Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.4% → 97.1%

Time: 10.6s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(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]

Derivation

1. Initial program 82.5%

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

   1. associate-/l* 96.9%

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

3. Simplified 96.9%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 58.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.26e+110)
   x
   (if (<= z -2.2e+75)
     (* x (/ y (- z)))
     (if (<= z -6.8e+69)
       x
       (if (<= z -2.2e-40)
         (/ (* x (- z)) t)
         (if (<= z 6.2e-173)
           (/ x (/ t y))
           (if (<= z 8.5e-89)
             (/ (* x (- y)) z)
             (if (<= z 4.6e-40) (* x (/ y t)) x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+110) {
		tmp = x;
	} else if (z <= -2.2e+75) {
		tmp = x * (y / -z);
	} else if (z <= -6.8e+69) {
		tmp = x;
	} else if (z <= -2.2e-40) {
		tmp = (x * -z) / t;
	} else if (z <= 6.2e-173) {
		tmp = x / (t / y);
	} else if (z <= 8.5e-89) {
		tmp = (x * -y) / z;
	} else if (z <= 4.6e-40) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.26d+110)) then
        tmp = x
    else if (z <= (-2.2d+75)) then
        tmp = x * (y / -z)
    else if (z <= (-6.8d+69)) then
        tmp = x
    else if (z <= (-2.2d-40)) then
        tmp = (x * -z) / t
    else if (z <= 6.2d-173) then
        tmp = x / (t / y)
    else if (z <= 8.5d-89) then
        tmp = (x * -y) / z
    else if (z <= 4.6d-40) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+110) {
		tmp = x;
	} else if (z <= -2.2e+75) {
		tmp = x * (y / -z);
	} else if (z <= -6.8e+69) {
		tmp = x;
	} else if (z <= -2.2e-40) {
		tmp = (x * -z) / t;
	} else if (z <= 6.2e-173) {
		tmp = x / (t / y);
	} else if (z <= 8.5e-89) {
		tmp = (x * -y) / z;
	} else if (z <= 4.6e-40) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.26e+110:
		tmp = x
	elif z <= -2.2e+75:
		tmp = x * (y / -z)
	elif z <= -6.8e+69:
		tmp = x
	elif z <= -2.2e-40:
		tmp = (x * -z) / t
	elif z <= 6.2e-173:
		tmp = x / (t / y)
	elif z <= 8.5e-89:
		tmp = (x * -y) / z
	elif z <= 4.6e-40:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.26e+110)
		tmp = x;
	elseif (z <= -2.2e+75)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= -6.8e+69)
		tmp = x;
	elseif (z <= -2.2e-40)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= 6.2e-173)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 8.5e-89)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 4.6e-40)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.26e+110)
		tmp = x;
	elseif (z <= -2.2e+75)
		tmp = x * (y / -z);
	elseif (z <= -6.8e+69)
		tmp = x;
	elseif (z <= -2.2e-40)
		tmp = (x * -z) / t;
	elseif (z <= 6.2e-173)
		tmp = x / (t / y);
	elseif (z <= 8.5e-89)
		tmp = (x * -y) / z;
	elseif (z <= 4.6e-40)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.26e+110], x, If[LessEqual[z, -2.2e+75], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e+69], x, If[LessEqual[z, -2.2e-40], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 6.2e-173], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-89], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.6e-40], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.25999999999999992e110 or -2.20000000000000012e75 < z < -6.79999999999999973e69 or 4.6e-40 < z

   1. Initial program 70.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.5%

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

   if -1.25999999999999992e110 < z < -2.20000000000000012e75

   1. Initial program 91.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.2%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

      4. mul-1-neg 57.4%

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

      5. associate-*r/ 57.4%

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

      6. neg-mul-1 57.4%

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

   10. Simplified 57.4%

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

   if -6.79999999999999973e69 < z < -2.20000000000000009e-40

   1. Initial program 99.8%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in y around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. neg-mul-1 66.1%

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

   9. Simplified 66.1%

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

   10. Taylor expanded in t around inf 50.8%

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

       1. associate-*r/ 50.8%

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

       2. mul-1-neg 50.8%

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

       3. *-commutative 50.8%

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

   12. Simplified 50.8%

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

   if -2.20000000000000009e-40 < z < 6.20000000000000011e-173

   1. Initial program 87.7%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 92.6%

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

      2. un-div-inv 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around 0 75.5%

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

   if 6.20000000000000011e-173 < z < 8.49999999999999937e-89

   1. Initial program 99.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 98.0%

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

      1. associate-/l* 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in t around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

   10. Simplified 82.5%

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

   if 8.49999999999999937e-89 < z < 4.6e-40

   1. Initial program 99.8%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.0%

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

      1. associate-/l* 64.5%

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

   7. Simplified 64.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{-z}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- z)))))
   (if (<= z -2.85e+110)
     x
     (if (<= z -3.2e+78)
       t_1
       (if (<= z -3e+69)
         x
         (if (<= z -1.62e-40)
           (/ (* x (- z)) t)
           (if (<= z 1.7e-154)
             (/ x (/ t y))
             (if (<= z 8.2e-89) t_1 (if (<= z 2.2e-38) (* x (/ y t)) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / -z);
	double tmp;
	if (z <= -2.85e+110) {
		tmp = x;
	} else if (z <= -3.2e+78) {
		tmp = t_1;
	} else if (z <= -3e+69) {
		tmp = x;
	} else if (z <= -1.62e-40) {
		tmp = (x * -z) / t;
	} else if (z <= 1.7e-154) {
		tmp = x / (t / y);
	} else if (z <= 8.2e-89) {
		tmp = t_1;
	} else if (z <= 2.2e-38) {
		tmp = x * (y / t);
	} else {
		tmp = 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 = x * (y / -z)
    if (z <= (-2.85d+110)) then
        tmp = x
    else if (z <= (-3.2d+78)) then
        tmp = t_1
    else if (z <= (-3d+69)) then
        tmp = x
    else if (z <= (-1.62d-40)) then
        tmp = (x * -z) / t
    else if (z <= 1.7d-154) then
        tmp = x / (t / y)
    else if (z <= 8.2d-89) then
        tmp = t_1
    else if (z <= 2.2d-38) then
        tmp = x * (y / t)
    else
        tmp = x
    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 <= -2.85e+110) {
		tmp = x;
	} else if (z <= -3.2e+78) {
		tmp = t_1;
	} else if (z <= -3e+69) {
		tmp = x;
	} else if (z <= -1.62e-40) {
		tmp = (x * -z) / t;
	} else if (z <= 1.7e-154) {
		tmp = x / (t / y);
	} else if (z <= 8.2e-89) {
		tmp = t_1;
	} else if (z <= 2.2e-38) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / -z)
	tmp = 0
	if z <= -2.85e+110:
		tmp = x
	elif z <= -3.2e+78:
		tmp = t_1
	elif z <= -3e+69:
		tmp = x
	elif z <= -1.62e-40:
		tmp = (x * -z) / t
	elif z <= 1.7e-154:
		tmp = x / (t / y)
	elif z <= 8.2e-89:
		tmp = t_1
	elif z <= 2.2e-38:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(-z)))
	tmp = 0.0
	if (z <= -2.85e+110)
		tmp = x;
	elseif (z <= -3.2e+78)
		tmp = t_1;
	elseif (z <= -3e+69)
		tmp = x;
	elseif (z <= -1.62e-40)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= 1.7e-154)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 8.2e-89)
		tmp = t_1;
	elseif (z <= 2.2e-38)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / -z);
	tmp = 0.0;
	if (z <= -2.85e+110)
		tmp = x;
	elseif (z <= -3.2e+78)
		tmp = t_1;
	elseif (z <= -3e+69)
		tmp = x;
	elseif (z <= -1.62e-40)
		tmp = (x * -z) / t;
	elseif (z <= 1.7e-154)
		tmp = x / (t / y);
	elseif (z <= 8.2e-89)
		tmp = t_1;
	elseif (z <= 2.2e-38)
		tmp = x * (y / t);
	else
		tmp = x;
	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, -2.85e+110], x, If[LessEqual[z, -3.2e+78], t$95$1, If[LessEqual[z, -3e+69], x, If[LessEqual[z, -1.62e-40], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.7e-154], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-89], t$95$1, If[LessEqual[z, 2.2e-38], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.8500000000000001e110 or -3.19999999999999994e78 < z < -2.99999999999999983e69 or 2.20000000000000007e-38 < z

   1. Initial program 70.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.5%

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

   if -2.8500000000000001e110 < z < -3.19999999999999994e78 or 1.6999999999999999e-154 < z < 8.1999999999999997e-89

   1. Initial program 95.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 81.3%

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

      1. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in t around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 68.4%

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

      3. distribute-rgt-neg-in 68.4%

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

      4. mul-1-neg 68.4%

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

      5. associate-*r/ 68.4%

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

      6. neg-mul-1 68.4%

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

   10. Simplified 68.4%

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

   if -2.99999999999999983e69 < z < -1.62e-40

   1. Initial program 99.8%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in y around 0 66.1%

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

      1. associate-*r/ 66.1%

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

      2. neg-mul-1 66.1%

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

   9. Simplified 66.1%

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

   10. Taylor expanded in t around inf 50.8%

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

       1. associate-*r/ 50.8%

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

       2. mul-1-neg 50.8%

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

       3. *-commutative 50.8%

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

   12. Simplified 50.8%

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

   if -1.62e-40 < z < 1.6999999999999999e-154

   1. Initial program 87.8%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

      1. clear-num 92.6%

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

      2. un-div-inv 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in z around 0 75.8%

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

   if 8.1999999999999997e-89 < z < 2.20000000000000007e-38

   1. Initial program 99.8%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.0%

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

      1. associate-/l* 64.5%

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

   7. Simplified 64.5%

      \[\leadsto \color{blue}{x \cdot \frac{y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-24} \lor \neg \left(z \leq 5.8 \cdot 10^{-38}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.8e+69)
     t_1
     (if (<= z -3e+36)
       (/ (* x (- z)) t)
       (if (or (<= z -6.6e-24) (not (<= z 5.8e-38)))
         t_1
         (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t_1;
	} else if (z <= -3e+36) {
		tmp = (x * -z) / t;
	} else if ((z <= -6.6e-24) || !(z <= 5.8e-38)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.8d+69)) then
        tmp = t_1
    else if (z <= (-3d+36)) then
        tmp = (x * -z) / t
    else if ((z <= (-6.6d-24)) .or. (.not. (z <= 5.8d-38))) then
        tmp = t_1
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t_1;
	} else if (z <= -3e+36) {
		tmp = (x * -z) / t;
	} else if ((z <= -6.6e-24) || !(z <= 5.8e-38)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.8e+69:
		tmp = t_1
	elif z <= -3e+36:
		tmp = (x * -z) / t
	elif (z <= -6.6e-24) or not (z <= 5.8e-38):
		tmp = t_1
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.8e+69)
		tmp = t_1;
	elseif (z <= -3e+36)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif ((z <= -6.6e-24) || !(z <= 5.8e-38))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.8e+69)
		tmp = t_1;
	elseif (z <= -3e+36)
		tmp = (x * -z) / t;
	elseif ((z <= -6.6e-24) || ~((z <= 5.8e-38)))
		tmp = t_1;
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+69], t$95$1, If[LessEqual[z, -3e+36], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -6.6e-24], N[Not[LessEqual[z, 5.8e-38]], $MachinePrecision]], t$95$1, N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e69 or -3e36 < z < -6.59999999999999968e-24 or 5.79999999999999988e-38 < z

   1. Initial program 74.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. associate-/l* 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

      4. distribute-frac-neg 75.9%

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

      5. neg-sub0 75.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 75.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 75.9%

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

      8. +-commutative 75.9%

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

      9. sub-neg 75.9%

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

      10. div-sub 75.9%

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

      11. *-inverses 75.9%

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

   7. Simplified 75.9%

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

   if -1.8000000000000001e69 < z < -3e36

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

   9. Simplified 79.2%

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

   10. Taylor expanded in t around inf 78.5%

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

       1. associate-*r/ 78.5%

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

       2. mul-1-neg 78.5%

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

       3. *-commutative 78.5%

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

   12. Simplified 78.5%

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

   if -6.59999999999999968e-24 < z < 5.79999999999999988e-38

   1. Initial program 90.0%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-24} \lor \neg \left(z \leq 5.8 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-24} \lor \neg \left(z \leq 1.7 \cdot 10^{-154}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.8e+69)
     t_1
     (if (<= z -3.9e+33)
       (/ (* x (- z)) t)
       (if (or (<= z -5.2e-24) (not (<= z 1.7e-154))) t_1 (/ x (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t_1;
	} else if (z <= -3.9e+33) {
		tmp = (x * -z) / t;
	} else if ((z <= -5.2e-24) || !(z <= 1.7e-154)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-1.8d+69)) then
        tmp = t_1
    else if (z <= (-3.9d+33)) then
        tmp = (x * -z) / t
    else if ((z <= (-5.2d-24)) .or. (.not. (z <= 1.7d-154))) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t_1;
	} else if (z <= -3.9e+33) {
		tmp = (x * -z) / t;
	} else if ((z <= -5.2e-24) || !(z <= 1.7e-154)) {
		tmp = t_1;
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.8e+69:
		tmp = t_1
	elif z <= -3.9e+33:
		tmp = (x * -z) / t
	elif (z <= -5.2e-24) or not (z <= 1.7e-154):
		tmp = t_1
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.8e+69)
		tmp = t_1;
	elseif (z <= -3.9e+33)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif ((z <= -5.2e-24) || !(z <= 1.7e-154))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.8e+69)
		tmp = t_1;
	elseif (z <= -3.9e+33)
		tmp = (x * -z) / t;
	elseif ((z <= -5.2e-24) || ~((z <= 1.7e-154)))
		tmp = t_1;
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+69], t$95$1, If[LessEqual[z, -3.9e+33], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, -5.2e-24], N[Not[LessEqual[z, 1.7e-154]], $MachinePrecision]], t$95$1, N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8000000000000001e69 or -3.9000000000000002e33 < z < -5.2e-24 or 1.6999999999999999e-154 < z

   1. Initial program 77.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. associate-/l* 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. distribute-frac-neg 73.0%

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

      5. neg-sub0 73.0%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 73.0%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 73.0%

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

      8. +-commutative 73.0%

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

      9. sub-neg 73.0%

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

      10. div-sub 73.0%

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

      11. *-inverses 73.0%

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

   7. Simplified 73.0%

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

   if -1.8000000000000001e69 < z < -3.9000000000000002e33

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

   9. Simplified 79.2%

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

   10. Taylor expanded in t around inf 78.5%

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

       1. associate-*r/ 78.5%

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

       2. mul-1-neg 78.5%

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

       3. *-commutative 78.5%

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

   12. Simplified 78.5%

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

   if -5.2e-24 < z < 1.6999999999999999e-154

   1. Initial program 88.2%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. clear-num 91.9%

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

      2. un-div-inv 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in z around 0 74.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-24} \lor \neg \left(z \leq 1.7 \cdot 10^{-154}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e+110)
   x
   (if (<= z -1.55e+78)
     (* x (/ y (- z)))
     (if (<= z -1.7e+47)
       (/ x (/ t (- z)))
       (if (<= z 6e-39) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+110) {
		tmp = x;
	} else if (z <= -1.55e+78) {
		tmp = x * (y / -z);
	} else if (z <= -1.7e+47) {
		tmp = x / (t / -z);
	} else if (z <= 6e-39) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.3d+110)) then
        tmp = x
    else if (z <= (-1.55d+78)) then
        tmp = x * (y / -z)
    else if (z <= (-1.7d+47)) then
        tmp = x / (t / -z)
    else if (z <= 6d-39) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+110) {
		tmp = x;
	} else if (z <= -1.55e+78) {
		tmp = x * (y / -z);
	} else if (z <= -1.7e+47) {
		tmp = x / (t / -z);
	} else if (z <= 6e-39) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e+110:
		tmp = x
	elif z <= -1.55e+78:
		tmp = x * (y / -z)
	elif z <= -1.7e+47:
		tmp = x / (t / -z)
	elif z <= 6e-39:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e+110)
		tmp = x;
	elseif (z <= -1.55e+78)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= -1.7e+47)
		tmp = Float64(x / Float64(t / Float64(-z)));
	elseif (z <= 6e-39)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e+110)
		tmp = x;
	elseif (z <= -1.55e+78)
		tmp = x * (y / -z);
	elseif (z <= -1.7e+47)
		tmp = x / (t / -z);
	elseif (z <= 6e-39)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e+110], x, If[LessEqual[z, -1.55e+78], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e+47], N[(x / N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-39], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e110 or 6.00000000000000055e-39 < z

   1. Initial program 69.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.1%

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

   if -1.3e110 < z < -1.55e78

   1. Initial program 91.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.2%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

      4. mul-1-neg 57.4%

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

      5. associate-*r/ 57.4%

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

      6. neg-mul-1 57.4%

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

   10. Simplified 57.4%

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

   if -1.55e78 < z < -1.6999999999999999e47

   1. Initial program 99.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 88.1%

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

      1. associate-*r/ 88.1%

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

      2. neg-mul-1 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in t around inf 63.9%

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

       1. associate-*r/ 63.9%

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

       2. neg-mul-1 63.9%

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

   12. Simplified 63.9%

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

   if -1.6999999999999999e47 < z < 6.00000000000000055e-39

   1. Initial program 91.1%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 65.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.42e+110)
   x
   (if (<= z -3.6e+76)
     (* x (/ y (- z)))
     (if (<= z -3.8e+45)
       (* x (/ (- z) t))
       (if (<= z 7.2e-38) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+110) {
		tmp = x;
	} else if (z <= -3.6e+76) {
		tmp = x * (y / -z);
	} else if (z <= -3.8e+45) {
		tmp = x * (-z / t);
	} else if (z <= 7.2e-38) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.42d+110)) then
        tmp = x
    else if (z <= (-3.6d+76)) then
        tmp = x * (y / -z)
    else if (z <= (-3.8d+45)) then
        tmp = x * (-z / t)
    else if (z <= 7.2d-38) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+110) {
		tmp = x;
	} else if (z <= -3.6e+76) {
		tmp = x * (y / -z);
	} else if (z <= -3.8e+45) {
		tmp = x * (-z / t);
	} else if (z <= 7.2e-38) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.42e+110:
		tmp = x
	elif z <= -3.6e+76:
		tmp = x * (y / -z)
	elif z <= -3.8e+45:
		tmp = x * (-z / t)
	elif z <= 7.2e-38:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.42e+110)
		tmp = x;
	elseif (z <= -3.6e+76)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= -3.8e+45)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 7.2e-38)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.42e+110)
		tmp = x;
	elseif (z <= -3.6e+76)
		tmp = x * (y / -z);
	elseif (z <= -3.8e+45)
		tmp = x * (-z / t);
	elseif (z <= 7.2e-38)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.42e+110], x, If[LessEqual[z, -3.6e+76], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e+45], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-38], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4200000000000001e110 or 7.2000000000000001e-38 < z

   1. Initial program 69.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 60.1%

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

   if -1.4200000000000001e110 < z < -3.6000000000000003e76

   1. Initial program 91.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 66.2%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in t around 0 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

      4. mul-1-neg 57.4%

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

      5. associate-*r/ 57.4%

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

      6. neg-mul-1 57.4%

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

   10. Simplified 57.4%

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

   if -3.6000000000000003e76 < z < -3.8000000000000002e45

   1. Initial program 99.8%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 88.1%

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

      1. associate-*r/ 88.1%

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

      2. neg-mul-1 88.1%

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

   9. Simplified 88.1%

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

   10. Taylor expanded in t around inf 75.6%

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

       1. associate-*r/ 75.6%

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

       2. mul-1-neg 75.6%

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

       3. *-commutative 75.6%

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

   12. Simplified 75.6%

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

   13. Taylor expanded in z around 0 75.6%

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

       1. mul-1-neg 75.6%

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

       2. associate-*r/ 63.9%

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

       3. distribute-rgt-neg-in 63.9%

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

   15. Simplified 63.9%

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

   if -3.8000000000000002e45 < z < 7.2000000000000001e-38

   1. Initial program 91.1%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

      1. clear-num 93.1%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 65.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -6600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-121}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= t -6600000.0)
     t_1
     (if (<= t 6.4e-121)
       (- x (* x (/ y z)))
       (if (<= t 1.1e+26) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (t <= -6600000.0) {
		tmp = t_1;
	} else if (t <= 6.4e-121) {
		tmp = x - (x * (y / z));
	} else if (t <= 1.1e+26) {
		tmp = x * (y / (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)
    if (t <= (-6600000.0d0)) then
        tmp = t_1
    else if (t <= 6.4d-121) then
        tmp = x - (x * (y / z))
    else if (t <= 1.1d+26) then
        tmp = x * (y / (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);
	double tmp;
	if (t <= -6600000.0) {
		tmp = t_1;
	} else if (t <= 6.4e-121) {
		tmp = x - (x * (y / z));
	} else if (t <= 1.1e+26) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if t <= -6600000.0:
		tmp = t_1
	elif t <= 6.4e-121:
		tmp = x - (x * (y / z))
	elif t <= 1.1e+26:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -6600000.0)
		tmp = t_1;
	elseif (t <= 6.4e-121)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (t <= 1.1e+26)
		tmp = Float64(x * Float64(y / 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);
	tmp = 0.0;
	if (t <= -6600000.0)
		tmp = t_1;
	elseif (t <= 6.4e-121)
		tmp = x - (x * (y / z));
	elseif (t <= 1.1e+26)
		tmp = x * (y / (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] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6600000.0], t$95$1, If[LessEqual[t, 6.4e-121], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+26], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.6e6 or 1.10000000000000004e26 < t

   1. Initial program 78.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.6%

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

      1. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   if -6.6e6 < t < 6.40000000000000038e-121

   1. Initial program 85.4%

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

      1. remove-double-neg 85.4%

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

      2. distribute-lft-neg-out 85.4%

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

      3. distribute-neg-frac 85.4%

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

      4. distribute-neg-frac2 85.4%

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

      5. distribute-lft-neg-out 85.4%

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

      6. distribute-rgt-neg-in 85.4%

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

      7. sub-neg 85.4%

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

      8. distribute-neg-in 85.4%

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

      9. remove-double-neg 85.4%

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

      10. +-commutative 85.4%

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

      11. sub-neg 85.4%

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

      12. sub-neg 85.4%

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

      13. distribute-neg-in 85.4%

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

      14. remove-double-neg 85.4%

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

      15. +-commutative 85.4%

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

      16. sub-neg 85.4%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in t around 0 77.1%

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

   6. Taylor expanded in z around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

      3. associate-/l* 89.2%

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

   8. Simplified 89.2%

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

   if 6.40000000000000038e-121 < t < 1.10000000000000004e26

   1. Initial program 90.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

Alternative 9: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -4100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= t -4100000.0)
     t_1
     (if (<= t 3.5e-120)
       (* x (- 1.0 (/ y z)))
       (if (<= t 9.5e+27) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (t <= -4100000.0) {
		tmp = t_1;
	} else if (t <= 3.5e-120) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 9.5e+27) {
		tmp = x * (y / (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)
    if (t <= (-4100000.0d0)) then
        tmp = t_1
    else if (t <= 3.5d-120) then
        tmp = x * (1.0d0 - (y / z))
    else if (t <= 9.5d+27) then
        tmp = x * (y / (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);
	double tmp;
	if (t <= -4100000.0) {
		tmp = t_1;
	} else if (t <= 3.5e-120) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 9.5e+27) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if t <= -4100000.0:
		tmp = t_1
	elif t <= 3.5e-120:
		tmp = x * (1.0 - (y / z))
	elif t <= 9.5e+27:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -4100000.0)
		tmp = t_1;
	elseif (t <= 3.5e-120)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (t <= 9.5e+27)
		tmp = Float64(x * Float64(y / 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);
	tmp = 0.0;
	if (t <= -4100000.0)
		tmp = t_1;
	elseif (t <= 3.5e-120)
		tmp = x * (1.0 - (y / z));
	elseif (t <= 9.5e+27)
		tmp = x * (y / (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] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4100000.0], t$95$1, If[LessEqual[t, 3.5e-120], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+27], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1e6 or 9.4999999999999997e27 < t

   1. Initial program 78.5%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.6%

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

      1. associate-/l* 75.5%

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

   7. Simplified 75.5%

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

   if -4.1e6 < t < 3.5e-120

   1. Initial program 85.4%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

      4. distribute-frac-neg 89.2%

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

      5. neg-sub0 89.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 89.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 89.2%

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

      8. +-commutative 89.2%

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

      9. sub-neg 89.2%

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

      10. div-sub 89.1%

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

      11. *-inverses 89.1%

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

   7. Simplified 89.1%

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

   if 3.5e-120 < t < 9.4999999999999997e27

   1. Initial program 90.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.0%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

Alternative 10: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.1e-24)
   (* x (/ z (- z t)))
   (if (<= z 8e-38) (* x (/ y (- t z))) (* x (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.1e-24) {
		tmp = x * (z / (z - t));
	} else if (z <= 8e-38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.1d-24)) then
        tmp = x * (z / (z - t))
    else if (z <= 8d-38) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.1e-24) {
		tmp = x * (z / (z - t));
	} else if (z <= 8e-38) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.1e-24:
		tmp = x * (z / (z - t))
	elif z <= 8e-38:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.1e-24)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 8e-38)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.1e-24)
		tmp = x * (z / (z - t));
	elseif (z <= 8e-38)
		tmp = x * (y / (t - z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.1e-24], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-38], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.10000000000000036e-24

   1. Initial program 82.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. distribute-neg-frac2 57.7%

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

      3. neg-sub0 57.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 57.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 57.7%

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

      6. +-commutative 57.7%

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

      7. sub-neg 57.7%

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

      8. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   if -6.10000000000000036e-24 < z < 7.9999999999999997e-38

   1. Initial program 90.0%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

   if 7.9999999999999997e-38 < z

   1. Initial program 68.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/l* 77.5%

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

      3. distribute-rgt-neg-in 77.5%

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

      4. distribute-frac-neg 77.5%

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

      5. neg-sub0 77.5%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 77.5%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 77.5%

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

      8. +-commutative 77.5%

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

      9. sub-neg 77.5%

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

      10. div-sub 77.5%

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

      11. *-inverses 77.5%

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

   7. Simplified 77.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e+99) x (if (<= z 2.2e-38) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+99) {
		tmp = x;
	} else if (z <= 2.2e-38) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7d+99)) then
        tmp = x
    else if (z <= 2.2d-38) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+99) {
		tmp = x;
	} else if (z <= 2.2e-38) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e+99:
		tmp = x
	elif z <= 2.2e-38:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e+99)
		tmp = x;
	elseif (z <= 2.2e-38)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7e+99)
		tmp = x;
	elseif (z <= 2.2e-38)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e+99], x, If[LessEqual[z, 2.2e-38], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999995e99 or 2.20000000000000007e-38 < z

   1. Initial program 69.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.9%

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

   if -6.9999999999999995e99 < z < 2.20000000000000007e-38

   1. Initial program 92.0%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

      1. clear-num 93.8%

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

      2. un-div-inv 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around 0 62.4%

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

Alternative 12: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+100) x (if (<= z 6e-38) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+100) {
		tmp = x;
	} else if (z <= 6e-38) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+100)) then
        tmp = x
    else if (z <= 6d-38) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+100) {
		tmp = x;
	} else if (z <= 6e-38) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+100:
		tmp = x
	elif z <= 6e-38:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+100)
		tmp = x;
	elseif (z <= 6e-38)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+100)
		tmp = x;
	elseif (z <= 6e-38)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+100], x, If[LessEqual[z, 6e-38], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000002e100 or 5.99999999999999977e-38 < z

   1. Initial program 69.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 58.9%

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

   if -1.00000000000000002e100 < z < 5.99999999999999977e-38

   1. Initial program 92.0%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 57.4%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

Alternative 13: 34.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 82.5%

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

   1. associate-/l* 96.9%

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

3. Simplified 96.9%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 31.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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