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

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 11

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 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. Final simplification 100.0%

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

Alternative 2: 58.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+144}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+152}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- y))))
   (if (<= y -3e+144)
     1.0
     (if (<= y -2.1e+80)
       t_0
       (if (<= y -4.5e-20)
         1.0
         (if (<= y 2.7e-5)
           (/ x z)
           (if (<= y 3.9e+102) (/ y (- z)) (if (<= y 7.5e+152) t_0 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / -y;
	double tmp;
	if (y <= -3e+144) {
		tmp = 1.0;
	} else if (y <= -2.1e+80) {
		tmp = t_0;
	} else if (y <= -4.5e-20) {
		tmp = 1.0;
	} else if (y <= 2.7e-5) {
		tmp = x / z;
	} else if (y <= 3.9e+102) {
		tmp = y / -z;
	} else if (y <= 7.5e+152) {
		tmp = t_0;
	} 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 = x / -y
    if (y <= (-3d+144)) then
        tmp = 1.0d0
    else if (y <= (-2.1d+80)) then
        tmp = t_0
    else if (y <= (-4.5d-20)) then
        tmp = 1.0d0
    else if (y <= 2.7d-5) then
        tmp = x / z
    else if (y <= 3.9d+102) then
        tmp = y / -z
    else if (y <= 7.5d+152) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x / -y;
	double tmp;
	if (y <= -3e+144) {
		tmp = 1.0;
	} else if (y <= -2.1e+80) {
		tmp = t_0;
	} else if (y <= -4.5e-20) {
		tmp = 1.0;
	} else if (y <= 2.7e-5) {
		tmp = x / z;
	} else if (y <= 3.9e+102) {
		tmp = y / -z;
	} else if (y <= 7.5e+152) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / -y
	tmp = 0
	if y <= -3e+144:
		tmp = 1.0
	elif y <= -2.1e+80:
		tmp = t_0
	elif y <= -4.5e-20:
		tmp = 1.0
	elif y <= 2.7e-5:
		tmp = x / z
	elif y <= 3.9e+102:
		tmp = y / -z
	elif y <= 7.5e+152:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(-y))
	tmp = 0.0
	if (y <= -3e+144)
		tmp = 1.0;
	elseif (y <= -2.1e+80)
		tmp = t_0;
	elseif (y <= -4.5e-20)
		tmp = 1.0;
	elseif (y <= 2.7e-5)
		tmp = Float64(x / z);
	elseif (y <= 3.9e+102)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 7.5e+152)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / -y;
	tmp = 0.0;
	if (y <= -3e+144)
		tmp = 1.0;
	elseif (y <= -2.1e+80)
		tmp = t_0;
	elseif (y <= -4.5e-20)
		tmp = 1.0;
	elseif (y <= 2.7e-5)
		tmp = x / z;
	elseif (y <= 3.9e+102)
		tmp = y / -z;
	elseif (y <= 7.5e+152)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / (-y)), $MachinePrecision]}, If[LessEqual[y, -3e+144], 1.0, If[LessEqual[y, -2.1e+80], t$95$0, If[LessEqual[y, -4.5e-20], 1.0, If[LessEqual[y, 2.7e-5], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.9e+102], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 7.5e+152], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9999999999999999e144 or -2.10000000000000001e80 < y < -4.5000000000000001e-20 or 7.50000000000000046e152 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -2.9999999999999999e144 < y < -2.10000000000000001e80 or 3.8999999999999998e102 < y < 7.50000000000000046e152

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.1%

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

   4. Taylor expanded in z around 0 58.2%

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

      1. associate-*r/ 58.2%

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

      2. neg-mul-1 58.2%

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

   6. Simplified 58.2%

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

   if -4.5000000000000001e-20 < y < 2.6999999999999999e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 61.9%

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

   if 2.6999999999999999e-5 < y < 3.8999999999999998e102

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.7%

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

   4. Taylor expanded in x around 0 46.8%

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

      1. neg-mul-1 46.8%

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

      2. distribute-neg-frac2 46.8%

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

   6. Simplified 46.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+144}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-25} \lor \neg \left(y \leq 8 \cdot 10^{+51}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -9.5e-111)
     t_0
     (if (<= y 3.8e-119)
       (/ x z)
       (if (or (<= y 6.8e-25) (not (<= y 8e+51))) t_0 (/ y (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -9.5e-111) {
		tmp = t_0;
	} else if (y <= 3.8e-119) {
		tmp = x / z;
	} else if ((y <= 6.8e-25) || !(y <= 8e+51)) {
		tmp = t_0;
	} else {
		tmp = 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 = 1.0d0 - (x / y)
    if (y <= (-9.5d-111)) then
        tmp = t_0
    else if (y <= 3.8d-119) then
        tmp = x / z
    else if ((y <= 6.8d-25) .or. (.not. (y <= 8d+51))) then
        tmp = t_0
    else
        tmp = y / -z
    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 <= -9.5e-111) {
		tmp = t_0;
	} else if (y <= 3.8e-119) {
		tmp = x / z;
	} else if ((y <= 6.8e-25) || !(y <= 8e+51)) {
		tmp = t_0;
	} else {
		tmp = y / -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -9.5e-111:
		tmp = t_0
	elif y <= 3.8e-119:
		tmp = x / z
	elif (y <= 6.8e-25) or not (y <= 8e+51):
		tmp = t_0
	else:
		tmp = y / -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -9.5e-111)
		tmp = t_0;
	elseif (y <= 3.8e-119)
		tmp = Float64(x / z);
	elseif ((y <= 6.8e-25) || !(y <= 8e+51))
		tmp = t_0;
	else
		tmp = Float64(y / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -9.5e-111)
		tmp = t_0;
	elseif (y <= 3.8e-119)
		tmp = x / z;
	elseif ((y <= 6.8e-25) || ~((y <= 8e+51)))
		tmp = t_0;
	else
		tmp = y / -z;
	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, -9.5e-111], t$95$0, If[LessEqual[y, 3.8e-119], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 6.8e-25], N[Not[LessEqual[y, 8e+51]], $MachinePrecision]], t$95$0, N[(y / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999995e-111 or 3.79999999999999975e-119 < y < 6.80000000000000003e-25 or 8e51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. div-sub 71.8%

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

      2. sub-neg 71.8%

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

      3. *-inverses 71.8%

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

      4. metadata-eval 71.8%

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

      5. distribute-lft-in 71.8%

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

      6. metadata-eval 71.8%

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

      7. +-commutative 71.8%

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

      8. mul-1-neg 71.8%

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

      9. unsub-neg 71.8%

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

   5. Simplified 71.8%

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

   if -9.4999999999999995e-111 < y < 3.79999999999999975e-119

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.2%

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

   if 6.80000000000000003e-25 < y < 8e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.2%

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

   4. Taylor expanded in x around 0 49.1%

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

      1. neg-mul-1 49.1%

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

      2. distribute-neg-frac2 49.1%

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

   6. Simplified 49.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-111}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-25} \lor \neg \left(y \leq 8 \cdot 10^{+51}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- z y))))
   (if (<= y -1.8e-19)
     t_0
     (if (<= y 2.9e-26)
       t_1
       (if (<= y 2.9e+55) (/ y (- y z)) (if (<= y 2.9e+137) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (z - y);
	double tmp;
	if (y <= -1.8e-19) {
		tmp = t_0;
	} else if (y <= 2.9e-26) {
		tmp = t_1;
	} else if (y <= 2.9e+55) {
		tmp = y / (y - z);
	} else if (y <= 2.9e+137) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / (z - y)
    if (y <= (-1.8d-19)) then
        tmp = t_0
    else if (y <= 2.9d-26) then
        tmp = t_1
    else if (y <= 2.9d+55) then
        tmp = y / (y - z)
    else if (y <= 2.9d+137) then
        tmp = t_1
    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 t_1 = x / (z - y);
	double tmp;
	if (y <= -1.8e-19) {
		tmp = t_0;
	} else if (y <= 2.9e-26) {
		tmp = t_1;
	} else if (y <= 2.9e+55) {
		tmp = y / (y - z);
	} else if (y <= 2.9e+137) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	t_1 = x / (z - y)
	tmp = 0
	if y <= -1.8e-19:
		tmp = t_0
	elif y <= 2.9e-26:
		tmp = t_1
	elif y <= 2.9e+55:
		tmp = y / (y - z)
	elif y <= 2.9e+137:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (y <= -1.8e-19)
		tmp = t_0;
	elseif (y <= 2.9e-26)
		tmp = t_1;
	elseif (y <= 2.9e+55)
		tmp = Float64(y / Float64(y - z));
	elseif (y <= 2.9e+137)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (y <= -1.8e-19)
		tmp = t_0;
	elseif (y <= 2.9e-26)
		tmp = t_1;
	elseif (y <= 2.9e+55)
		tmp = y / (y - z);
	elseif (y <= 2.9e+137)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e-19], t$95$0, If[LessEqual[y, 2.9e-26], t$95$1, If[LessEqual[y, 2.9e+55], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+137], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8000000000000001e-19 or 2.89999999999999985e137 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.3%

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

      1. div-sub 84.4%

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

      2. sub-neg 84.4%

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

      3. *-inverses 84.4%

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

      4. metadata-eval 84.4%

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

      5. distribute-lft-in 84.4%

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

      6. metadata-eval 84.4%

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

      7. +-commutative 84.4%

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

      8. mul-1-neg 84.4%

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

      9. unsub-neg 84.4%

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

   5. Simplified 84.4%

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

   if -1.8000000000000001e-19 < y < 2.8999999999999998e-26 or 2.8999999999999999e55 < y < 2.89999999999999985e137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

   if 2.8999999999999998e-26 < y < 2.8999999999999999e55

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 65.8%

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

      1. neg-mul-1 65.8%

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

      2. distribute-neg-frac 65.8%

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

   5. Simplified 65.8%

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

      1. frac-2neg 65.8%

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

      2. div-inv 65.6%

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

      3. remove-double-neg 65.6%

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

      4. sub-neg 65.6%

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

      5. distribute-neg-in 65.6%

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

      6. remove-double-neg 65.6%

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

   7. Applied egg-rr 65.6%

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

      1. associate-*r/ 65.8%

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

      2. *-rgt-identity 65.8%

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

      3. +-commutative 65.8%

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

      4. unsub-neg 65.8%

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

   9. Simplified 65.8%

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

Alternative 5: 59.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+108}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e-20)
   1.0
   (if (<= y 6.5e-5)
     (/ x z)
     (if (<= y 1.55e+108) (/ y (- z)) (if (<= y 2.9e+137) (/ 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 <= 6.5e-5) {
		tmp = x / z;
	} else if (y <= 1.55e+108) {
		tmp = y / -z;
	} else if (y <= 2.9e+137) {
		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 <= 6.5d-5) then
        tmp = x / z
    else if (y <= 1.55d+108) then
        tmp = y / -z
    else if (y <= 2.9d+137) 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 <= 6.5e-5) {
		tmp = x / z;
	} else if (y <= 1.55e+108) {
		tmp = y / -z;
	} else if (y <= 2.9e+137) {
		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 <= 6.5e-5:
		tmp = x / z
	elif y <= 1.55e+108:
		tmp = y / -z
	elif y <= 2.9e+137:
		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 <= 6.5e-5)
		tmp = Float64(x / z);
	elseif (y <= 1.55e+108)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 2.9e+137)
		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 <= 6.5e-5)
		tmp = x / z;
	elseif (y <= 1.55e+108)
		tmp = y / -z;
	elseif (y <= 2.9e+137)
		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, 6.5e-5], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.55e+108], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 2.9e+137], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999993e-20 or 2.89999999999999985e137 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.5%

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

   if -2.39999999999999993e-20 < y < 6.49999999999999943e-5 or 1.5500000000000001e108 < y < 2.89999999999999985e137

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 61.0%

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

   if 6.49999999999999943e-5 < y < 1.5500000000000001e108

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.7%

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

   4. Taylor expanded in x around 0 46.8%

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

      1. neg-mul-1 46.8%

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

      2. distribute-neg-frac2 46.8%

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

   6. Simplified 46.8%

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

Alternative 6: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{z} - \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -5.5e-19)
     t_0
     (if (<= y 2.3e-30)
       (/ x (- z y))
       (if (<= y 7e+119) (- (/ x z) (/ y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -5.5e-19) {
		tmp = t_0;
	} else if (y <= 2.3e-30) {
		tmp = x / (z - y);
	} else if (y <= 7e+119) {
		tmp = (x / z) - (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 = 1.0d0 - (x / y)
    if (y <= (-5.5d-19)) then
        tmp = t_0
    else if (y <= 2.3d-30) then
        tmp = x / (z - y)
    else if (y <= 7d+119) then
        tmp = (x / z) - (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 = 1.0 - (x / y);
	double tmp;
	if (y <= -5.5e-19) {
		tmp = t_0;
	} else if (y <= 2.3e-30) {
		tmp = x / (z - y);
	} else if (y <= 7e+119) {
		tmp = (x / z) - (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -5.5e-19:
		tmp = t_0
	elif y <= 2.3e-30:
		tmp = x / (z - y)
	elif y <= 7e+119:
		tmp = (x / z) - (y / 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 <= -5.5e-19)
		tmp = t_0;
	elseif (y <= 2.3e-30)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 7e+119)
		tmp = Float64(Float64(x / z) - Float64(y / 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 <= -5.5e-19)
		tmp = t_0;
	elseif (y <= 2.3e-30)
		tmp = x / (z - y);
	elseif (y <= 7e+119)
		tmp = (x / z) - (y / 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, -5.5e-19], t$95$0, If[LessEqual[y, 2.3e-30], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+119], N[(N[(x / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999996e-19 or 7.0000000000000001e119 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.8%

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

      1. div-sub 83.9%

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

      2. sub-neg 83.9%

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

      3. *-inverses 83.9%

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

      4. metadata-eval 83.9%

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

      5. distribute-lft-in 83.9%

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

      6. metadata-eval 83.9%

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

      7. +-commutative 83.9%

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

      8. mul-1-neg 83.9%

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

      9. unsub-neg 83.9%

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

   5. Simplified 83.9%

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

   if -5.4999999999999996e-19 < y < 2.29999999999999984e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.5%

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

   if 2.29999999999999984e-30 < y < 7.0000000000000001e119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 69.5%

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

      1. div-sub 69.6%

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

   5. Applied egg-rr 69.6%

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

Alternative 7: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+119}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -5.5e-19)
     t_0
     (if (<= y 2.5e-30) (/ x (- z y)) (if (<= y 7e+119) (/ (- x y) z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -5.5e-19) {
		tmp = t_0;
	} else if (y <= 2.5e-30) {
		tmp = x / (z - y);
	} else if (y <= 7e+119) {
		tmp = (x - 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 = 1.0d0 - (x / y)
    if (y <= (-5.5d-19)) then
        tmp = t_0
    else if (y <= 2.5d-30) then
        tmp = x / (z - y)
    else if (y <= 7d+119) then
        tmp = (x - 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 = 1.0 - (x / y);
	double tmp;
	if (y <= -5.5e-19) {
		tmp = t_0;
	} else if (y <= 2.5e-30) {
		tmp = x / (z - y);
	} else if (y <= 7e+119) {
		tmp = (x - y) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -5.5e-19:
		tmp = t_0
	elif y <= 2.5e-30:
		tmp = x / (z - y)
	elif y <= 7e+119:
		tmp = (x - y) / 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 <= -5.5e-19)
		tmp = t_0;
	elseif (y <= 2.5e-30)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 7e+119)
		tmp = Float64(Float64(x - y) / 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 <= -5.5e-19)
		tmp = t_0;
	elseif (y <= 2.5e-30)
		tmp = x / (z - y);
	elseif (y <= 7e+119)
		tmp = (x - y) / 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, -5.5e-19], t$95$0, If[LessEqual[y, 2.5e-30], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+119], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999996e-19 or 7.0000000000000001e119 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 83.8%

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

      1. div-sub 83.9%

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

      2. sub-neg 83.9%

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

      3. *-inverses 83.9%

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

      4. metadata-eval 83.9%

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

      5. distribute-lft-in 83.9%

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

      6. metadata-eval 83.9%

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

      7. +-commutative 83.9%

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

      8. mul-1-neg 83.9%

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

      9. unsub-neg 83.9%

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

   5. Simplified 83.9%

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

   if -5.4999999999999996e-19 < y < 2.49999999999999986e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.5%

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

   if 2.49999999999999986e-30 < y < 7.0000000000000001e119

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 69.5%

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

Alternative 8: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-19} \lor \neg \left(y \leq 2.9 \cdot 10^{+137}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e-19) (not (<= y 2.9e+137)))
   (- 1.0 (/ x y))
   (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e-19) || !(y <= 2.9e+137)) {
		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 <= (-2.05d-19)) .or. (.not. (y <= 2.9d+137))) 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 <= -2.05e-19) || !(y <= 2.9e+137)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e-19) or not (y <= 2.9e+137):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e-19) || !(y <= 2.9e+137))
		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 <= -2.05e-19) || ~((y <= 2.9e+137)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e-19], N[Not[LessEqual[y, 2.9e+137]], $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 < -2.04999999999999993e-19 or 2.89999999999999985e137 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.3%

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

      1. div-sub 84.4%

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

      2. sub-neg 84.4%

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

      3. *-inverses 84.4%

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

      4. metadata-eval 84.4%

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

      5. distribute-lft-in 84.4%

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

      6. metadata-eval 84.4%

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

      7. +-commutative 84.4%

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

      8. mul-1-neg 84.4%

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

      9. unsub-neg 84.4%

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

   5. Simplified 84.4%

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

   if -2.04999999999999993e-19 < y < 2.89999999999999985e137

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-19} \lor \neg \left(y \leq 2.9 \cdot 10^{+137}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e-20) 1.0 (if (<= y 2.9e+137) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e-20) {
		tmp = 1.0;
	} else if (y <= 2.9e+137) {
		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 <= (-5.1d-20)) then
        tmp = 1.0d0
    else if (y <= 2.9d+137) 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 <= -5.1e-20) {
		tmp = 1.0;
	} else if (y <= 2.9e+137) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.1e-20:
		tmp = 1.0
	elif y <= 2.9e+137:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e-20)
		tmp = 1.0;
	elseif (y <= 2.9e+137)
		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 <= -5.1e-20)
		tmp = 1.0;
	elseif (y <= 2.9e+137)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.1e-20], 1.0, If[LessEqual[y, 2.9e+137], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000019e-20 or 2.89999999999999985e137 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.5%

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

   if -5.10000000000000019e-20 < y < 2.89999999999999985e137

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 56.4%

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

Alternative 10: 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 11: 34.9% 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 99.9%

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

3. Taylor expanded in y around inf 32.1%

   \[\leadsto \color{blue}{1} \]
4. 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 2024107 
(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)))