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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

Alternatives: 7

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. Add Preprocessing

Alternative 2: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-44}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+17}:\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) z)))
   (if (<= z -7.2e+96)
     t_0
     (if (<= z -1.45e-44)
       (/ y (- y z))
       (if (<= z -6.8e-140)
         (/ x (- z y))
         (if (<= z 1.35e+17) (/ (- y x) y) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / z;
	double tmp;
	if (z <= -7.2e+96) {
		tmp = t_0;
	} else if (z <= -1.45e-44) {
		tmp = y / (y - z);
	} else if (z <= -6.8e-140) {
		tmp = x / (z - y);
	} else if (z <= 1.35e+17) {
		tmp = (y - x) / y;
	} 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 - y) / z
    if (z <= (-7.2d+96)) then
        tmp = t_0
    else if (z <= (-1.45d-44)) then
        tmp = y / (y - z)
    else if (z <= (-6.8d-140)) then
        tmp = x / (z - y)
    else if (z <= 1.35d+17) then
        tmp = (y - x) / y
    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 - y) / z;
	double tmp;
	if (z <= -7.2e+96) {
		tmp = t_0;
	} else if (z <= -1.45e-44) {
		tmp = y / (y - z);
	} else if (z <= -6.8e-140) {
		tmp = x / (z - y);
	} else if (z <= 1.35e+17) {
		tmp = (y - x) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / z
	tmp = 0
	if z <= -7.2e+96:
		tmp = t_0
	elif z <= -1.45e-44:
		tmp = y / (y - z)
	elif z <= -6.8e-140:
		tmp = x / (z - y)
	elif z <= 1.35e+17:
		tmp = (y - x) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / z)
	tmp = 0.0
	if (z <= -7.2e+96)
		tmp = t_0;
	elseif (z <= -1.45e-44)
		tmp = Float64(y / Float64(y - z));
	elseif (z <= -6.8e-140)
		tmp = Float64(x / Float64(z - y));
	elseif (z <= 1.35e+17)
		tmp = Float64(Float64(y - x) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / z;
	tmp = 0.0;
	if (z <= -7.2e+96)
		tmp = t_0;
	elseif (z <= -1.45e-44)
		tmp = y / (y - z);
	elseif (z <= -6.8e-140)
		tmp = x / (z - y);
	elseif (z <= 1.35e+17)
		tmp = (y - x) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -7.2e+96], t$95$0, If[LessEqual[z, -1.45e-44], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-140], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+17], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000026e96 or 1.35e17 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.6%

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

   if -7.20000000000000026e96 < z < -1.4500000000000001e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. neg-mul-1 73.2%

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

      2. distribute-neg-frac2 73.2%

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

      3. sub-neg 73.2%

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

      4. +-commutative 73.2%

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

      5. distribute-neg-in 73.2%

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

      6. remove-double-neg 73.2%

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

      7. sub-neg 73.2%

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

   5. Simplified 73.2%

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

   if -1.4500000000000001e-44 < z < -6.80000000000000017e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.9%

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

   if -6.80000000000000017e-140 < z < 1.35e17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.0%

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

      1. associate-*r/ 84.0%

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

      2. neg-mul-1 84.0%

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

      3. sub-neg 84.0%

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

      4. +-commutative 84.0%

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

      5. distribute-neg-in 84.0%

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

      6. remove-double-neg 84.0%

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

      7. sub-neg 84.0%

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

   5. Simplified 84.0%

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

Alternative 3: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.9e+15)
   1.0
   (if (<= y 1.4e-98) (/ x z) (if (<= y 3.7e-28) (/ (- x) y) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.9e+15) {
		tmp = 1.0;
	} else if (y <= 1.4e-98) {
		tmp = x / z;
	} else if (y <= 3.7e-28) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.9d+15)) then
        tmp = 1.0d0
    else if (y <= 1.4d-98) then
        tmp = x / z
    else if (y <= 3.7d-28) then
        tmp = -x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.9e+15) {
		tmp = 1.0;
	} else if (y <= 1.4e-98) {
		tmp = x / z;
	} else if (y <= 3.7e-28) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.9e+15:
		tmp = 1.0
	elif y <= 1.4e-98:
		tmp = x / z
	elif y <= 3.7e-28:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.9e+15)
		tmp = 1.0;
	elseif (y <= 1.4e-98)
		tmp = Float64(x / z);
	elseif (y <= 3.7e-28)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.9e+15)
		tmp = 1.0;
	elseif (y <= 1.4e-98)
		tmp = x / z;
	elseif (y <= 3.7e-28)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.9e+15], 1.0, If[LessEqual[y, 1.4e-98], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.7e-28], N[((-x) / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9e15 or 3.7000000000000002e-28 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.3%

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

   if -6.9e15 < y < 1.3999999999999999e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.3%

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

   if 1.3999999999999999e-98 < y < 3.7000000000000002e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 66.2%

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

   4. Taylor expanded in z around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-frac-neg 48.1%

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

   6. Simplified 48.1%

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

Alternative 4: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-34} \lor \neg \left(y \leq 1.08 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.6e-34) (not (<= y 1.08e-27))) (/ y (- y z)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.6e-34) || !(y <= 1.08e-27)) {
		tmp = y / (y - z);
	} 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 <= (-5.6d-34)) .or. (.not. (y <= 1.08d-27))) then
        tmp = y / (y - z)
    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 <= -5.6e-34) || !(y <= 1.08e-27)) {
		tmp = y / (y - z);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.6e-34) or not (y <= 1.08e-27):
		tmp = y / (y - z)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.6e-34) || !(y <= 1.08e-27))
		tmp = Float64(y / Float64(y - z));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.6e-34) || ~((y <= 1.08e-27)))
		tmp = y / (y - z);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.6e-34], N[Not[LessEqual[y, 1.08e-27]], $MachinePrecision]], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.59999999999999994e-34 or 1.08e-27 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

      2. distribute-neg-frac2 76.8%

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

      3. sub-neg 76.8%

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

      4. +-commutative 76.8%

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

      5. distribute-neg-in 76.8%

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

      6. remove-double-neg 76.8%

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

      7. sub-neg 76.8%

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

   5. Simplified 76.8%

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

   if -5.59999999999999994e-34 < y < 1.08e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.1%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-34} \lor \neg \left(y \leq 1.08 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+110}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.9e+110) 1.0 (if (<= y 1.2e-27) (/ x (- z y)) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.9e+110) {
		tmp = 1.0;
	} else if (y <= 1.2e-27) {
		tmp = x / (z - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.9d+110)) then
        tmp = 1.0d0
    else if (y <= 1.2d-27) then
        tmp = x / (z - y)
    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 <= -5.9e+110) {
		tmp = 1.0;
	} else if (y <= 1.2e-27) {
		tmp = x / (z - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.9e+110:
		tmp = 1.0
	elif y <= 1.2e-27:
		tmp = x / (z - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.9e+110)
		tmp = 1.0;
	elseif (y <= 1.2e-27)
		tmp = Float64(x / Float64(z - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.9e+110)
		tmp = 1.0;
	elseif (y <= 1.2e-27)
		tmp = x / (z - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.9e+110], 1.0, If[LessEqual[y, 1.2e-27], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8999999999999997e110 or 1.20000000000000001e-27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 64.6%

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

   if -5.8999999999999997e110 < y < 1.20000000000000001e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.8%

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

Alternative 6: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e+15) 1.0 (if (<= y 1.15e-27) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e+15) {
		tmp = 1.0;
	} else if (y <= 1.15e-27) {
		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 <= (-1.7d+15)) then
        tmp = 1.0d0
    else if (y <= 1.15d-27) 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 <= -1.7e+15) {
		tmp = 1.0;
	} else if (y <= 1.15e-27) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.7e+15:
		tmp = 1.0
	elif y <= 1.15e-27:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e+15)
		tmp = 1.0;
	elseif (y <= 1.15e-27)
		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 <= -1.7e+15)
		tmp = 1.0;
	elseif (y <= 1.15e-27)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.7e+15], 1.0, If[LessEqual[y, 1.15e-27], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e15 or 1.15e-27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -1.7e15 < y < 1.15e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 60.4%

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

Alternative 7: 34.8% 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 32.0%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Developer Target 1: 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 2024163 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- z y)) (/ y (- z y))))

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