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

Percentage Accurate: 100.0% → 100.0%

Time: 6.7s

Alternatives: 10

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: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-47} \lor \neg \left(x \leq 8.1 \cdot 10^{-19}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z y))))
   (if (<= x -4.5e+28)
     t_0
     (if (<= x -9.5e-40)
       (- 1.0 (/ x y))
       (if (or (<= x -1.9e-47) (not (<= x 8.1e-19))) t_0 (/ y (- y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (x <= -4.5e+28) {
		tmp = t_0;
	} else if (x <= -9.5e-40) {
		tmp = 1.0 - (x / y);
	} else if ((x <= -1.9e-47) || !(x <= 8.1e-19)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (z - y)
    if (x <= (-4.5d+28)) then
        tmp = t_0
    else if (x <= (-9.5d-40)) then
        tmp = 1.0d0 - (x / y)
    else if ((x <= (-1.9d-47)) .or. (.not. (x <= 8.1d-19))) then
        tmp = t_0
    else
        tmp = y / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (x <= -4.5e+28) {
		tmp = t_0;
	} else if (x <= -9.5e-40) {
		tmp = 1.0 - (x / y);
	} else if ((x <= -1.9e-47) || !(x <= 8.1e-19)) {
		tmp = t_0;
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z - y)
	tmp = 0
	if x <= -4.5e+28:
		tmp = t_0
	elif x <= -9.5e-40:
		tmp = 1.0 - (x / y)
	elif (x <= -1.9e-47) or not (x <= 8.1e-19):
		tmp = t_0
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (x <= -4.5e+28)
		tmp = t_0;
	elseif (x <= -9.5e-40)
		tmp = Float64(1.0 - Float64(x / y));
	elseif ((x <= -1.9e-47) || !(x <= 8.1e-19))
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z - y);
	tmp = 0.0;
	if (x <= -4.5e+28)
		tmp = t_0;
	elseif (x <= -9.5e-40)
		tmp = 1.0 - (x / y);
	elseif ((x <= -1.9e-47) || ~((x <= 8.1e-19)))
		tmp = t_0;
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+28], t$95$0, If[LessEqual[x, -9.5e-40], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.9e-47], N[Not[LessEqual[x, 8.1e-19]], $MachinePrecision]], t$95$0, N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4999999999999997e28 or -9.5000000000000006e-40 < x < -1.90000000000000007e-47 or 8.10000000000000023e-19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.2%

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

   if -4.4999999999999997e28 < x < -9.5000000000000006e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 86.3%

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

      1. div-sub 86.3%

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

      2. sub-neg 86.3%

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

      3. *-inverses 86.3%

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

      4. metadata-eval 86.3%

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

      5. distribute-lft-in 86.3%

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

      6. metadata-eval 86.3%

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

      7. +-commutative 86.3%

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

      8. mul-1-neg 86.3%

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

      9. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   if -1.90000000000000007e-47 < x < 8.10000000000000023e-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. Step-by-step derivation

      1. sub-div 100.0%

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

      2. clear-num 98.2%

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

   6. Applied egg-rr 98.2%

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

   7. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-neg-frac2 84.8%

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

      3. neg-sub0 84.8%

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

      4. associate-+l- 84.8%

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

      5. neg-sub0 84.8%

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

      6. +-commutative 84.8%

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

      7. unsub-neg 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-47} \lor \neg \left(x \leq 8.1 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.9e-109)
     t_0
     (if (<= y 8.5e-156)
       (/ x z)
       (if (<= y 2.8e-112) (/ y (- z)) (if (<= y 5.2e-102) (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.9e-109) {
		tmp = t_0;
	} else if (y <= 8.5e-156) {
		tmp = x / z;
	} else if (y <= 2.8e-112) {
		tmp = y / -z;
	} else if (y <= 5.2e-102) {
		tmp = x / z;
	} else {
		tmp = t_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 = 1.0d0 - (x / y)
    if (y <= (-2.9d-109)) then
        tmp = t_0
    else if (y <= 8.5d-156) then
        tmp = x / z
    else if (y <= 2.8d-112) then
        tmp = y / -z
    else if (y <= 5.2d-102) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.9e-109) {
		tmp = t_0;
	} else if (y <= 8.5e-156) {
		tmp = x / z;
	} else if (y <= 2.8e-112) {
		tmp = y / -z;
	} else if (y <= 5.2e-102) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.9e-109:
		tmp = t_0
	elif y <= 8.5e-156:
		tmp = x / z
	elif y <= 2.8e-112:
		tmp = y / -z
	elif y <= 5.2e-102:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -2.9e-109)
		tmp = t_0;
	elseif (y <= 8.5e-156)
		tmp = Float64(x / z);
	elseif (y <= 2.8e-112)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 5.2e-102)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -2.9e-109)
		tmp = t_0;
	elseif (y <= 8.5e-156)
		tmp = x / z;
	elseif (y <= 2.8e-112)
		tmp = y / -z;
	elseif (y <= 5.2e-102)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e-109], t$95$0, If[LessEqual[y, 8.5e-156], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.8e-112], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 5.2e-102], N[(x / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e-109 or 5.19999999999999973e-102 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 69.2%

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

      1. div-sub 69.2%

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

      2. sub-neg 69.2%

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

      3. *-inverses 69.2%

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

      4. metadata-eval 69.2%

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

      5. distribute-lft-in 69.2%

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

      6. metadata-eval 69.2%

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

      7. +-commutative 69.2%

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

      8. mul-1-neg 69.2%

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

      9. unsub-neg 69.2%

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

   5. Simplified 69.2%

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

   if -2.9e-109 < y < 8.5e-156 or 2.80000000000000023e-112 < y < 5.19999999999999973e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.0%

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

   if 8.5e-156 < y < 2.80000000000000023e-112

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 70.4%

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

   4. Taylor expanded in x around 0 57.2%

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

      1. neg-mul-1 57.2%

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

      2. distribute-neg-frac 57.2%

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

   6. Simplified 57.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-109}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-112}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-42}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z y))))
   (if (<= x -9.4e+27)
     t_0
     (if (<= x -1.4e-42)
       (- 1.0 (/ x y))
       (if (<= x -4.5e-74)
         (/ (- x y) z)
         (if (<= x 7.2e-20) (/ y (- y z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (x <= -9.4e+27) {
		tmp = t_0;
	} else if (x <= -1.4e-42) {
		tmp = 1.0 - (x / y);
	} else if (x <= -4.5e-74) {
		tmp = (x - y) / z;
	} else if (x <= 7.2e-20) {
		tmp = y / (y - z);
	} else {
		tmp = t_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 = x / (z - y)
    if (x <= (-9.4d+27)) then
        tmp = t_0
    else if (x <= (-1.4d-42)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-4.5d-74)) then
        tmp = (x - y) / z
    else if (x <= 7.2d-20) then
        tmp = y / (y - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / (z - y);
	double tmp;
	if (x <= -9.4e+27) {
		tmp = t_0;
	} else if (x <= -1.4e-42) {
		tmp = 1.0 - (x / y);
	} else if (x <= -4.5e-74) {
		tmp = (x - y) / z;
	} else if (x <= 7.2e-20) {
		tmp = y / (y - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z - y)
	tmp = 0
	if x <= -9.4e+27:
		tmp = t_0
	elif x <= -1.4e-42:
		tmp = 1.0 - (x / y)
	elif x <= -4.5e-74:
		tmp = (x - y) / z
	elif x <= 7.2e-20:
		tmp = y / (y - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (x <= -9.4e+27)
		tmp = t_0;
	elseif (x <= -1.4e-42)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -4.5e-74)
		tmp = Float64(Float64(x - y) / z);
	elseif (x <= 7.2e-20)
		tmp = Float64(y / Float64(y - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z - y);
	tmp = 0.0;
	if (x <= -9.4e+27)
		tmp = t_0;
	elseif (x <= -1.4e-42)
		tmp = 1.0 - (x / y);
	elseif (x <= -4.5e-74)
		tmp = (x - y) / z;
	elseif (x <= 7.2e-20)
		tmp = y / (y - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.4e+27], t$95$0, If[LessEqual[x, -1.4e-42], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-74], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 7.2e-20], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.39999999999999952e27 or 7.19999999999999948e-20 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.4%

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

   if -9.39999999999999952e27 < x < -1.39999999999999999e-42

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 88.0%

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

      1. div-sub 88.0%

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

      2. sub-neg 88.0%

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

      3. *-inverses 88.0%

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

      4. metadata-eval 88.0%

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

      5. distribute-lft-in 88.0%

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

      6. metadata-eval 88.0%

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

      7. +-commutative 88.0%

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

      8. mul-1-neg 88.0%

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

      9. unsub-neg 88.0%

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

   5. Simplified 88.0%

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

   if -1.39999999999999999e-42 < x < -4.4999999999999999e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -4.4999999999999999e-74 < x < 7.19999999999999948e-20

   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. Step-by-step derivation

      1. sub-div 100.0%

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

      2. clear-num 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in x around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. neg-sub0 86.2%

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

      4. associate-+l- 86.2%

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

      5. neg-sub0 86.2%

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

      6. +-commutative 86.2%

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

      7. unsub-neg 86.2%

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

   9. Simplified 86.2%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-42}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-91}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-155}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 0.0013:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.05e-91)
   1.0
   (if (<= y 1e-155)
     (/ x z)
     (if (<= y 1.1e-81) (/ y (- z)) (if (<= y 0.0013) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.05e-91) {
		tmp = 1.0;
	} else if (y <= 1e-155) {
		tmp = x / z;
	} else if (y <= 1.1e-81) {
		tmp = y / -z;
	} else if (y <= 0.0013) {
		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 <= (-2.05d-91)) then
        tmp = 1.0d0
    else if (y <= 1d-155) then
        tmp = x / z
    else if (y <= 1.1d-81) then
        tmp = y / -z
    else if (y <= 0.0013d0) 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 <= -2.05e-91) {
		tmp = 1.0;
	} else if (y <= 1e-155) {
		tmp = x / z;
	} else if (y <= 1.1e-81) {
		tmp = y / -z;
	} else if (y <= 0.0013) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.05e-91:
		tmp = 1.0
	elif y <= 1e-155:
		tmp = x / z
	elif y <= 1.1e-81:
		tmp = y / -z
	elif y <= 0.0013:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.05e-91)
		tmp = 1.0;
	elseif (y <= 1e-155)
		tmp = Float64(x / z);
	elseif (y <= 1.1e-81)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 0.0013)
		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 <= -2.05e-91)
		tmp = 1.0;
	elseif (y <= 1e-155)
		tmp = x / z;
	elseif (y <= 1.1e-81)
		tmp = y / -z;
	elseif (y <= 0.0013)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.05e-91], 1.0, If[LessEqual[y, 1e-155], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.1e-81], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 0.0013], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000012e-91 or 0.0012999999999999999 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.6%

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

   if -2.05000000000000012e-91 < y < 1.00000000000000001e-155 or 1.1e-81 < y < 0.0012999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.9%

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

   if 1.00000000000000001e-155 < y < 1.1e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.4%

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

   4. Taylor expanded in x around 0 51.0%

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

      1. neg-mul-1 51.0%

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

      2. distribute-neg-frac 51.0%

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

   6. Simplified 51.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-91}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-155}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 0.0013:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+35} \lor \neg \left(z \leq 1.45 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} - -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e+35) (not (<= z 1.45e+53)))
   (/ (- x y) z)
   (- (/ x (- z y)) -1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e+35) || !(z <= 1.45e+53)) {
		tmp = (x - y) / z;
	} else {
		tmp = (x / (z - y)) - -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 ((z <= (-2.7d+35)) .or. (.not. (z <= 1.45d+53))) then
        tmp = (x - y) / z
    else
        tmp = (x / (z - y)) - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e+35) || !(z <= 1.45e+53)) {
		tmp = (x - y) / z;
	} else {
		tmp = (x / (z - y)) - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e+35) or not (z <= 1.45e+53):
		tmp = (x - y) / z
	else:
		tmp = (x / (z - y)) - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e+35) || !(z <= 1.45e+53))
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(Float64(x / Float64(z - y)) - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e+35) || ~((z <= 1.45e+53)))
		tmp = (x - y) / z;
	else
		tmp = (x / (z - y)) - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e+35], N[Not[LessEqual[z, 1.45e+53]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000003e35 or 1.4500000000000001e53 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 82.5%

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

   if -2.70000000000000003e35 < z < 1.4500000000000001e53

   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 y around inf 87.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+35} \lor \neg \left(z \leq 1.45 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} - -1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-89} \lor \neg \left(y \leq 0.04\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e-89) (not (<= y 0.04))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e-89) || !(y <= 0.04)) {
		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 <= (-2.7d-89)) .or. (.not. (y <= 0.04d0))) 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 <= -2.7e-89) || !(y <= 0.04)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e-89) or not (y <= 0.04):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e-89) || !(y <= 0.04))
		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 <= -2.7e-89) || ~((y <= 0.04)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e-89], N[Not[LessEqual[y, 0.04]], $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 < -2.69999999999999988e-89 or 0.0400000000000000008 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 74.7%

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

      1. div-sub 74.7%

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

      2. sub-neg 74.7%

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

      3. *-inverses 74.7%

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

      4. metadata-eval 74.7%

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

      5. distribute-lft-in 74.7%

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

      6. metadata-eval 74.7%

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

      7. +-commutative 74.7%

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

      8. mul-1-neg 74.7%

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

      9. unsub-neg 74.7%

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

   5. Simplified 74.7%

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

   if -2.69999999999999988e-89 < y < 0.0400000000000000008

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-89} \lor \neg \left(y \leq 0.04\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e-89) 1.0 (if (<= y 0.00165) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e-89) {
		tmp = 1.0;
	} else if (y <= 0.00165) {
		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 <= (-2.7d-89)) then
        tmp = 1.0d0
    else if (y <= 0.00165d0) 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 <= -2.7e-89) {
		tmp = 1.0;
	} else if (y <= 0.00165) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e-89:
		tmp = 1.0
	elif y <= 0.00165:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e-89)
		tmp = 1.0;
	elseif (y <= 0.00165)
		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 <= -2.7e-89)
		tmp = 1.0;
	elseif (y <= 0.00165)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e-89], 1.0, If[LessEqual[y, 0.00165], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999988e-89 or 0.00165 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.6%

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

   if -2.69999999999999988e-89 < y < 0.00165

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 10: 34.4% 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 36.1%

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

4. Final simplification 36.1%

   \[\leadsto 1 \]
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 2024067 
(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)))