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

Percentage Accurate: 88.9% → 98.0%

Time: 13.5s

Alternatives: 20

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% 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: 98.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -0.0

   1. Initial program 86.7%

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

      1. *-un-lft-identity 86.7%

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

      2. times-frac 99.0%

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

   3. Applied egg-rr 99.0%

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

   if -0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.7%

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

4. Final simplification 99.1%

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

Alternative 2: 97.5% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

   1. add-cube-cbrt 89.3%

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

   2. times-frac 97.8%

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

   3. pow2 97.8%

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

3. Applied egg-rr 97.8%

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

4. Final simplification 97.8%

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

Alternative 3: 92.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 5e+304) (/ x t_1) (* (/ -1.0 z) (/ x (- y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) * (x / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= 5d+304) then
        tmp = x / t_1
    else
        tmp = ((-1.0d0) / z) * (x / (y - z))
    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 (t_1 <= 5e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) * (x / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 5e+304:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) * (x / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) * Float64(x / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) * (x / (y - z));
	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[LessEqual[t$95$1, 5e+304], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 4.9999999999999997e304

   1. Initial program 95.5%

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

   if 4.9999999999999997e304 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 75.8%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x}{y - z} \cdot \color{blue}{\frac{-1}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{y - z}\\ \end{array} \]

Alternative 4: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 5e+304) (/ x t_1) (/ (/ -1.0 z) (/ (- y z) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= 5d+304) then
        tmp = x / t_1
    else
        tmp = ((-1.0d0) / z) / ((y - z) / x)
    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 (t_1 <= 5e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / z) / ((y - z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 5e+304:
		tmp = x / t_1
	else:
		tmp = (-1.0 / z) / ((y - z) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(y - z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = x / t_1;
	else
		tmp = (-1.0 / z) / ((y - z) / x);
	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[LessEqual[t$95$1, 5e+304], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 4.9999999999999997e304

   1. Initial program 95.5%

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

   if 4.9999999999999997e304 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 75.8%

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

      1. add-cube-cbrt 75.8%

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

      2. times-frac 99.5%

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

      3. pow2 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. frac-times 75.8%

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

      2. unpow2 75.8%

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

      3. add-cube-cbrt 75.8%

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

      4. associate-/r* 99.9%

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

      5. un-div-inv 99.8%

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

      6. *-commutative 99.8%

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

      7. clear-num 99.8%

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

      8. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 81.6%

      \[\leadsto \frac{\color{blue}{\frac{-1}{z}}}{\frac{y - z}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{y - z}{x}}\\ \end{array} \]

Alternative 5: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{y \cdot z}\\ \mathbf{if}\;z \leq -1260:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* y z))))
   (if (<= z -1260.0)
     t_1
     (if (<= z 3.8e-140)
       (/ (/ x y) t)
       (if (<= z 6.5e+143) t_1 (/ (/ x z) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (y * z);
	double tmp;
	if (z <= -1260.0) {
		tmp = t_1;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 6.5e+143) {
		tmp = t_1;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (y * z)
    if (z <= (-1260.0d0)) then
        tmp = t_1
    else if (z <= 3.8d-140) then
        tmp = (x / y) / t
    else if (z <= 6.5d+143) then
        tmp = t_1
    else
        tmp = (x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (y * z);
	double tmp;
	if (z <= -1260.0) {
		tmp = t_1;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 6.5e+143) {
		tmp = t_1;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (y * z)
	tmp = 0
	if z <= -1260.0:
		tmp = t_1
	elif z <= 3.8e-140:
		tmp = (x / y) / t
	elif z <= 6.5e+143:
		tmp = t_1
	else:
		tmp = (x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(y * z))
	tmp = 0.0
	if (z <= -1260.0)
		tmp = t_1;
	elseif (z <= 3.8e-140)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 6.5e+143)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (y * z);
	tmp = 0.0;
	if (z <= -1260.0)
		tmp = t_1;
	elseif (z <= 3.8e-140)
		tmp = (x / y) / t;
	elseif (z <= 6.5e+143)
		tmp = t_1;
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1260.0], t$95$1, If[LessEqual[z, 3.8e-140], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.5e+143], t$95$1, N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1260 or 3.79999999999999998e-140 < z < 6.4999999999999997e143

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   4. Simplified 51.3%

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

   5. Taylor expanded in t around 0 40.0%

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

      1. associate-*r/ 40.0%

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

      2. neg-mul-1 40.0%

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

      3. *-commutative 40.0%

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

   7. Simplified 40.0%

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

   if -1260 < z < 3.79999999999999998e-140

   1. Initial program 91.5%

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

      1. add-cube-cbrt 90.6%

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

      2. times-frac 96.0%

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

      3. pow2 96.0%

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

   3. Applied egg-rr 96.0%

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

      1. frac-times 90.6%

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

      2. unpow2 90.6%

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

      3. add-cube-cbrt 91.5%

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

      4. associate-/r* 92.8%

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

      5. un-div-inv 92.7%

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

      6. *-commutative 92.7%

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

      7. clear-num 92.6%

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

      8. un-div-inv 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in z around 0 71.4%

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

      1. associate-/l/ 73.6%

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

   8. Simplified 73.6%

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

   if 6.4999999999999997e143 < z

   1. Initial program 74.5%

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

   2. Taylor expanded in y around 0 74.5%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in z around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. neg-mul-1 42.0%

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

   7. Simplified 42.0%

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

      1. clear-num 42.1%

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

      2. associate-/r/ 42.0%

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

      3. add-sqr-sqrt 16.8%

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

      4. sqrt-unprod 46.7%

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

      5. sqr-neg 46.7%

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

      6. sqrt-unprod 25.3%

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

      7. add-sqr-sqrt 42.2%

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

   9. Applied egg-rr 42.2%

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

       1. associate-/r/ 42.3%

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

       2. associate-/l* 50.2%

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

       3. clear-num 50.0%

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

   11. Applied egg-rr 50.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1260:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -55000:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -55000.0)
   (/ (/ x z) (- t))
   (if (<= z 3.8e-140)
     (/ (/ x y) t)
     (if (<= z 8.5e+144) (/ (- x) (* y z)) (/ (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -55000.0) {
		tmp = (x / z) / -t;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 8.5e+144) {
		tmp = -x / (y * z);
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-55000.0d0)) then
        tmp = (x / z) / -t
    else if (z <= 3.8d-140) then
        tmp = (x / y) / t
    else if (z <= 8.5d+144) then
        tmp = -x / (y * z)
    else
        tmp = (x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -55000.0) {
		tmp = (x / z) / -t;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 8.5e+144) {
		tmp = -x / (y * z);
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -55000.0:
		tmp = (x / z) / -t
	elif z <= 3.8e-140:
		tmp = (x / y) / t
	elif z <= 8.5e+144:
		tmp = -x / (y * z)
	else:
		tmp = (x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -55000.0)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (z <= 3.8e-140)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 8.5e+144)
		tmp = Float64(Float64(-x) / Float64(y * z));
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -55000.0)
		tmp = (x / z) / -t;
	elseif (z <= 3.8e-140)
		tmp = (x / y) / t;
	elseif (z <= 8.5e+144)
		tmp = -x / (y * z);
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -55000.0], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 3.8e-140], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 8.5e+144], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -55000

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in z around 0 39.1%

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

      1. associate-*r/ 39.1%

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

      2. neg-mul-1 39.1%

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

   7. Simplified 39.1%

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

      1. clear-num 39.5%

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

      2. associate-/r/ 39.1%

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

      3. add-sqr-sqrt 19.6%

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

      4. sqrt-unprod 43.1%

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

      5. sqr-neg 43.1%

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

      6. sqrt-unprod 16.1%

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

      7. add-sqr-sqrt 30.7%

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

   9. Applied egg-rr 30.7%

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

       1. *-commutative 30.7%

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

       2. add-sqr-sqrt 16.1%

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

       3. sqrt-unprod 43.1%

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

       4. sqr-neg 43.1%

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

       5. sqrt-unprod 19.6%

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

       6. add-sqr-sqrt 39.1%

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

       7. div-inv 39.1%

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

       8. associate-/r* 43.0%

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

       9. div-inv 43.0%

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

       10. div-inv 43.0%

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

       11. distribute-lft-neg-out 43.0%

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

       12. div-inv 43.0%

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

       13. remove-double-neg 43.0%

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

       14. distribute-frac-neg 43.0%

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

       15. distribute-frac-neg 43.0%

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

       16. remove-double-neg 43.0%

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

       17. frac-2neg 43.0%

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

       18. distribute-frac-neg 43.0%

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

       19. remove-double-neg 43.0%

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

       20. associate-*l/ 53.4%

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

       21. div-inv 53.4%

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

   11. Applied egg-rr 53.4%

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

   if -55000 < z < 3.79999999999999998e-140

   1. Initial program 91.6%

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

      1. add-cube-cbrt 90.6%

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

      2. times-frac 96.0%

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

      3. pow2 96.0%

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

   3. Applied egg-rr 96.0%

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

      1. frac-times 90.6%

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

      2. unpow2 90.6%

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

      3. add-cube-cbrt 91.6%

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

      4. associate-/r* 92.8%

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

      5. un-div-inv 92.7%

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

      6. *-commutative 92.7%

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

      7. clear-num 92.7%

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

      8. un-div-inv 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in z around 0 70.9%

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

      1. associate-/l/ 73.0%

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

   8. Simplified 73.0%

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

   if 3.79999999999999998e-140 < z < 8.4999999999999998e144

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf 54.8%

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

      1. *-commutative 54.8%

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

   4. Simplified 54.8%

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

   5. Taylor expanded in t around 0 37.6%

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

      1. associate-*r/ 37.6%

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

      2. neg-mul-1 37.6%

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

      3. *-commutative 37.6%

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

   7. Simplified 37.6%

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

   if 8.4999999999999998e144 < z

   1. Initial program 74.5%

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

   2. Taylor expanded in y around 0 74.5%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in z around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. neg-mul-1 42.0%

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

   7. Simplified 42.0%

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

      1. clear-num 42.1%

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

      2. associate-/r/ 42.0%

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

      3. add-sqr-sqrt 16.8%

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

      4. sqrt-unprod 46.7%

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

      5. sqr-neg 46.7%

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

      6. sqrt-unprod 25.3%

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

      7. add-sqr-sqrt 42.2%

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

   9. Applied egg-rr 42.2%

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

       1. associate-/r/ 42.3%

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

       2. associate-/l* 50.2%

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

       3. clear-num 50.0%

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

   11. Applied egg-rr 50.0%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -55000:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 7: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6600:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6600.0)
   (/ (/ x z) (- t))
   (if (<= z 3.6e-140)
     (/ (/ x y) t)
     (if (<= z 1.4e+258) (/ (/ (- x) y) z) (/ (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6600.0) {
		tmp = (x / z) / -t;
	} else if (z <= 3.6e-140) {
		tmp = (x / y) / t;
	} else if (z <= 1.4e+258) {
		tmp = (-x / y) / z;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6600.0d0)) then
        tmp = (x / z) / -t
    else if (z <= 3.6d-140) then
        tmp = (x / y) / t
    else if (z <= 1.4d+258) then
        tmp = (-x / y) / z
    else
        tmp = (x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6600.0) {
		tmp = (x / z) / -t;
	} else if (z <= 3.6e-140) {
		tmp = (x / y) / t;
	} else if (z <= 1.4e+258) {
		tmp = (-x / y) / z;
	} else {
		tmp = (x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6600.0:
		tmp = (x / z) / -t
	elif z <= 3.6e-140:
		tmp = (x / y) / t
	elif z <= 1.4e+258:
		tmp = (-x / y) / z
	else:
		tmp = (x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6600.0)
		tmp = Float64(Float64(x / z) / Float64(-t));
	elseif (z <= 3.6e-140)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.4e+258)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	else
		tmp = Float64(Float64(x / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6600.0)
		tmp = (x / z) / -t;
	elseif (z <= 3.6e-140)
		tmp = (x / y) / t;
	elseif (z <= 1.4e+258)
		tmp = (-x / y) / z;
	else
		tmp = (x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6600.0], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 3.6e-140], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.4e+258], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6600

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in z around 0 39.1%

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

      1. associate-*r/ 39.1%

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

      2. neg-mul-1 39.1%

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

   7. Simplified 39.1%

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

      1. clear-num 39.5%

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

      2. associate-/r/ 39.1%

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

      3. add-sqr-sqrt 19.6%

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

      4. sqrt-unprod 43.1%

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

      5. sqr-neg 43.1%

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

      6. sqrt-unprod 16.1%

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

      7. add-sqr-sqrt 30.7%

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

   9. Applied egg-rr 30.7%

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

       1. *-commutative 30.7%

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

       2. add-sqr-sqrt 16.1%

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

       3. sqrt-unprod 43.1%

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

       4. sqr-neg 43.1%

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

       5. sqrt-unprod 19.6%

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

       6. add-sqr-sqrt 39.1%

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

       7. div-inv 39.1%

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

       8. associate-/r* 43.0%

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

       9. div-inv 43.0%

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

       10. div-inv 43.0%

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

       11. distribute-lft-neg-out 43.0%

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

       12. div-inv 43.0%

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

       13. remove-double-neg 43.0%

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

       14. distribute-frac-neg 43.0%

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

       15. distribute-frac-neg 43.0%

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

       16. remove-double-neg 43.0%

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

       17. frac-2neg 43.0%

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

       18. distribute-frac-neg 43.0%

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

       19. remove-double-neg 43.0%

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

       20. associate-*l/ 53.4%

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

       21. div-inv 53.4%

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

   11. Applied egg-rr 53.4%

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

   if -6600 < z < 3.6e-140

   1. Initial program 91.6%

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

      1. add-cube-cbrt 90.6%

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

      2. times-frac 96.0%

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

      3. pow2 96.0%

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

   3. Applied egg-rr 96.0%

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

      1. frac-times 90.6%

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

      2. unpow2 90.6%

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

      3. add-cube-cbrt 91.6%

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

      4. associate-/r* 92.8%

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

      5. un-div-inv 92.7%

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

      6. *-commutative 92.7%

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

      7. clear-num 92.7%

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

      8. un-div-inv 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in z around 0 70.9%

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

      1. associate-/l/ 73.0%

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

   8. Simplified 73.0%

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

   if 3.6e-140 < z < 1.39999999999999991e258

   1. Initial program 87.5%

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

      1. add-cube-cbrt 87.0%

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

      2. times-frac 99.1%

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

      3. pow2 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in y around inf 46.1%

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

      1. associate-/r* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in t around 0 33.8%

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

      1. mul-1-neg 33.8%

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

      2. associate-/r* 34.7%

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

      3. distribute-neg-frac 34.7%

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

      4. distribute-neg-frac 34.7%

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

   9. Simplified 34.7%

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

   if 1.39999999999999991e258 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 58.0%

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

      1. associate-*r/ 58.0%

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

      2. neg-mul-1 58.0%

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

   7. Simplified 58.0%

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

      1. clear-num 58.0%

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

      2. associate-/r/ 58.0%

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

      3. add-sqr-sqrt 34.0%

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

      4. sqrt-unprod 68.3%

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

      5. sqr-neg 68.3%

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

      6. sqrt-unprod 24.0%

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

      7. add-sqr-sqrt 58.0%

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

   9. Applied egg-rr 58.0%

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

       1. associate-/r/ 58.0%

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

       2. associate-/l* 78.3%

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

       3. clear-num 78.3%

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

   11. Applied egg-rr 78.3%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6600:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+258}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 8: 56.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{z}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) z)))
   (if (<= z -1.16e+72)
     t_1
     (if (<= z 3.8e-140)
       (/ (/ x y) t)
       (if (<= z 1.5e+143) (/ (- x) (* y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / z;
	double tmp;
	if (z <= -1.16e+72) {
		tmp = t_1;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 1.5e+143) {
		tmp = -x / (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-x / z) / z
    if (z <= (-1.16d+72)) then
        tmp = t_1
    else if (z <= 3.8d-140) then
        tmp = (x / y) / t
    else if (z <= 1.5d+143) then
        tmp = -x / (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / z;
	double tmp;
	if (z <= -1.16e+72) {
		tmp = t_1;
	} else if (z <= 3.8e-140) {
		tmp = (x / y) / t;
	} else if (z <= 1.5e+143) {
		tmp = -x / (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-x / z) / z
	tmp = 0
	if z <= -1.16e+72:
		tmp = t_1
	elif z <= 3.8e-140:
		tmp = (x / y) / t
	elif z <= 1.5e+143:
		tmp = -x / (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / z)
	tmp = 0.0
	if (z <= -1.16e+72)
		tmp = t_1;
	elseif (z <= 3.8e-140)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= 1.5e+143)
		tmp = Float64(Float64(-x) / Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-x / z) / z;
	tmp = 0.0;
	if (z <= -1.16e+72)
		tmp = t_1;
	elseif (z <= 3.8e-140)
		tmp = (x / y) / t;
	elseif (z <= 1.5e+143)
		tmp = -x / (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.16e+72], t$95$1, If[LessEqual[z, 3.8e-140], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.5e+143], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16000000000000003e72 or 1.5e143 < z

   1. Initial program 80.5%

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

      1. add-cube-cbrt 80.4%

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

      2. times-frac 99.5%

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

      3. pow2 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in t around 0 77.9%

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

      1. associate-/r* 90.0%

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

      2. associate-*r/ 90.0%

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

      3. associate-*r/ 90.0%

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

      4. neg-mul-1 90.0%

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

   6. Simplified 90.0%

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

      1. expm1-log1p-u 87.2%

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

      2. expm1-udef 71.6%

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

      3. associate-/l/ 71.6%

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

      4. add-sqr-sqrt 31.0%

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

      5. sqrt-unprod 67.5%

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

      6. sqr-neg 67.5%

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

      7. sqrt-unprod 39.3%

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

      8. add-sqr-sqrt 70.4%

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

      9. *-commutative 70.4%

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

   8. Applied egg-rr 70.4%

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

      1. expm1-def 70.3%

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

      2. expm1-log1p 70.3%

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

      3. *-rgt-identity 70.3%

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

      4. times-frac 69.4%

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

      5. associate-*l/ 69.4%

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

      6. associate-*r/ 69.4%

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

      7. *-rgt-identity 69.4%

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

   10. Simplified 69.4%

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

   11. Taylor expanded in y around 0 65.9%

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

       1. associate-*r/ 65.9%

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

       2. neg-mul-1 65.9%

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

   13. Simplified 65.9%

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

   if -1.16000000000000003e72 < z < 3.79999999999999998e-140

   1. Initial program 92.6%

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

      1. add-cube-cbrt 91.6%

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

      2. times-frac 96.3%

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

      3. pow2 96.3%

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

   3. Applied egg-rr 96.3%

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

      1. frac-times 91.6%

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

      2. unpow2 91.6%

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

      3. add-cube-cbrt 92.6%

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

      4. associate-/r* 93.7%

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

      5. un-div-inv 93.6%

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

      6. *-commutative 93.6%

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

      7. clear-num 93.5%

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

      8. un-div-inv 93.6%

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

   5. Applied egg-rr 93.6%

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

   6. Taylor expanded in z around 0 65.0%

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

      1. associate-/l/ 67.6%

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

   8. Simplified 67.6%

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

   if 3.79999999999999998e-140 < z < 1.5e143

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 55.7%

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

      1. *-commutative 55.7%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in t around 0 38.2%

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

      1. associate-*r/ 38.2%

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

      2. neg-mul-1 38.2%

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

      3. *-commutative 38.2%

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

   7. Simplified 38.2%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{-x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+143}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{z}\\ \end{array} \]

Alternative 9: 70.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-55)
   (/ (/ x y) (- t z))
   (if (<= y 2.3e-104) (/ (- x) (* z (- t z))) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-55) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.3e-104) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d-55)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.3d-104) then
        tmp = -x / (z * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-55) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.3e-104) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e-55:
		tmp = (x / y) / (t - z)
	elif y <= 2.3e-104:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e-55)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.3e-104)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e-55)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.3e-104)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e-55], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-104], 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 3 regimes

2. if y < -3.99999999999999998e-55

   1. Initial program 90.2%

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

      1. add-cube-cbrt 89.5%

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

      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%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. associate-/r* 85.2%

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

   6. Simplified 85.2%

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

   if -3.99999999999999998e-55 < y < 2.2999999999999999e-104

   1. Initial program 88.4%

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

   2. Taylor expanded in y around 0 71.3%

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

      1. associate-*r/ 71.3%

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

      2. neg-mul-1 71.3%

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

   4. Simplified 71.3%

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

   if 2.2999999999999999e-104 < y

   1. Initial program 91.4%

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

      1. add-cube-cbrt 90.9%

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

      2. times-frac 99.1%

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

      3. pow2 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in t around inf 63.9%

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

      1. associate-/r* 70.1%

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

   6. Simplified 70.1%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-104}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.45e-26)
   (/ (/ x y) (- t z))
   (if (<= y 1.06e-106) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e-26) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.06e-106) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.45d-26)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.06d-106) then
        tmp = (-x / z) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e-26) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.06e-106) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.45e-26:
		tmp = (x / y) / (t - z)
	elif y <= 1.06e-106:
		tmp = (-x / z) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.45e-26)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.06e-106)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.45e-26)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.06e-106)
		tmp = (-x / z) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.45e-26], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e-106], 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 3 regimes

2. if y < -2.45e-26

   1. Initial program 91.1%

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

      1. add-cube-cbrt 90.4%

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

      2. times-frac 99.0%

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

      3. pow2 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in y around inf 83.5%

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

      1. associate-/r* 85.9%

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

   6. Simplified 85.9%

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

   if -2.45e-26 < y < 1.06e-106

   1. Initial program 87.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. 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 95.6%

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

      3. pow2 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in y around 0 69.8%

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

      1. associate-/r* 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. neg-mul-1 77.9%

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

   6. Simplified 77.9%

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

   if 1.06e-106 < y

   1. Initial program 91.5%

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

      1. add-cube-cbrt 91.0%

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

      2. times-frac 99.1%

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

      3. pow2 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in t around inf 64.3%

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

      1. associate-/r* 70.4%

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

   6. Simplified 70.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-26}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+291}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+126}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+291)
   (/ x (* y t))
   (if (<= y -2.9e+126) (/ (/ (- x) y) z) (/ x (* (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+291) {
		tmp = x / (y * t);
	} else if (y <= -2.9e+126) {
		tmp = (-x / y) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d+291)) then
        tmp = x / (y * t)
    else if (y <= (-2.9d+126)) then
        tmp = (-x / y) / z
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+291) {
		tmp = x / (y * t);
	} else if (y <= -2.9e+126) {
		tmp = (-x / y) / z;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+291:
		tmp = x / (y * t)
	elif y <= -2.9e+126:
		tmp = (-x / y) / z
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+291)
		tmp = Float64(x / Float64(y * t));
	elseif (y <= -2.9e+126)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+291)
		tmp = x / (y * t);
	elseif (y <= -2.9e+126)
		tmp = (-x / y) / z;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+291], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e+126], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000006e291

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   if -2.60000000000000006e291 < y < -2.89999999999999986e126

   1. Initial program 91.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. 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 99.3%

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

      3. pow2 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in y around inf 91.0%

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

      1. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/r* 79.3%

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

      3. distribute-neg-frac 79.3%

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

      4. distribute-neg-frac 79.3%

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

   9. Simplified 79.3%

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

   if -2.89999999999999986e126 < y

   1. Initial program 89.6%

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

   2. Taylor expanded in t around inf 61.3%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+291}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+126}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 12: 46.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+125} \lor \neg \left(z \leq 1.5 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e+125) (not (<= z 1.5e+116))) (/ x (* z t)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+125) || !(z <= 1.5e+116)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d+125)) .or. (.not. (z <= 1.5d+116))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+125) || !(z <= 1.5e+116)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e+125) or not (z <= 1.5e+116):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e+125) || !(z <= 1.5e+116))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e+125) || ~((z <= 1.5e+116)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e+125], N[Not[LessEqual[z, 1.5e+116]], $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 < -1.65000000000000003e125 or 1.4999999999999999e116 < z

   1. Initial program 81.5%

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

   2. Taylor expanded in y around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. neg-mul-1 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around 0 42.4%

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

      1. associate-*r/ 42.4%

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

      2. neg-mul-1 42.4%

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

   7. Simplified 42.4%

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

      1. expm1-log1p-u 42.1%

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

      2. expm1-udef 62.5%

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

      3. add-sqr-sqrt 31.0%

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

      4. sqrt-unprod 61.4%

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

      5. sqr-neg 61.4%

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

      6. sqrt-unprod 31.7%

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

      7. add-sqr-sqrt 62.6%

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

      8. associate-/r* 62.6%

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

   9. Applied egg-rr 62.6%

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

       1. expm1-def 41.2%

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

       2. expm1-log1p 41.4%

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

       3. associate-/l/ 42.4%

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

   11. Simplified 42.4%

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

   if -1.65000000000000003e125 < z < 1.4999999999999999e116

   1. Initial program 93.4%

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

   2. Taylor expanded in z around 0 54.6%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+125} \lor \neg \left(z \leq 1.5 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+53} \lor \neg \left(z \leq 2.7 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e+53) (not (<= z 2.7e+89))) (/ x (* y z)) (/ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+53) || !(z <= 2.7e+89)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4d+53)) .or. (.not. (z <= 2.7d+89))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+53) || !(z <= 2.7e+89)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e+53) or not (z <= 2.7e+89):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e+53) || !(z <= 2.7e+89))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e+53) || ~((z <= 2.7e+89)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e+53], N[Not[LessEqual[z, 2.7e+89]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e53 or 2.7e89 < z

   1. Initial program 84.1%

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

      1. add-cube-cbrt 83.8%

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

      2. times-frac 99.3%

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

      3. pow2 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in t around 0 79.2%

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

      1. associate-/r* 88.5%

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

      2. associate-*r/ 88.5%

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

      3. associate-*r/ 88.5%

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

      4. neg-mul-1 88.5%

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

   6. Simplified 88.5%

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

      1. expm1-log1p-u 83.3%

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

      2. expm1-udef 67.9%

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

      3. associate-/l/ 67.9%

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

      4. add-sqr-sqrt 28.9%

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

      5. sqrt-unprod 63.2%

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

      6. sqr-neg 63.2%

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

      7. sqrt-unprod 36.5%

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

      8. add-sqr-sqrt 65.5%

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

      9. *-commutative 65.5%

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

   8. Applied egg-rr 65.5%

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

      1. expm1-def 63.4%

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

      2. expm1-log1p 63.5%

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

      3. *-rgt-identity 63.5%

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

      4. times-frac 62.8%

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

      5. associate-*l/ 62.8%

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

      6. associate-*r/ 62.8%

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

      7. *-rgt-identity 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in y around inf 38.2%

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

       1. *-commutative 38.2%

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

   13. Simplified 38.2%

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

   if -4e53 < z < 2.7e89

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 59.3%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+53} \lor \neg \left(z \leq 2.7 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+53} \lor \neg \left(z \leq 1.15 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e+53) (not (<= z 1.15e+82))) (/ x (* y z)) (/ (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+53) || !(z <= 1.15e+82)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d+53)) .or. (.not. (z <= 1.15d+82))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+53) || !(z <= 1.15e+82)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+53) or not (z <= 1.15e+82):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+53) || !(z <= 1.15e+82))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e+53) || ~((z <= 1.15e+82)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+53], N[Not[LessEqual[z, 1.15e+82]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e53 or 1.14999999999999994e82 < z

   1. Initial program 84.1%

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

      1. add-cube-cbrt 83.8%

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

      2. times-frac 99.3%

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

      3. pow2 99.3%

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

   3. Applied egg-rr 99.3%

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

   4. Taylor expanded in t around 0 79.2%

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

      1. associate-/r* 88.5%

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

      2. associate-*r/ 88.5%

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

      3. associate-*r/ 88.5%

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

      4. neg-mul-1 88.5%

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

   6. Simplified 88.5%

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

      1. expm1-log1p-u 83.3%

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

      2. expm1-udef 67.9%

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

      3. associate-/l/ 67.9%

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

      4. add-sqr-sqrt 28.9%

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

      5. sqrt-unprod 63.2%

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

      6. sqr-neg 63.2%

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

      7. sqrt-unprod 36.5%

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

      8. add-sqr-sqrt 65.5%

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

      9. *-commutative 65.5%

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

   8. Applied egg-rr 65.5%

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

      1. expm1-def 63.4%

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

      2. expm1-log1p 63.5%

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

      3. *-rgt-identity 63.5%

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

      4. times-frac 62.8%

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

      5. associate-*l/ 62.8%

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

      6. associate-*r/ 62.8%

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

      7. *-rgt-identity 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in y around inf 38.2%

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

       1. *-commutative 38.2%

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

   13. Simplified 38.2%

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

   if -3.2e53 < z < 1.14999999999999994e82

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 59.3%

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

      1. associate-/r* 63.4%

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

      2. div-inv 63.2%

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

   4. Applied egg-rr 63.2%

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

      1. un-div-inv 63.4%

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

   6. Applied egg-rr 63.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+53} \lor \neg \left(z \leq 1.15 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+67} \lor \neg \left(z \leq 1.4 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+67) (not (<= z 1.4e+81))) (/ (/ x z) t) (/ (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+67) || !(z <= 1.4e+81)) {
		tmp = (x / z) / t;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.8d+67)) .or. (.not. (z <= 1.4d+81))) then
        tmp = (x / z) / t
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+67) || !(z <= 1.4e+81)) {
		tmp = (x / z) / t;
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+67) or not (z <= 1.4e+81):
		tmp = (x / z) / t
	else:
		tmp = (x / y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+67) || !(z <= 1.4e+81))
		tmp = Float64(Float64(x / z) / t);
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e+67) || ~((z <= 1.4e+81)))
		tmp = (x / z) / t;
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+67], N[Not[LessEqual[z, 1.4e+81]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e67 or 1.39999999999999997e81 < z

   1. Initial program 83.6%

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

   2. Taylor expanded in y around 0 79.7%

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

      1. associate-*r/ 79.7%

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

      2. neg-mul-1 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in z around 0 37.0%

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

      1. associate-*r/ 37.0%

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

      2. neg-mul-1 37.0%

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

   7. Simplified 37.0%

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

      1. clear-num 37.3%

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

      2. associate-/r/ 37.0%

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

      3. add-sqr-sqrt 17.6%

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

      4. sqrt-unprod 42.9%

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

      5. sqr-neg 42.9%

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

      6. sqrt-unprod 19.4%

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

      7. add-sqr-sqrt 36.1%

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

   9. Applied egg-rr 36.1%

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

       1. associate-/r/ 36.4%

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

       2. associate-/l* 46.5%

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

       3. clear-num 46.3%

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

   11. Applied egg-rr 46.3%

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

   if -1.7999999999999999e67 < z < 1.39999999999999997e81

   1. Initial program 93.7%

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

      1. add-cube-cbrt 92.8%

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

      2. times-frac 97.0%

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

      3. pow2 97.0%

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

   3. Applied egg-rr 97.0%

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

      1. frac-times 92.8%

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

      2. unpow2 92.8%

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

      3. add-cube-cbrt 93.7%

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

      4. associate-/r* 94.6%

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

      5. un-div-inv 94.5%

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

      6. *-commutative 94.5%

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

      7. clear-num 94.4%

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

      8. un-div-inv 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around 0 58.3%

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

      1. associate-/l/ 60.4%

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

   8. Simplified 60.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+67} \lor \neg \left(z \leq 1.4 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 16: 48.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+125)
   (/ x (* y z))
   (if (<= z 1.65e+143) (/ (/ x y) t) (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+125) {
		tmp = x / (y * z);
	} else if (z <= 1.65e+143) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.5d+125)) then
        tmp = x / (y * z)
    else if (z <= 1.65d+143) then
        tmp = (x / y) / t
    else
        tmp = x / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+125) {
		tmp = x / (y * z);
	} else if (z <= 1.65e+143) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+125:
		tmp = x / (y * z)
	elif z <= 1.65e+143:
		tmp = (x / y) / t
	else:
		tmp = x / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+125)
		tmp = Float64(x / Float64(y * z));
	elseif (z <= 1.65e+143)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+125)
		tmp = x / (y * z);
	elseif (z <= 1.65e+143)
		tmp = (x / y) / t;
	else
		tmp = x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+125], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+143], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.50000000000000008e125

   1. Initial program 83.6%

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

      1. add-cube-cbrt 83.6%

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

      2. times-frac 99.6%

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

      3. pow2 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in t around 0 83.6%

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

      1. associate-/r* 91.3%

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

      2. associate-*r/ 91.3%

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

      3. associate-*r/ 91.3%

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

      4. neg-mul-1 91.3%

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

   6. Simplified 91.3%

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

      1. expm1-log1p-u 91.3%

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

      2. expm1-udef 80.8%

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

      3. associate-/l/ 80.8%

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

      4. add-sqr-sqrt 42.5%

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

      5. sqrt-unprod 78.4%

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

      6. sqr-neg 78.4%

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

      7. sqrt-unprod 38.3%

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

      8. add-sqr-sqrt 80.8%

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

      9. *-commutative 80.8%

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

   8. Applied egg-rr 80.8%

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

      1. expm1-def 80.7%

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

      2. expm1-log1p 80.7%

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

      3. *-rgt-identity 80.7%

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

      4. times-frac 79.2%

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

      5. associate-*l/ 79.2%

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

      6. associate-*r/ 79.2%

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

      7. *-rgt-identity 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in y around inf 51.8%

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

       1. *-commutative 51.8%

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

   13. Simplified 51.8%

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

   if -1.50000000000000008e125 < z < 1.65e143

   1. Initial program 93.7%

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

      1. add-cube-cbrt 92.7%

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

      2. times-frac 97.2%

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

      3. pow2 97.2%

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

   3. Applied egg-rr 97.2%

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

      1. frac-times 92.7%

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

      2. unpow2 92.7%

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

      3. add-cube-cbrt 93.7%

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

      4. associate-/r* 95.4%

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

      5. un-div-inv 95.2%

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

      6. *-commutative 95.2%

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

      7. clear-num 95.2%

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

      8. un-div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in z around 0 53.5%

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

      1. associate-/l/ 56.3%

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

   8. Simplified 56.3%

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

   if 1.65e143 < z

   1. Initial program 75.2%

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

   2. Taylor expanded in y around 0 75.2%

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

      1. associate-*r/ 75.2%

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

      2. neg-mul-1 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. associate-*r/ 40.8%

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

      2. neg-mul-1 40.8%

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

   7. Simplified 40.8%

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

      1. expm1-log1p-u 40.3%

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

      2. expm1-udef 51.2%

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

      3. add-sqr-sqrt 21.4%

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

      4. sqrt-unprod 50.9%

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

      5. sqr-neg 50.9%

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

      6. sqrt-unprod 30.1%

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

      7. add-sqr-sqrt 51.6%

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

      8. associate-/r* 51.5%

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

   9. Applied egg-rr 51.5%

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

       1. expm1-def 40.4%

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

       2. expm1-log1p 40.7%

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

       3. associate-/l/ 41.0%

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

   11. Simplified 41.0%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 17: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.36e-92) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e-92) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.36d-92)) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e-92) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.36e-92:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.36e-92)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.36e-92)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.36e-92], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.36e-92

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if -1.36e-92 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in t around inf 61.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 18: 63.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e-93) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-93) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.2d-93)) then
        tmp = x / (y * (t - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-93) {
		tmp = x / (y * (t - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e-93:
		tmp = x / (y * (t - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-93)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-93)
		tmp = x / (y * (t - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e-93], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999998e-93

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 78.4%

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

      1. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if -8.1999999999999998e-93 < y

   1. Initial program 89.4%

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

      1. add-cube-cbrt 88.7%

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

      2. times-frac 97.3%

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

      3. pow2 97.3%

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

   3. Applied egg-rr 97.3%

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

   4. Taylor expanded in t around inf 61.4%

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

      1. associate-/r* 66.1%

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

   6. Simplified 66.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 19: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e-92) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-92) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.7d-92)) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e-92) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e-92:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e-92)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e-92)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e-92], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999977e-92

   1. Initial program 91.1%

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

      1. add-cube-cbrt 90.4%

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

      2. times-frac 98.9%

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

      3. pow2 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in y around inf 78.4%

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

      1. associate-/r* 80.5%

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

   6. Simplified 80.5%

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

   if -3.69999999999999977e-92 < y

   1. Initial program 89.4%

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

      1. add-cube-cbrt 88.7%

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

      2. times-frac 97.3%

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

      3. pow2 97.3%

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

   3. Applied egg-rr 97.3%

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

   4. Taylor expanded in t around inf 61.4%

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

      1. associate-/r* 66.1%

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

   6. Simplified 66.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 20: 39.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.0%

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

2. Taylor expanded in z around 0 44.1%

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

3. Final simplification 44.1%

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

Developer target: 87.8% 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 2023336 
(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))))