) or not (z <= 2.05e+56):
		tmp = (1.0 / z) * (x / z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -70000.0) || !(z <= 2.05e+56))
		tmp = Float64(Float64(1.0 / z) * Float64(x / z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -70000.0) || ~((z <= 2.05e+56)))
		tmp = (1.0 / z) * (x / z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -70000.0], N[Not[LessEqual[z, 2.05e+56]], $MachinePrecision]], N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e4 or 2.0500000000000002e56 < z

   1. Initial program 82.0%

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

      1. add-cube-cbrt 81.5%

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

      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%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/r* 85.1%

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

      3. distribute-neg-frac 85.1%

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

      4. distribute-frac-neg 85.1%

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

   7. Simplified 85.1%

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

      1. associate-/l/ 73.0%

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

      2. neg-mul-1 73.0%

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

      3. times-frac 85.0%

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

   9. Applied egg-rr 85.0%

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

   10. Taylor expanded in y around 0 77.1%

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

   if -7e4 < z < 2.0500000000000002e56

   1. Initial program 92.4%

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

   3. Taylor expanded in t around inf 75.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000 \lor \neg \left(z \leq 2.05 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -70000 \lor \neg \left(z \leq 9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -70000.0) (not (<= z 9e+56)))
   (* (/ 1.0 z) (/ x z))
   (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -70000.0) || !(z <= 9e+56)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-70000.0d0)) .or. (.not. (z <= 9d+56))) then
        tmp = (1.0d0 / z) * (x / z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -70000.0) || !(z <= 9e+56)) {
		tmp = (1.0 / z) * (x / z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -70000.0) or not (z <= 9e+56):
		tmp = (1.0 / z) * (x / z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -70000.0) || !(z <= 9e+56))
		tmp = Float64(Float64(1.0 / z) * Float64(x / z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -70000.0) || ~((z <= 9e+56)))
		tmp = (1.0 / z) * (x / z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -70000.0], N[Not[LessEqual[z, 9e+56]], $MachinePrecision]], N[(N[(1.0 / z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e4 or 9.0000000000000006e56 < z

   1. Initial program 82.0%

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

      1. add-cube-cbrt 81.5%

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

      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%

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

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in t around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/r* 85.1%

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

      3. distribute-neg-frac 85.1%

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

      4. distribute-frac-neg 85.1%

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

   7. Simplified 85.1%

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

      1. associate-/l/ 73.0%

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

      2. neg-mul-1 73.0%

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

      3. times-frac 85.0%

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

   9. Applied egg-rr 85.0%

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

   10. Taylor expanded in y around 0 77.1%

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

   if -7e4 < z < 9.0000000000000006e56

   1. Initial program 92.4%

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

      1. add-cube-cbrt 91.3%

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

      2. times-frac 95.9%

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

      3. pow2 95.9%

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

   4. Applied egg-rr 95.9%

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

      1. frac-times 91.3%

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

      2. unpow2 91.3%

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

      3. add-cube-cbrt 92.4%

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

      4. *-commutative 92.4%

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

      5. associate-/r* 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in t around inf 75.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000 \lor \neg \left(z \leq 9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{1}{z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e-93)
   (/ (- x) (* z t))
   (if (<= z 2.05e+170) (/ (/ x t) y) (/ (- x) (* y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-93) {
		tmp = -x / (z * t);
	} else if (z <= 2.05e+170) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d-93)) then
        tmp = -x / (z * t)
    else if (z <= 2.05d+170) then
        tmp = (x / t) / y
    else
        tmp = -x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-93) {
		tmp = -x / (z * t);
	} else if (z <= 2.05e+170) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e-93:
		tmp = -x / (z * t)
	elif z <= 2.05e+170:
		tmp = (x / t) / y
	else:
		tmp = -x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e-93)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 2.05e+170)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-x) / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e-93)
		tmp = -x / (z * t);
	elseif (z <= 2.05e+170)
		tmp = (x / t) / y;
	else
		tmp = -x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e-93], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+170], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2000000000000001e-93

   1. Initial program 85.5%

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

   3. Taylor expanded in z around 0 60.5%

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

      1. fma-def 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. mul-1-neg 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 35.0%

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

      1. associate-*r/ 35.0%

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

      2. neg-mul-1 35.0%

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

   8. Simplified 35.0%

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

   if -1.2000000000000001e-93 < z < 2.05e170

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/r* 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around inf 62.6%

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

   if 2.05e170 < z

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-/r* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. associate-*r/ 44.5%

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

      2. neg-mul-1 44.5%

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

      3. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+170}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e-87)
   (/ (/ (- x) t) z)
   (if (<= z 5.4e+169) (/ (/ x t) y) (/ (- x) (* y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-87) {
		tmp = (-x / t) / z;
	} else if (z <= 5.4e+169) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d-87)) then
        tmp = (-x / t) / z
    else if (z <= 5.4d+169) then
        tmp = (x / t) / y
    else
        tmp = -x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-87) {
		tmp = (-x / t) / z;
	} else if (z <= 5.4e+169) {
		tmp = (x / t) / y;
	} else {
		tmp = -x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e-87:
		tmp = (-x / t) / z
	elif z <= 5.4e+169:
		tmp = (x / t) / y
	else:
		tmp = -x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e-87)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	elseif (z <= 5.4e+169)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(-x) / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e-87)
		tmp = (-x / t) / z;
	elseif (z <= 5.4e+169)
		tmp = (x / t) / y;
	else
		tmp = -x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e-87], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.4e+169], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000012e-87

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 40.4%

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

   4. Taylor expanded in y around 0 35.0%

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

      1. associate-*r/ 35.0%

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

      2. associate-/r* 36.7%

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

      3. neg-mul-1 36.7%

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

   6. Simplified 36.7%

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

   if -3.50000000000000012e-87 < z < 5.39999999999999981e169

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/r* 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around inf 62.6%

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

   if 5.39999999999999981e169 < z

   1. Initial program 78.6%

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

   3. Taylor expanded in y around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-/r* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in t around 0 44.5%

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

      1. associate-*r/ 44.5%

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

      2. neg-mul-1 44.5%

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

      3. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+169}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -92000000000000 \lor \neg \left(z \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -92000000000000.0) (not (<= z 1.95e+18)))
   (/ x (* z t))
   (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -92000000000000.0) || !(z <= 1.95e+18)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-92000000000000.0d0)) .or. (.not. (z <= 1.95d+18))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -92000000000000.0) || !(z <= 1.95e+18)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -92000000000000.0) or not (z <= 1.95e+18):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -92000000000000.0) || !(z <= 1.95e+18))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -92000000000000.0) || ~((z <= 1.95e+18)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -92000000000000.0], N[Not[LessEqual[z, 1.95e+18]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e13 or 1.95e18 < z

   1. Initial program 81.9%

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

   3. Taylor expanded in t around inf 40.5%

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

   4. Taylor expanded in y around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. associate-/r* 39.8%

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

      3. neg-mul-1 39.8%

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

   6. Simplified 39.8%

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

      1. expm1-log1p-u 38.6%

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

      2. expm1-udef 53.1%

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

      3. associate-/l/ 52.9%

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

      4. add-sqr-sqrt 24.5%

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

      5. sqrt-unprod 51.2%

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

      6. sqr-neg 51.2%

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

      7. sqrt-unprod 28.3%

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

      8. add-sqr-sqrt 52.8%

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

      9. *-commutative 52.8%

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

   8. Applied egg-rr 52.8%

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

      1. expm1-def 34.1%

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

      2. expm1-log1p 34.4%

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

   10. Simplified 34.4%

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

   if -9.2e13 < z < 1.95e18

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 62.1%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -92000000000000 \lor \neg \left(z \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -36000000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -36000000000000.0)
   (/ x (* z t))
   (if (<= z 6.5e+77) (/ x (* y t)) (/ x (* y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -36000000000000.0) {
		tmp = x / (z * t);
	} else if (z <= 6.5e+77) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-36000000000000.0d0)) then
        tmp = x / (z * t)
    else if (z <= 6.5d+77) then
        tmp = x / (y * t)
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -36000000000000.0) {
		tmp = x / (z * t);
	} else if (z <= 6.5e+77) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -36000000000000.0:
		tmp = x / (z * t)
	elif z <= 6.5e+77:
		tmp = x / (y * t)
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -36000000000000.0)
		tmp = Float64(x / Float64(z * t));
	elseif (z <= 6.5e+77)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -36000000000000.0)
		tmp = x / (z * t);
	elseif (z <= 6.5e+77)
		tmp = x / (y * t);
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -36000000000000.0], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+77], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e13

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 37.7%

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

   4. Taylor expanded in y around 0 37.1%

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

      1. associate-*r/ 37.1%

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

      2. associate-/r* 37.9%

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

      3. neg-mul-1 37.9%

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

   6. Simplified 37.9%

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

      1. expm1-log1p-u 37.4%

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

      2. expm1-udef 53.5%

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

      3. associate-/l/ 53.1%

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

      4. add-sqr-sqrt 20.1%

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

      5. sqrt-unprod 52.9%

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

      6. sqr-neg 52.9%

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

      7. sqrt-unprod 33.2%

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

      8. add-sqr-sqrt 53.3%

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

      9. *-commutative 53.3%

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

   8. Applied egg-rr 53.3%

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

      1. expm1-def 31.8%

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

      2. expm1-log1p 32.0%

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

   10. Simplified 32.0%

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

   if -3.6e13 < z < 6.5e77

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 56.8%

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

   if 6.5e77 < z

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-/r* 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in t around 0 56.3%

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

      1. associate-*r/ 56.3%

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

      2. neg-mul-1 56.3%

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

   8. Simplified 56.3%

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

      1. expm1-log1p-u 56.1%

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

      2. expm1-udef 64.5%

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

      3. associate-/l/ 64.5%

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

      4. add-sqr-sqrt 37.6%

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

      5. sqrt-unprod 64.0%

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

      6. sqr-neg 64.0%

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

      7. sqrt-unprod 26.9%

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

      8. add-sqr-sqrt 64.5%

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

   10. Applied egg-rr 64.5%

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

       1. expm1-def 41.9%

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

       2. expm1-log1p 42.1%

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

       3. *-commutative 42.1%

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

   12. Simplified 42.1%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -92000000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -92000000000000.0)
   (/ x (* z t))
   (if (<= z 3.8e+128) (/ (/ x t) y) (/ x (* y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -92000000000000.0) {
		tmp = x / (z * t);
	} else if (z <= 3.8e+128) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-92000000000000.0d0)) then
        tmp = x / (z * t)
    else if (z <= 3.8d+128) then
        tmp = (x / t) / y
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -92000000000000.0) {
		tmp = x / (z * t);
	} else if (z <= 3.8e+128) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -92000000000000.0:
		tmp = x / (z * t)
	elif z <= 3.8e+128:
		tmp = (x / t) / y
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -92000000000000.0)
		tmp = Float64(x / Float64(z * t));
	elseif (z <= 3.8e+128)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -92000000000000.0)
		tmp = x / (z * t);
	elseif (z <= 3.8e+128)
		tmp = (x / t) / y;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -92000000000000.0], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+128], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2e13

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 37.7%

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

   4. Taylor expanded in y around 0 37.1%

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

      1. associate-*r/ 37.1%

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

      2. associate-/r* 37.9%

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

      3. neg-mul-1 37.9%

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

   6. Simplified 37.9%

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

      1. expm1-log1p-u 37.4%

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

      2. expm1-udef 53.5%

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

      3. associate-/l/ 53.1%

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

      4. add-sqr-sqrt 20.1%

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

      5. sqrt-unprod 52.9%

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

      6. sqr-neg 52.9%

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

      7. sqrt-unprod 33.2%

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

      8. add-sqr-sqrt 53.3%

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

      9. *-commutative 53.3%

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

   8. Applied egg-rr 53.3%

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

      1. expm1-def 31.8%

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

      2. expm1-log1p 32.0%

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

   10. Simplified 32.0%

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

   if -9.2e13 < z < 3.7999999999999999e128

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-/r* 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around inf 60.2%

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

   if 3.7999999999999999e128 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-/r* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in t around 0 54.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y} \]
   7. 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%

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

   8. Simplified 54.8%

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

      1. expm1-log1p-u 54.7%

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

      2. expm1-udef 71.4%

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

      3. associate-/l/ 71.4%

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

      4. add-sqr-sqrt 47.1%

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

      5. sqrt-unprod 70.7%

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

      6. sqr-neg 70.7%

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

      7. sqrt-unprod 24.2%

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

      8. add-sqr-sqrt 71.4%

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

   10. Applied egg-rr 71.4%

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

       1. expm1-def 43.6%

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

       2. expm1-log1p 43.9%

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

       3. *-commutative 43.9%

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

   12. Simplified 43.9%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -92000000000000:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e-88)
   (/ (- x) (* z t))
   (if (<= z 1.9e+128) (/ (/ x t) y) (/ x (* y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e-88) {
		tmp = -x / (z * t);
	} else if (z <= 1.9e+128) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.5d-88)) then
        tmp = -x / (z * t)
    else if (z <= 1.9d+128) then
        tmp = (x / t) / y
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e-88) {
		tmp = -x / (z * t);
	} else if (z <= 1.9e+128) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e-88:
		tmp = -x / (z * t)
	elif z <= 1.9e+128:
		tmp = (x / t) / y
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e-88)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (z <= 1.9e+128)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e-88)
		tmp = -x / (z * t);
	elseif (z <= 1.9e+128)
		tmp = (x / t) / y;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e-88], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+128], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000006e-88

   1. Initial program 85.5%

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

   3. Taylor expanded in z around 0 60.5%

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

      1. fma-def 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. mul-1-neg 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in y around 0 35.0%

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

      1. associate-*r/ 35.0%

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

      2. neg-mul-1 35.0%

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

   8. Simplified 35.0%

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

   if -6.50000000000000006e-88 < z < 1.89999999999999995e128

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-/r* 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in t around inf 63.7%

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

   if 1.89999999999999995e128 < z

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-/r* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in t around 0 54.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y} \]
   7. 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%

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

   8. Simplified 54.8%

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

      1. expm1-log1p-u 54.7%

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

      2. expm1-udef 71.4%

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

      3. associate-/l/ 71.4%

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

      4. add-sqr-sqrt 47.1%

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

      5. sqrt-unprod 70.7%

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

      6. sqr-neg 70.7%

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

      7. sqrt-unprod 24.2%

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

      8. add-sqr-sqrt 71.4%

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

   10. Applied egg-rr 71.4%

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

       1. expm1-def 43.6%

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

       2. expm1-log1p 43.9%

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

       3. *-commutative 43.9%

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

   12. Simplified 43.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+204) (/ (/ x (- t z)) y) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+204) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d+204)) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+204) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+204:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+204)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e+204)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+204], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.4999999999999998e204

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 95.1%

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

   5. Simplified 95.1%

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

   if -7.4999999999999998e204 < y

   1. Initial program 90.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+204}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. add-cube-cbrt 86.7%

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

   2. times-frac 97.4%

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

   3. pow2 97.4%

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

4. Applied egg-rr 97.4%

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

   1. frac-times 86.7%

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

   2. unpow2 86.7%

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

   3. add-cube-cbrt 87.5%

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

   4. *-commutative 87.5%

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

   5. associate-/r* 96.8%

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

6. Applied egg-rr 96.8%

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

7. Final simplification 96.8%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]
8. Add Preprocessing

Alternative 18: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. add-cube-cbrt 86.7%

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

   2. times-frac 97.4%

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

   3. pow2 97.4%

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

4. Applied egg-rr 97.4%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}} \]
5. 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/ 96.1%

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

   3. unpow2 96.1%

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

   4. add-cube-cbrt 97.1%

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

6. Applied egg-rr 97.1%

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

7. Final simplification 97.1%

   \[\leadsto \frac{\frac{x}{y - z}}{t - z} \]
8. Add Preprocessing

Alternative 19: 39.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

3. Taylor expanded in z around 0 40.7%

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

4. Final simplification 40.7%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024027 
(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))))