Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-sub 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \frac{x}{z - y} + \frac{y}{y - z} \]
6. Add Preprocessing

Alternative 2: 58.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{-z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- z))))
   (if (<= y -1.7e+131)
     1.0
     (if (<= y -2.1e+80)
       t_0
       (if (<= y -3.6e-20)
         1.0
         (if (<= y 4.1e-41)
           (/ x z)
           (if (<= y 3.4e+14)
             1.0
             (if (<= y 1.8e+61)
               t_0
               (if (<= y 4.2e+181) (/ x (- y)) 1.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -1.7e+131) {
		tmp = 1.0;
	} else if (y <= -2.1e+80) {
		tmp = t_0;
	} else if (y <= -3.6e-20) {
		tmp = 1.0;
	} else if (y <= 4.1e-41) {
		tmp = x / z;
	} else if (y <= 3.4e+14) {
		tmp = 1.0;
	} else if (y <= 1.8e+61) {
		tmp = t_0;
	} else if (y <= 4.2e+181) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / -z
    if (y <= (-1.7d+131)) then
        tmp = 1.0d0
    else if (y <= (-2.1d+80)) then
        tmp = t_0
    else if (y <= (-3.6d-20)) then
        tmp = 1.0d0
    else if (y <= 4.1d-41) then
        tmp = x / z
    else if (y <= 3.4d+14) then
        tmp = 1.0d0
    else if (y <= 1.8d+61) then
        tmp = t_0
    else if (y <= 4.2d+181) then
        tmp = x / -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -1.7e+131) {
		tmp = 1.0;
	} else if (y <= -2.1e+80) {
		tmp = t_0;
	} else if (y <= -3.6e-20) {
		tmp = 1.0;
	} else if (y <= 4.1e-41) {
		tmp = x / z;
	} else if (y <= 3.4e+14) {
		tmp = 1.0;
	} else if (y <= 1.8e+61) {
		tmp = t_0;
	} else if (y <= 4.2e+181) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / -z
	tmp = 0
	if y <= -1.7e+131:
		tmp = 1.0
	elif y <= -2.1e+80:
		tmp = t_0
	elif y <= -3.6e-20:
		tmp = 1.0
	elif y <= 4.1e-41:
		tmp = x / z
	elif y <= 3.4e+14:
		tmp = 1.0
	elif y <= 1.8e+61:
		tmp = t_0
	elif y <= 4.2e+181:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(-z))
	tmp = 0.0
	if (y <= -1.7e+131)
		tmp = 1.0;
	elseif (y <= -2.1e+80)
		tmp = t_0;
	elseif (y <= -3.6e-20)
		tmp = 1.0;
	elseif (y <= 4.1e-41)
		tmp = Float64(x / z);
	elseif (y <= 3.4e+14)
		tmp = 1.0;
	elseif (y <= 1.8e+61)
		tmp = t_0;
	elseif (y <= 4.2e+181)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / -z;
	tmp = 0.0;
	if (y <= -1.7e+131)
		tmp = 1.0;
	elseif (y <= -2.1e+80)
		tmp = t_0;
	elseif (y <= -3.6e-20)
		tmp = 1.0;
	elseif (y <= 4.1e-41)
		tmp = x / z;
	elseif (y <= 3.4e+14)
		tmp = 1.0;
	elseif (y <= 1.8e+61)
		tmp = t_0;
	elseif (y <= 4.2e+181)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / (-z)), $MachinePrecision]}, If[LessEqual[y, -1.7e+131], 1.0, If[LessEqual[y, -2.1e+80], t$95$0, If[LessEqual[y, -3.6e-20], 1.0, If[LessEqual[y, 4.1e-41], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.4e+14], 1.0, If[LessEqual[y, 1.8e+61], t$95$0, If[LessEqual[y, 4.2e+181], N[(x / (-y)), $MachinePrecision], 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999993e131 or -2.10000000000000001e80 < y < -3.59999999999999974e-20 or 4.10000000000000014e-41 < y < 3.4e14 or 4.19999999999999995e181 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.7%

      \[\leadsto \color{blue}{1} \]

   if -1.69999999999999993e131 < y < -2.10000000000000001e80 or 3.4e14 < y < 1.80000000000000005e61

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 68.8%

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

   6. Taylor expanded in x around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   8. Simplified 52.5%

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

   if -3.59999999999999974e-20 < y < 4.10000000000000014e-41

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.1%

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

   if 1.80000000000000005e61 < y < 4.19999999999999995e181

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.2%

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

   4. Taylor expanded in z around 0 48.0%

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

      1. associate-*r/ 48.0%

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

      2. neg-mul-1 48.0%

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

   6. Simplified 48.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{-z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;1 + \frac{z}{y}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+80}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 25000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- z))))
   (if (<= y -3.4e+131)
     (+ 1.0 (/ z y))
     (if (<= y -2.15e+80)
       t_0
       (if (<= y -2.45e-20)
         1.0
         (if (<= y 4.1e-41)
           (/ x z)
           (if (<= y 25000000000000.0)
             1.0
             (if (<= y 2.7e+61)
               t_0
               (if (<= y 4.2e+181) (/ x (- y)) 1.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -3.4e+131) {
		tmp = 1.0 + (z / y);
	} else if (y <= -2.15e+80) {
		tmp = t_0;
	} else if (y <= -2.45e-20) {
		tmp = 1.0;
	} else if (y <= 4.1e-41) {
		tmp = x / z;
	} else if (y <= 25000000000000.0) {
		tmp = 1.0;
	} else if (y <= 2.7e+61) {
		tmp = t_0;
	} else if (y <= 4.2e+181) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / -z
    if (y <= (-3.4d+131)) then
        tmp = 1.0d0 + (z / y)
    else if (y <= (-2.15d+80)) then
        tmp = t_0
    else if (y <= (-2.45d-20)) then
        tmp = 1.0d0
    else if (y <= 4.1d-41) then
        tmp = x / z
    else if (y <= 25000000000000.0d0) then
        tmp = 1.0d0
    else if (y <= 2.7d+61) then
        tmp = t_0
    else if (y <= 4.2d+181) then
        tmp = x / -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -3.4e+131) {
		tmp = 1.0 + (z / y);
	} else if (y <= -2.15e+80) {
		tmp = t_0;
	} else if (y <= -2.45e-20) {
		tmp = 1.0;
	} else if (y <= 4.1e-41) {
		tmp = x / z;
	} else if (y <= 25000000000000.0) {
		tmp = 1.0;
	} else if (y <= 2.7e+61) {
		tmp = t_0;
	} else if (y <= 4.2e+181) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / -z
	tmp = 0
	if y <= -3.4e+131:
		tmp = 1.0 + (z / y)
	elif y <= -2.15e+80:
		tmp = t_0
	elif y <= -2.45e-20:
		tmp = 1.0
	elif y <= 4.1e-41:
		tmp = x / z
	elif y <= 25000000000000.0:
		tmp = 1.0
	elif y <= 2.7e+61:
		tmp = t_0
	elif y <= 4.2e+181:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(-z))
	tmp = 0.0
	if (y <= -3.4e+131)
		tmp = Float64(1.0 + Float64(z / y));
	elseif (y <= -2.15e+80)
		tmp = t_0;
	elseif (y <= -2.45e-20)
		tmp = 1.0;
	elseif (y <= 4.1e-41)
		tmp = Float64(x / z);
	elseif (y <= 25000000000000.0)
		tmp = 1.0;
	elseif (y <= 2.7e+61)
		tmp = t_0;
	elseif (y <= 4.2e+181)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / -z;
	tmp = 0.0;
	if (y <= -3.4e+131)
		tmp = 1.0 + (z / y);
	elseif (y <= -2.15e+80)
		tmp = t_0;
	elseif (y <= -2.45e-20)
		tmp = 1.0;
	elseif (y <= 4.1e-41)
		tmp = x / z;
	elseif (y <= 25000000000000.0)
		tmp = 1.0;
	elseif (y <= 2.7e+61)
		tmp = t_0;
	elseif (y <= 4.2e+181)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / (-z)), $MachinePrecision]}, If[LessEqual[y, -3.4e+131], N[(1.0 + N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e+80], t$95$0, If[LessEqual[y, -2.45e-20], 1.0, If[LessEqual[y, 4.1e-41], N[(x / z), $MachinePrecision], If[LessEqual[y, 25000000000000.0], 1.0, If[LessEqual[y, 2.7e+61], t$95$0, If[LessEqual[y, 4.2e+181], N[(x / (-y)), $MachinePrecision], 1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.39999999999999986e131

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 91.7%

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

      1. associate-*r/ 91.7%

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

      2. neg-mul-1 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in y around inf 83.7%

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

   if -3.39999999999999986e131 < y < -2.15000000000000002e80 or 2.5e13 < y < 2.7000000000000002e61

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 68.8%

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

   6. Taylor expanded in x around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   8. Simplified 52.5%

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

   if -2.15000000000000002e80 < y < -2.4500000000000001e-20 or 4.10000000000000014e-41 < y < 2.5e13 or 4.19999999999999995e181 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.5%

      \[\leadsto \color{blue}{1} \]

   if -2.4500000000000001e-20 < y < 4.10000000000000014e-41

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.1%

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

   if 2.7000000000000002e61 < y < 4.19999999999999995e181

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.2%

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

   4. Taylor expanded in z around 0 48.0%

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

      1. associate-*r/ 48.0%

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

      2. neg-mul-1 48.0%

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

   6. Simplified 48.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;1 + \frac{z}{y}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 25000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) z)))
   (if (<= y -1.85e-19)
     (/ y (- y z))
     (if (<= y 7.2e-47)
       t_0
       (if (<= y 1.5e+15)
         (- 1.0 (/ x y))
         (if (<= y 4.1e+60) t_0 (+ 1.0 (/ (- z x) y))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / z;
	double tmp;
	if (y <= -1.85e-19) {
		tmp = y / (y - z);
	} else if (y <= 7.2e-47) {
		tmp = t_0;
	} else if (y <= 1.5e+15) {
		tmp = 1.0 - (x / y);
	} else if (y <= 4.1e+60) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((z - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / z
    if (y <= (-1.85d-19)) then
        tmp = y / (y - z)
    else if (y <= 7.2d-47) then
        tmp = t_0
    else if (y <= 1.5d+15) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 4.1d+60) then
        tmp = t_0
    else
        tmp = 1.0d0 + ((z - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / z;
	double tmp;
	if (y <= -1.85e-19) {
		tmp = y / (y - z);
	} else if (y <= 7.2e-47) {
		tmp = t_0;
	} else if (y <= 1.5e+15) {
		tmp = 1.0 - (x / y);
	} else if (y <= 4.1e+60) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((z - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / z
	tmp = 0
	if y <= -1.85e-19:
		tmp = y / (y - z)
	elif y <= 7.2e-47:
		tmp = t_0
	elif y <= 1.5e+15:
		tmp = 1.0 - (x / y)
	elif y <= 4.1e+60:
		tmp = t_0
	else:
		tmp = 1.0 + ((z - x) / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / z)
	tmp = 0.0
	if (y <= -1.85e-19)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= 7.2e-47)
		tmp = t_0;
	elseif (y <= 1.5e+15)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 4.1e+60)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(Float64(z - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / z;
	tmp = 0.0;
	if (y <= -1.85e-19)
		tmp = y / (y - z);
	elseif (y <= 7.2e-47)
		tmp = t_0;
	elseif (y <= 1.5e+15)
		tmp = 1.0 - (x / y);
	elseif (y <= 4.1e+60)
		tmp = t_0;
	else
		tmp = 1.0 + ((z - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.85e-19], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-47], t$95$0, If[LessEqual[y, 1.5e+15], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+60], t$95$0, N[(1.0 + N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85000000000000003e-19

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

   7. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.4%

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

      3. remove-double-neg 83.4%

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

      4. sub-neg 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

   9. Applied egg-rr 83.4%

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

       1. associate-*r/ 83.5%

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

       2. *-rgt-identity 83.5%

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

       3. +-commutative 83.5%

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

       4. sub-neg 83.5%

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

   11. Simplified 83.5%

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

   if -1.85000000000000003e-19 < y < 7.19999999999999982e-47 or 1.5e15 < y < 4.1e60

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.0%

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

   if 7.19999999999999982e-47 < y < 1.5e15

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

   7. Simplified 82.4%

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

   if 4.1e60 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.3%

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

      1. associate--l+ 88.3%

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

      2. distribute-lft-out-- 88.3%

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

      3. div-sub 88.3%

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

      4. mul-1-neg 88.3%

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

      5. unsub-neg 88.3%

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

   5. Simplified 88.3%

      \[\leadsto \color{blue}{1 - \frac{x - z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+60}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 66000000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{z} - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e-19)
   (/ y (- y z))
   (if (<= y 3.4e-49)
     (/ (- x y) z)
     (if (<= y 66000000000000.0)
       (- 1.0 (/ x y))
       (if (<= y 4e+60) (- (/ x z) (/ y z)) (+ 1.0 (/ (- z x) y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e-19) {
		tmp = y / (y - z);
	} else if (y <= 3.4e-49) {
		tmp = (x - y) / z;
	} else if (y <= 66000000000000.0) {
		tmp = 1.0 - (x / y);
	} else if (y <= 4e+60) {
		tmp = (x / z) - (y / z);
	} else {
		tmp = 1.0 + ((z - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.1d-19)) then
        tmp = y / (y - z)
    else if (y <= 3.4d-49) then
        tmp = (x - y) / z
    else if (y <= 66000000000000.0d0) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 4d+60) then
        tmp = (x / z) - (y / z)
    else
        tmp = 1.0d0 + ((z - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e-19) {
		tmp = y / (y - z);
	} else if (y <= 3.4e-49) {
		tmp = (x - y) / z;
	} else if (y <= 66000000000000.0) {
		tmp = 1.0 - (x / y);
	} else if (y <= 4e+60) {
		tmp = (x / z) - (y / z);
	} else {
		tmp = 1.0 + ((z - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.1e-19:
		tmp = y / (y - z)
	elif y <= 3.4e-49:
		tmp = (x - y) / z
	elif y <= 66000000000000.0:
		tmp = 1.0 - (x / y)
	elif y <= 4e+60:
		tmp = (x / z) - (y / z)
	else:
		tmp = 1.0 + ((z - x) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e-19)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= 3.4e-49)
		tmp = Float64(Float64(x - y) / z);
	elseif (y <= 66000000000000.0)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 4e+60)
		tmp = Float64(Float64(x / z) - Float64(y / z));
	else
		tmp = Float64(1.0 + Float64(Float64(z - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.1e-19)
		tmp = y / (y - z);
	elseif (y <= 3.4e-49)
		tmp = (x - y) / z;
	elseif (y <= 66000000000000.0)
		tmp = 1.0 - (x / y);
	elseif (y <= 4e+60)
		tmp = (x / z) - (y / z);
	else
		tmp = 1.0 + ((z - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.1e-19], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-49], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 66000000000000.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+60], N[(N[(x / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.0999999999999998e-19

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

   7. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.4%

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

      3. remove-double-neg 83.4%

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

      4. sub-neg 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

   9. Applied egg-rr 83.4%

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

       1. associate-*r/ 83.5%

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

       2. *-rgt-identity 83.5%

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

       3. +-commutative 83.5%

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

       4. sub-neg 83.5%

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

   11. Simplified 83.5%

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

   if -5.0999999999999998e-19 < y < 3.40000000000000005e-49

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.5%

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

   if 3.40000000000000005e-49 < y < 6.6e13

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

   7. Simplified 82.4%

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

   if 6.6e13 < y < 3.9999999999999998e60

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 79.1%

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

   6. Taylor expanded in z around inf 79.5%

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

   if 3.9999999999999998e60 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.3%

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

      1. associate--l+ 88.3%

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

      2. distribute-lft-out-- 88.3%

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

      3. div-sub 88.3%

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

      4. mul-1-neg 88.3%

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

      5. unsub-neg 88.3%

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

   5. Simplified 88.3%

      \[\leadsto \color{blue}{1 - \frac{x - z}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-49}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 66000000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{z} - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+91} \lor \neg \left(x \leq 2.25 \cdot 10^{-42}\right) \land \left(x \leq 1.55 \cdot 10^{-29} \lor \neg \left(x \leq 5.8 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.6e+91)
         (and (not (<= x 2.25e-42)) (or (<= x 1.55e-29) (not (<= x 5.8e+99)))))
   (/ x (- z y))
   (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e+91) || (!(x <= 2.25e-42) && ((x <= 1.55e-29) || !(x <= 5.8e+99)))) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.6d+91)) .or. (.not. (x <= 2.25d-42)) .and. (x <= 1.55d-29) .or. (.not. (x <= 5.8d+99))) then
        tmp = x / (z - y)
    else
        tmp = y / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.6e+91) || (!(x <= 2.25e-42) && ((x <= 1.55e-29) || !(x <= 5.8e+99)))) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.6e+91) or (not (x <= 2.25e-42) and ((x <= 1.55e-29) or not (x <= 5.8e+99))):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.6e+91) || (!(x <= 2.25e-42) && ((x <= 1.55e-29) || !(x <= 5.8e+99))))
		tmp = Float64(x / Float64(z - y));
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.6e+91) || (~((x <= 2.25e-42)) && ((x <= 1.55e-29) || ~((x <= 5.8e+99)))))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.6e+91], And[N[Not[LessEqual[x, 2.25e-42]], $MachinePrecision], Or[LessEqual[x, 1.55e-29], N[Not[LessEqual[x, 5.8e+99]], $MachinePrecision]]]], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.6000000000000001e91 or 2.25e-42 < x < 1.55000000000000013e-29 or 5.8000000000000004e99 < x

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 84.9%

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

   if -8.6000000000000001e91 < x < 2.25e-42 or 1.55000000000000013e-29 < x < 5.8000000000000004e99

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   7. Simplified 83.9%

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

      1. frac-2neg 83.9%

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

      2. div-inv 83.7%

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

      3. remove-double-neg 83.7%

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

      4. sub-neg 83.7%

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

      5. distribute-neg-in 83.7%

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

      6. remove-double-neg 83.7%

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

   9. Applied egg-rr 83.7%

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

       1. associate-*r/ 83.9%

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

       2. *-rgt-identity 83.9%

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

       3. +-commutative 83.9%

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

       4. sub-neg 83.9%

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

   11. Simplified 83.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+91} \lor \neg \left(x \leq 2.25 \cdot 10^{-42}\right) \land \left(x \leq 1.55 \cdot 10^{-29} \lor \neg \left(x \leq 5.8 \cdot 10^{+99}\right)\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-46} \lor \neg \left(y \leq 1.35 \cdot 10^{+14}\right) \land y \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e-19)
   (/ y (- y z))
   (if (or (<= y 1.05e-46) (and (not (<= y 1.35e+14)) (<= y 4.2e+60)))
     (/ (- x y) z)
     (- 1.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-19) {
		tmp = y / (y - z);
	} else if ((y <= 1.05e-46) || (!(y <= 1.35e+14) && (y <= 4.2e+60))) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.8d-19)) then
        tmp = y / (y - z)
    else if ((y <= 1.05d-46) .or. (.not. (y <= 1.35d+14)) .and. (y <= 4.2d+60)) then
        tmp = (x - y) / z
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e-19) {
		tmp = y / (y - z);
	} else if ((y <= 1.05e-46) || (!(y <= 1.35e+14) && (y <= 4.2e+60))) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e-19:
		tmp = y / (y - z)
	elif (y <= 1.05e-46) or (not (y <= 1.35e+14) and (y <= 4.2e+60)):
		tmp = (x - y) / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e-19)
		tmp = Float64(y / Float64(y - z));
	elseif ((y <= 1.05e-46) || (!(y <= 1.35e+14) && (y <= 4.2e+60)))
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e-19)
		tmp = y / (y - z);
	elseif ((y <= 1.05e-46) || (~((y <= 1.35e+14)) && (y <= 4.2e+60)))
		tmp = (x - y) / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e-19], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.05e-46], And[N[Not[LessEqual[y, 1.35e+14]], $MachinePrecision], LessEqual[y, 4.2e+60]]], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.80000000000000003e-19

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

   7. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.4%

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

      3. remove-double-neg 83.4%

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

      4. sub-neg 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

   9. Applied egg-rr 83.4%

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

       1. associate-*r/ 83.5%

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

       2. *-rgt-identity 83.5%

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

       3. +-commutative 83.5%

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

       4. sub-neg 83.5%

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

   11. Simplified 83.5%

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

   if -2.80000000000000003e-19 < y < 1.04999999999999994e-46 or 1.35e14 < y < 4.2000000000000002e60

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.0%

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

   if 1.04999999999999994e-46 < y < 1.35e14 or 4.2000000000000002e60 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-46} \lor \neg \left(y \leq 1.35 \cdot 10^{+14}\right) \land y \leq 4.2 \cdot 10^{+60}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-19} \lor \neg \left(y \leq 1.95 \cdot 10^{-94}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-19) (not (<= y 1.95e-94))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-19) || !(y <= 1.95e-94)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.3d-19)) .or. (.not. (y <= 1.95d-94))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-19) || !(y <= 1.95e-94)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e-19) or not (y <= 1.95e-94):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-19) || !(y <= 1.95e-94))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e-19) || ~((y <= 1.95e-94)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-19], N[Not[LessEqual[y, 1.95e-94]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e-19 or 1.9500000000000001e-94 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. unsub-neg 76.1%

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

   7. Simplified 76.1%

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

   if -2.2999999999999998e-19 < y < 1.9500000000000001e-94

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-19} \lor \neg \left(y \leq 1.95 \cdot 10^{-94}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-19} \lor \neg \left(y \leq 7 \cdot 10^{-47}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e-19) (not (<= y 7e-47))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-19) || !(y <= 7e-47)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.3d-19)) .or. (.not. (y <= 7d-47))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-19) || !(y <= 7e-47)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e-19) or not (y <= 7e-47):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e-19) || !(y <= 7e-47))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.3e-19) || ~((y <= 7e-47)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e-19], N[Not[LessEqual[y, 7e-47]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999998e-19 or 6.9999999999999996e-47 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-sub 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

   7. Simplified 78.1%

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

   if -3.2999999999999998e-19 < y < 6.9999999999999996e-47

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-19} \lor \neg \left(y \leq 7 \cdot 10^{-47}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e-20) 1.0 (if (<= y 3.9e-41) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e-20) {
		tmp = 1.0;
	} else if (y <= 3.9e-41) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.4d-20)) then
        tmp = 1.0d0
    else if (y <= 3.9d-41) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e-20) {
		tmp = 1.0;
	} else if (y <= 3.9e-41) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e-20:
		tmp = 1.0
	elif y <= 3.9e-41:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e-20)
		tmp = 1.0;
	elseif (y <= 3.9e-41)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e-20)
		tmp = 1.0;
	elseif (y <= 3.9e-41)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e-20], 1.0, If[LessEqual[y, 3.9e-41], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999993e-20 or 3.89999999999999991e-41 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{1} \]

   if -2.39999999999999993e-20 < y < 3.89999999999999991e-41

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 12: 35.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 42.4%

   \[\leadsto \color{blue}{1} \]

4. Final simplification 42.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

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

  (/ (- x y) (- z y)))