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

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

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: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+74} \lor \neg \left(y \leq 8.8 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+74) (not (<= y 8.8e-33))) (/ y (- y z)) (/ (- x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+74) || !(y <= 8.8e-33)) {
		tmp = y / (y - z);
	} else {
		tmp = (x - 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 ((y <= (-3.8d+74)) .or. (.not. (y <= 8.8d-33))) then
        tmp = y / (y - z)
    else
        tmp = (x - y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+74) || !(y <= 8.8e-33)) {
		tmp = y / (y - z);
	} else {
		tmp = (x - y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+74) or not (y <= 8.8e-33):
		tmp = y / (y - z)
	else:
		tmp = (x - y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+74) || !(y <= 8.8e-33))
		tmp = Float64(y / Float64(y - z));
	else
		tmp = Float64(Float64(x - y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e+74) || ~((y <= 8.8e-33)))
		tmp = y / (y - z);
	else
		tmp = (x - y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+74], N[Not[LessEqual[y, 8.8e-33]], $MachinePrecision]], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e74 or 8.80000000000000022e-33 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.6%

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

      1. neg-mul-1 80.6%

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

      2. distribute-neg-frac2 80.6%

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

      3. sub-neg 80.6%

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

      4. +-commutative 80.6%

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

      5. distribute-neg-in 80.6%

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

      6. remove-double-neg 80.6%

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

      7. sub-neg 80.6%

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

   5. Simplified 80.6%

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

   if -3.7999999999999998e74 < y < 8.80000000000000022e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 78.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+74} \lor \neg \left(y \leq 8.8 \cdot 10^{-33}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+74} \lor \neg \left(y \leq 3.9 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+74) (not (<= y 3.9e+17))) (/ y (- y z)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+74) || !(y <= 3.9e+17)) {
		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 <= (-7.5d+74)) .or. (.not. (y <= 3.9d+17))) 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 <= -7.5e+74) || !(y <= 3.9e+17)) {
		tmp = y / (y - z);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+74) or not (y <= 3.9e+17):
		tmp = y / (y - z)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+74) || !(y <= 3.9e+17))
		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 <= -7.5e+74) || ~((y <= 3.9e+17)))
		tmp = y / (y - z);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+74], N[Not[LessEqual[y, 3.9e+17]], $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 < -7.5e74 or 3.9e17 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac2 84.1%

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

      3. sub-neg 84.1%

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

      4. +-commutative 84.1%

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

      5. distribute-neg-in 84.1%

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

      6. remove-double-neg 84.1%

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

      7. sub-neg 84.1%

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

   5. Simplified 84.1%

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

   if -7.5e74 < y < 3.9e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+74} \lor \neg \left(y \leq 3.9 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+36} \lor \neg \left(y \leq 6 \cdot 10^{-74}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+36) (not (<= y 6e-74))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+36) || !(y <= 6e-74)) {
		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 <= (-1.1d+36)) .or. (.not. (y <= 6d-74))) 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 <= -1.1e+36) || !(y <= 6e-74)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+36) or not (y <= 6e-74):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+36) || !(y <= 6e-74))
		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 <= -1.1e+36) || ~((y <= 6e-74)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+36], N[Not[LessEqual[y, 6e-74]], $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 < -1.1e36 or 6.00000000000000014e-74 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.4%

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

      1. associate-*r/ 73.4%

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

      2. neg-mul-1 73.4%

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

      3. sub-neg 73.4%

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

      4. +-commutative 73.4%

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

      5. distribute-neg-in 73.4%

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

      6. remove-double-neg 73.4%

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

      7. sub-neg 73.4%

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

      8. div-sub 73.4%

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

      9. *-inverses 73.4%

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

   5. Simplified 73.4%

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

   if -1.1e36 < y < 6.00000000000000014e-74

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.6%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+36} \lor \neg \left(y \leq 6 \cdot 10^{-74}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-82} \lor \neg \left(y \leq 3.1 \cdot 10^{-118}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e-82) (not (<= y 3.1e-118))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-82) || !(y <= 3.1e-118)) {
		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 <= (-4.4d-82)) .or. (.not. (y <= 3.1d-118))) 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 <= -4.4e-82) || !(y <= 3.1e-118)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e-82) or not (y <= 3.1e-118):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e-82) || !(y <= 3.1e-118))
		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 <= -4.4e-82) || ~((y <= 3.1e-118)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e-82], N[Not[LessEqual[y, 3.1e-118]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.39999999999999971e-82 or 3.1000000000000001e-118 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-*r/ 68.2%

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

      2. neg-mul-1 68.2%

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

      3. sub-neg 68.2%

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

      4. +-commutative 68.2%

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

      5. distribute-neg-in 68.2%

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

      6. remove-double-neg 68.2%

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

      7. sub-neg 68.2%

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

      8. div-sub 68.3%

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

      9. *-inverses 68.3%

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

   5. Simplified 68.3%

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

   if -4.39999999999999971e-82 < y < 3.1000000000000001e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-82} \lor \neg \left(y \leq 3.1 \cdot 10^{-118}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+37) 1.0 (if (<= y 1.8e-35) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+37) {
		tmp = 1.0;
	} else if (y <= 1.8e-35) {
		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 <= (-1.2d+37)) then
        tmp = 1.0d0
    else if (y <= 1.8d-35) 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 <= -1.2e+37) {
		tmp = 1.0;
	} else if (y <= 1.8e-35) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+37:
		tmp = 1.0
	elif y <= 1.8e-35:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+37)
		tmp = 1.0;
	elseif (y <= 1.8e-35)
		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 <= -1.2e+37)
		tmp = 1.0;
	elseif (y <= 1.8e-35)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+37], 1.0, If[LessEqual[y, 1.8e-35], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e37 or 1.80000000000000009e-35 < 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 -1.2e37 < y < 1.80000000000000009e-35

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 66.0%

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

Alternative 7: 35.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 36.9%

   \[\leadsto \color{blue}{1} \]
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 2024176 
(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)))