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

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 6

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: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+27)
   (- 1.0 (/ x y))
   (if (<= y 2.15e+15) (/ (- x y) z) (/ y (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+27) {
		tmp = 1.0 - (x / y);
	} else if (y <= 2.15e+15) {
		tmp = (x - y) / z;
	} 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 (y <= (-1.2d+27)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 2.15d+15) then
        tmp = (x - y) / z
    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 (y <= -1.2e+27) {
		tmp = 1.0 - (x / y);
	} else if (y <= 2.15e+15) {
		tmp = (x - y) / z;
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+27:
		tmp = 1.0 - (x / y)
	elif y <= 2.15e+15:
		tmp = (x - y) / z
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+27)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 2.15e+15)
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+27)
		tmp = 1.0 - (x / y);
	elseif (y <= 2.15e+15)
		tmp = (x - y) / z;
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+27], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+15], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999999e27

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. *-inverses N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      4. /-lowering-/.f64 81.6%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 81.6%

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

   if -1.19999999999999999e27 < y < 2.15e15

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(y - x\right)\right), \color{blue}{z}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(y - x\right)\right)\right), z\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right), z\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + y\right)\right)\right), z\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), z\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - y\right), z\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x - y\right), z\right) \]

      9. --lowering--.f64 82.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right) \]

   7. Simplified 82.2%

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

   if 2.15e15 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 82.6%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 82.6%

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

Alternative 3: 71.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{-62}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.45e-62)
   (- 1.0 (/ x y))
   (if (<= y 3.6e-25) (/ x z) (/ y (- y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.45e-62) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3.6e-25) {
		tmp = x / z;
	} 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 (y <= (-3.45d-62)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 3.6d-25) then
        tmp = x / z
    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 (y <= -3.45e-62) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3.6e-25) {
		tmp = x / z;
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.45e-62:
		tmp = 1.0 - (x / y)
	elif y <= 3.6e-25:
		tmp = x / z
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.45e-62)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 3.6e-25)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.45e-62)
		tmp = 1.0 - (x / y);
	elseif (y <= 3.6e-25)
		tmp = x / z;
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.45e-62], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-25], N[(x / z), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.44999999999999979e-62

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. *-inverses N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      4. /-lowering-/.f64 75.0%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 75.0%

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

   if -3.44999999999999979e-62 < y < 3.5999999999999999e-25

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 75.3%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{z}\right) \]

   7. Simplified 75.3%

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

   if 3.5999999999999999e-25 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 79.3%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 79.3%

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

Alternative 4: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.76 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.76e-62) t_0 (if (<= y 1.55e-39) (/ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.76e-62) {
		tmp = t_0;
	} else if (y <= 1.55e-39) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-1.76d-62)) then
        tmp = t_0
    else if (y <= 1.55d-39) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.76e-62) {
		tmp = t_0;
	} else if (y <= 1.55e-39) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -1.76e-62:
		tmp = t_0
	elif y <= 1.55e-39:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -1.76e-62)
		tmp = t_0;
	elseif (y <= 1.55e-39)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -1.76e-62)
		tmp = t_0;
	elseif (y <= 1.55e-39)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.76e-62], t$95$0, If[LessEqual[y, 1.55e-39], N[(x / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.76e-62 or 1.54999999999999985e-39 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. *-inverses N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      4. /-lowering-/.f64 73.2%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 73.2%

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

   if -1.76e-62 < y < 1.54999999999999985e-39

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{z}\right) \]

   7. Simplified 75.8%

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

Alternative 5: 62.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+49) 1.0 (if (<= y 1.18e+24) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+49) {
		tmp = 1.0;
	} else if (y <= 1.18e+24) {
		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 <= (-2.1d+49)) then
        tmp = 1.0d0
    else if (y <= 1.18d+24) 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 <= -2.1e+49) {
		tmp = 1.0;
	} else if (y <= 1.18e+24) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e+49:
		tmp = 1.0
	elif y <= 1.18e+24:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+49)
		tmp = 1.0;
	elseif (y <= 1.18e+24)
		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 <= -2.1e+49)
		tmp = 1.0;
	elseif (y <= 1.18e+24)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+49], 1.0, If[LessEqual[y, 1.18e+24], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000011e49 or 1.17999999999999997e24 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 65.2%

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

   if -2.10000000000000011e49 < y < 1.17999999999999997e24

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. neg-sub0 N/A

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

      4. associate-+l- N/A

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

      5. sub0-neg N/A

         \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

      6. distribute-frac-neg2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

      7. distribute-neg-frac N/A

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

      8. sub-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

      9. +-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

      10. distribute-neg-out N/A

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

      11. remove-double-neg N/A

          \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

      12. sub-neg N/A

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

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

      15. --lowering--.f64 100.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 65.9%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{z}\right) \]

   7. Simplified 65.9%

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

Alternative 6: 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. Step-by-step derivation

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. neg-sub0 N/A

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

   4. associate-+l- N/A

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

   5. sub0-neg N/A

      \[\leadsto \frac{x - y}{\mathsf{neg}\left(\left(y - z\right)\right)} \]

   6. distribute-frac-neg2 N/A

      \[\leadsto \mathsf{neg}\left(\frac{x - y}{y - z}\right) \]

   7. distribute-neg-frac N/A

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

   8. sub-neg N/A

      \[\leadsto \frac{\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)}{y - z} \]

   9. +-commutative N/A

      \[\leadsto \frac{\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)}{y - z} \]

   10. distribute-neg-out N/A

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

   11. remove-double-neg N/A

       \[\leadsto \frac{y + \left(\mathsf{neg}\left(x\right)\right)}{y - z} \]

   12. sub-neg N/A

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

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\left(y - x\right), \color{blue}{\left(y - z\right)}\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{y} - z\right)\right) \]

   15. --lowering--.f64 100.0%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
6. Step-by-step derivation

7. Simplified 36.3%

   \[\leadsto \color{blue}{1} \]
8. 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 2024138 
(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)))