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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 8

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, 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 2: 60.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{-z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-34}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4500:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- z))))
   (if (<= y -4.6e+77)
     1.0
     (if (<= y -2.1e-34)
       t_0
       (if (<= y 4e-76)
         (/ x z)
         (if (<= y 4500.0)
           (/ x (- y))
           (if (<= y 3e+50) 1.0 (if (<= y 2.5e+101) t_0 1.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / -z;
	double tmp;
	if (y <= -4.6e+77) {
		tmp = 1.0;
	} else if (y <= -2.1e-34) {
		tmp = t_0;
	} else if (y <= 4e-76) {
		tmp = x / z;
	} else if (y <= 4500.0) {
		tmp = x / -y;
	} else if (y <= 3e+50) {
		tmp = 1.0;
	} else if (y <= 2.5e+101) {
		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 = y / -z
    if (y <= (-4.6d+77)) then
        tmp = 1.0d0
    else if (y <= (-2.1d-34)) then
        tmp = t_0
    else if (y <= 4d-76) then
        tmp = x / z
    else if (y <= 4500.0d0) then
        tmp = x / -y
    else if (y <= 3d+50) then
        tmp = 1.0d0
    else if (y <= 2.5d+101) 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 = y / -z;
	double tmp;
	if (y <= -4.6e+77) {
		tmp = 1.0;
	} else if (y <= -2.1e-34) {
		tmp = t_0;
	} else if (y <= 4e-76) {
		tmp = x / z;
	} else if (y <= 4500.0) {
		tmp = x / -y;
	} else if (y <= 3e+50) {
		tmp = 1.0;
	} else if (y <= 2.5e+101) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / -z
	tmp = 0
	if y <= -4.6e+77:
		tmp = 1.0
	elif y <= -2.1e-34:
		tmp = t_0
	elif y <= 4e-76:
		tmp = x / z
	elif y <= 4500.0:
		tmp = x / -y
	elif y <= 3e+50:
		tmp = 1.0
	elif y <= 2.5e+101:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(-z))
	tmp = 0.0
	if (y <= -4.6e+77)
		tmp = 1.0;
	elseif (y <= -2.1e-34)
		tmp = t_0;
	elseif (y <= 4e-76)
		tmp = Float64(x / z);
	elseif (y <= 4500.0)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 3e+50)
		tmp = 1.0;
	elseif (y <= 2.5e+101)
		tmp = t_0;
	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 <= -4.6e+77)
		tmp = 1.0;
	elseif (y <= -2.1e-34)
		tmp = t_0;
	elseif (y <= 4e-76)
		tmp = x / z;
	elseif (y <= 4500.0)
		tmp = x / -y;
	elseif (y <= 3e+50)
		tmp = 1.0;
	elseif (y <= 2.5e+101)
		tmp = t_0;
	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, -4.6e+77], 1.0, If[LessEqual[y, -2.1e-34], t$95$0, If[LessEqual[y, 4e-76], N[(x / z), $MachinePrecision], If[LessEqual[y, 4500.0], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 3e+50], 1.0, If[LessEqual[y, 2.5e+101], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.5999999999999999e77 or 4500 < y < 2.9999999999999998e50 or 2.49999999999999994e101 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.8%

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

   if -4.5999999999999999e77 < y < -2.1000000000000001e-34 or 2.9999999999999998e50 < y < 2.49999999999999994e101

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 57.1%

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

   4. Taylor expanded in x around 0 48.8%

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

      1. neg-mul-1 48.8%

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

      2. distribute-neg-frac2 48.8%

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

   6. Simplified 48.8%

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

   if -2.1000000000000001e-34 < y < 3.99999999999999971e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.4%

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

   if 3.99999999999999971e-76 < y < 4500

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 58.9%

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

      1. div-sub 58.9%

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

      2. sub-neg 58.9%

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

      3. *-inverses 58.9%

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

      4. metadata-eval 58.9%

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

      5. distribute-lft-in 58.9%

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

      6. metadata-eval 58.9%

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

      7. +-commutative 58.9%

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

      8. mul-1-neg 58.9%

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

      9. unsub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 48.5%

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

      1. associate-*r/ 48.5%

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

      2. mul-1-neg 48.5%

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

   8. Simplified 48.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4500:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+77)
   1.0
   (if (<= y -3.75e-34) (/ y (- z)) (if (<= y 4.8e-26) (/ x z) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+77) {
		tmp = 1.0;
	} else if (y <= -3.75e-34) {
		tmp = y / -z;
	} else if (y <= 4.8e-26) {
		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 <= (-4.1d+77)) then
        tmp = 1.0d0
    else if (y <= (-3.75d-34)) then
        tmp = y / -z
    else if (y <= 4.8d-26) 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 <= -4.1e+77) {
		tmp = 1.0;
	} else if (y <= -3.75e-34) {
		tmp = y / -z;
	} else if (y <= 4.8e-26) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+77:
		tmp = 1.0
	elif y <= -3.75e-34:
		tmp = y / -z
	elif y <= 4.8e-26:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+77)
		tmp = 1.0;
	elseif (y <= -3.75e-34)
		tmp = Float64(y / Float64(-z));
	elseif (y <= 4.8e-26)
		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 <= -4.1e+77)
		tmp = 1.0;
	elseif (y <= -3.75e-34)
		tmp = y / -z;
	elseif (y <= 4.8e-26)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+77], 1.0, If[LessEqual[y, -3.75e-34], N[(y / (-z)), $MachinePrecision], If[LessEqual[y, 4.8e-26], N[(x / z), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1000000000000001e77 or 4.8000000000000002e-26 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 58.2%

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

   if -4.1000000000000001e77 < y < -3.7500000000000002e-34

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 57.8%

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

   4. Taylor expanded in x around 0 45.4%

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

      1. neg-mul-1 45.4%

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

      2. distribute-neg-frac2 45.4%

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

   6. Simplified 45.4%

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

   if -3.7500000000000002e-34 < y < 4.8000000000000002e-26

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-7} \lor \neg \left(y \leq 2.5 \cdot 10^{-76}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e-7) (not (<= y 2.5e-76))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e-7) || !(y <= 2.5e-76)) {
		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 <= (-1.85d-7)) .or. (.not. (y <= 2.5d-76))) 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 <= -1.85e-7) || !(y <= 2.5e-76)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e-7) or not (y <= 2.5e-76):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e-7) || !(y <= 2.5e-76))
		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 <= -1.85e-7) || ~((y <= 2.5e-76)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e-7], N[Not[LessEqual[y, 2.5e-76]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000002e-7 or 2.4999999999999999e-76 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.3%

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

      1. div-sub 72.3%

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

      2. sub-neg 72.3%

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

      3. *-inverses 72.3%

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

      4. metadata-eval 72.3%

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

      5. distribute-lft-in 72.3%

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

      6. metadata-eval 72.3%

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

      7. +-commutative 72.3%

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

      8. mul-1-neg 72.3%

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

      9. unsub-neg 72.3%

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

   5. Simplified 72.3%

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

   if -1.85000000000000002e-7 < y < 2.4999999999999999e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-7} \lor \neg \left(y \leq 2.5 \cdot 10^{-76}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+83} \lor \neg \left(y \leq 10^{-24}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.35e+83) (not (<= y 1e-24))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e+83) || !(y <= 1e-24)) {
		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 <= (-2.35d+83)) .or. (.not. (y <= 1d-24))) 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 <= -2.35e+83) || !(y <= 1e-24)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.35e+83) or not (y <= 1e-24):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.35e+83) || !(y <= 1e-24))
		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 <= -2.35e+83) || ~((y <= 1e-24)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.35e+83], N[Not[LessEqual[y, 1e-24]], $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 < -2.3499999999999999e83 or 9.99999999999999924e-25 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 77.4%

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

      1. div-sub 77.4%

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

      2. sub-neg 77.4%

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

      3. *-inverses 77.4%

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

      4. metadata-eval 77.4%

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

      5. distribute-lft-in 77.4%

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

      6. metadata-eval 77.4%

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

      7. +-commutative 77.4%

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

      8. mul-1-neg 77.4%

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

      9. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   if -2.3499999999999999e83 < y < 9.99999999999999924e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+83} \lor \neg \left(y \leq 10^{-24}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-41} \lor \neg \left(x \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-41) (not (<= x 2.9e+49))) (/ x (- z y)) (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e-41) || !(x <= 2.9e+49)) {
		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 <= (-3.7d-41)) .or. (.not. (x <= 2.9d+49))) 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 <= -3.7e-41) || !(x <= 2.9e+49)) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e-41) or not (x <= 2.9e+49):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e-41) || !(x <= 2.9e+49))
		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 <= -3.7e-41) || ~((x <= 2.9e+49)))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e-41], N[Not[LessEqual[x, 2.9e+49]], $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 < -3.7000000000000002e-41 or 2.9e49 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.4%

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

   if -3.7000000000000002e-41 < x < 2.9e49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

      1. neg-mul-1 81.5%

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

      2. distribute-neg-frac 81.5%

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

   5. Simplified 81.5%

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

      1. frac-2neg 81.5%

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

      2. div-inv 81.3%

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

      3. remove-double-neg 81.3%

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

      4. sub-neg 81.3%

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

      5. distribute-neg-in 81.3%

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

      6. remove-double-neg 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. associate-*r/ 81.5%

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

      2. *-rgt-identity 81.5%

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

      3. +-commutative 81.5%

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

      4. unsub-neg 81.5%

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

   9. Simplified 81.5%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-41} \lor \neg \left(x \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -65000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -65000000.0) 1.0 (if (<= y 1.6e-25) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -65000000.0) {
		tmp = 1.0;
	} else if (y <= 1.6e-25) {
		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 <= (-65000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.6d-25) 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 <= -65000000.0) {
		tmp = 1.0;
	} else if (y <= 1.6e-25) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -65000000.0:
		tmp = 1.0
	elif y <= 1.6e-25:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -65000000.0)
		tmp = 1.0;
	elseif (y <= 1.6e-25)
		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 <= -65000000.0)
		tmp = 1.0;
	elseif (y <= 1.6e-25)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -65000000.0], 1.0, If[LessEqual[y, 1.6e-25], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e7 or 1.6000000000000001e-25 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 53.7%

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

   if -6.5e7 < y < 1.6000000000000001e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 65.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.7% 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 31.3%

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

4. Final simplification 31.3%

   \[\leadsto 1 \]
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 2024055 
(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)))