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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 9

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: 58.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1300:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1300.0)
   1.0
   (if (<= y -3.5e-129)
     (/ (- x) y)
     (if (<= y 2.6e-98)
       (/ x z)
       (if (<= y 4.5e-27) (/ (- y) z) (if (<= y 1.52e+35) (/ x z) 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1300.0) {
		tmp = 1.0;
	} else if (y <= -3.5e-129) {
		tmp = -x / y;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if (y <= 4.5e-27) {
		tmp = -y / z;
	} else if (y <= 1.52e+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 <= (-1300.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.5d-129)) then
        tmp = -x / y
    else if (y <= 2.6d-98) then
        tmp = x / z
    else if (y <= 4.5d-27) then
        tmp = -y / z
    else if (y <= 1.52d+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 <= -1300.0) {
		tmp = 1.0;
	} else if (y <= -3.5e-129) {
		tmp = -x / y;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if (y <= 4.5e-27) {
		tmp = -y / z;
	} else if (y <= 1.52e+35) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1300.0:
		tmp = 1.0
	elif y <= -3.5e-129:
		tmp = -x / y
	elif y <= 2.6e-98:
		tmp = x / z
	elif y <= 4.5e-27:
		tmp = -y / z
	elif y <= 1.52e+35:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1300.0)
		tmp = 1.0;
	elseif (y <= -3.5e-129)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= 2.6e-98)
		tmp = Float64(x / z);
	elseif (y <= 4.5e-27)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 1.52e+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 <= -1300.0)
		tmp = 1.0;
	elseif (y <= -3.5e-129)
		tmp = -x / y;
	elseif (y <= 2.6e-98)
		tmp = x / z;
	elseif (y <= 4.5e-27)
		tmp = -y / z;
	elseif (y <= 1.52e+35)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1300.0], 1.0, If[LessEqual[y, -3.5e-129], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 2.6e-98], N[(x / z), $MachinePrecision], If[LessEqual[y, 4.5e-27], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 1.52e+35], N[(x / z), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1300 or 1.5200000000000001e35 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 58.7%

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

   if -1300 < y < -3.4999999999999997e-129

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. +-commutative 99.9%

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

      5. sub-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. associate-/r* 99.9%

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

      8. div-sub 99.9%

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

      9. remove-double-neg 99.9%

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

      10. neg-mul-1 99.9%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 99.9%

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

      13. metadata-eval 99.9%

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

      14. *-lft-identity 99.9%

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

      15. remove-double-neg 99.9%

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

      16. neg-mul-1 99.9%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 99.9%

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

      19. metadata-eval 99.9%

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

      20. *-lft-identity 99.9%

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

      21. unsub-neg 99.9%

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

      22. remove-double-neg 99.9%

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

      23. +-commutative 99.9%

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

      24. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in y around inf 42.9%

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

      1. associate-*r/ 42.9%

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

      2. mul-1-neg 42.9%

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

   10. Simplified 42.9%

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

   if -3.4999999999999997e-129 < y < 2.60000000000000013e-98 or 4.5000000000000002e-27 < y < 1.5200000000000001e35

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.5%

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

   if 2.60000000000000013e-98 < y < 4.5000000000000002e-27

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. sub-neg 83.5%

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

      3. mul-1-neg 83.5%

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

      4. distribute-lft-in 83.5%

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

      5. neg-mul-1 83.5%

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

      6. neg-mul-1 83.5%

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

      7. mul-1-neg 83.5%

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

      8. remove-double-neg 83.5%

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

      9. +-commutative 83.5%

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

      10. unsub-neg 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in x around 0 66.6%

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

       1. neg-mul-1 66.6%

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

       2. distribute-neg-frac 66.6%

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

   12. Simplified 66.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1300:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+61} \lor \neg \left(y \leq 1.75 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -3.5e-129)
     t_0
     (if (<= y 2.6e-98)
       (/ x z)
       (if (or (<= y 1e+61) (not (<= y 1.75e+174))) (/ y (- y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.5e-129) {
		tmp = t_0;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if ((y <= 1e+61) || !(y <= 1.75e+174)) {
		tmp = y / (y - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-3.5d-129)) then
        tmp = t_0
    else if (y <= 2.6d-98) then
        tmp = x / z
    else if ((y <= 1d+61) .or. (.not. (y <= 1.75d+174))) then
        tmp = y / (y - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.5e-129) {
		tmp = t_0;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if ((y <= 1e+61) || !(y <= 1.75e+174)) {
		tmp = y / (y - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -3.5e-129:
		tmp = t_0
	elif y <= 2.6e-98:
		tmp = x / z
	elif (y <= 1e+61) or not (y <= 1.75e+174):
		tmp = y / (y - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -3.5e-129)
		tmp = t_0;
	elseif (y <= 2.6e-98)
		tmp = Float64(x / z);
	elseif ((y <= 1e+61) || !(y <= 1.75e+174))
		tmp = Float64(y / Float64(y - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -3.5e-129)
		tmp = t_0;
	elseif (y <= 2.6e-98)
		tmp = x / z;
	elseif ((y <= 1e+61) || ~((y <= 1.75e+174)))
		tmp = y / (y - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-129], t$95$0, If[LessEqual[y, 2.6e-98], N[(x / z), $MachinePrecision], If[Or[LessEqual[y, 1e+61], N[Not[LessEqual[y, 1.75e+174]], $MachinePrecision]], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999997e-129 or 9.99999999999999949e60 < y < 1.7500000000000001e174

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 72.5%

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

      1. div-sub 72.5%

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

      2. *-inverses 72.5%

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

   7. Simplified 72.5%

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

   if -3.4999999999999997e-129 < y < 2.60000000000000013e-98

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.8%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 87.3%

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

   if 2.60000000000000013e-98 < y < 9.99999999999999949e60 or 1.7500000000000001e174 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 73.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{+61} \lor \neg \left(y \leq 1.75 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1.95e-131)
     t_0
     (if (<= y 2.6e-98)
       (/ x z)
       (if (<= y 3.6e-27) (/ (- y) z) (if (<= y 1.75e+31) (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1.95e-131) {
		tmp = t_0;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if (y <= 3.6e-27) {
		tmp = -y / z;
	} else if (y <= 1.75e+31) {
		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 <= (-1.95d-131)) then
        tmp = t_0
    else if (y <= 2.6d-98) then
        tmp = x / z
    else if (y <= 3.6d-27) then
        tmp = -y / z
    else if (y <= 1.75d+31) 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 <= -1.95e-131) {
		tmp = t_0;
	} else if (y <= 2.6e-98) {
		tmp = x / z;
	} else if (y <= 3.6e-27) {
		tmp = -y / z;
	} else if (y <= 1.75e+31) {
		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 <= -1.95e-131:
		tmp = t_0
	elif y <= 2.6e-98:
		tmp = x / z
	elif y <= 3.6e-27:
		tmp = -y / z
	elif y <= 1.75e+31:
		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 <= -1.95e-131)
		tmp = t_0;
	elseif (y <= 2.6e-98)
		tmp = Float64(x / z);
	elseif (y <= 3.6e-27)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 1.75e+31)
		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 <= -1.95e-131)
		tmp = t_0;
	elseif (y <= 2.6e-98)
		tmp = x / z;
	elseif (y <= 3.6e-27)
		tmp = -y / z;
	elseif (y <= 1.75e+31)
		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, -1.95e-131], t$95$0, If[LessEqual[y, 2.6e-98], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.6e-27], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 1.75e+31], N[(x / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e-131 or 1.75e31 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 72.4%

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

      1. div-sub 72.4%

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

      2. *-inverses 72.4%

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

   7. Simplified 72.4%

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

   if -1.9500000000000001e-131 < y < 2.60000000000000013e-98 or 3.5999999999999999e-27 < y < 1.75e31

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.8%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.3%

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

   if 2.60000000000000013e-98 < y < 3.5999999999999999e-27

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. sub-neg 83.5%

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

      3. mul-1-neg 83.5%

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

      4. distribute-lft-in 83.5%

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

      5. neg-mul-1 83.5%

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

      6. neg-mul-1 83.5%

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

      7. mul-1-neg 83.5%

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

      8. remove-double-neg 83.5%

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

      9. +-commutative 83.5%

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

      10. unsub-neg 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in x around 0 66.6%

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

       1. neg-mul-1 66.6%

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

       2. distribute-neg-frac 66.6%

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

   12. Simplified 66.6%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-131}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1050000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1050000.0)
   1.0
   (if (<= y -2.5e-130) (/ (- x) y) (if (<= y 2.35e+35) (/ x z) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1050000.0) {
		tmp = 1.0;
	} else if (y <= -2.5e-130) {
		tmp = -x / y;
	} else if (y <= 2.35e+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 <= (-1050000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-2.5d-130)) then
        tmp = -x / y
    else if (y <= 2.35d+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 <= -1050000.0) {
		tmp = 1.0;
	} else if (y <= -2.5e-130) {
		tmp = -x / y;
	} else if (y <= 2.35e+35) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1050000.0:
		tmp = 1.0
	elif y <= -2.5e-130:
		tmp = -x / y
	elif y <= 2.35e+35:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1050000.0)
		tmp = 1.0;
	elseif (y <= -2.5e-130)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= 2.35e+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 <= -1050000.0)
		tmp = 1.0;
	elseif (y <= -2.5e-130)
		tmp = -x / y;
	elseif (y <= 2.35e+35)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1050000.0], 1.0, If[LessEqual[y, -2.5e-130], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 2.35e+35], N[(x / z), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e6 or 2.35000000000000017e35 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 58.7%

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

   if -1.05e6 < y < -2.4999999999999998e-130

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-neg-in 99.9%

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

      4. +-commutative 99.9%

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

      5. sub-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. associate-/r* 99.9%

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

      8. div-sub 99.9%

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

      9. remove-double-neg 99.9%

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

      10. neg-mul-1 99.9%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 99.9%

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

      13. metadata-eval 99.9%

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

      14. *-lft-identity 99.9%

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

      15. remove-double-neg 99.9%

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

      16. neg-mul-1 99.9%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 99.9%

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

      19. metadata-eval 99.9%

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

      20. *-lft-identity 99.9%

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

      21. unsub-neg 99.9%

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

      22. remove-double-neg 99.9%

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

      23. +-commutative 99.9%

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

      24. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in y around inf 42.9%

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

      1. associate-*r/ 42.9%

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

      2. mul-1-neg 42.9%

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

   10. Simplified 42.9%

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

   if -2.4999999999999998e-130 < y < 2.35000000000000017e35

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1050000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2200 \lor \neg \left(x \leq 0.0006\right):\\ \;\;\;\;\frac{-x}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2200.0) (not (<= x 0.0006))) (/ (- x) (- y z)) (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2200.0) || !(x <= 0.0006)) {
		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 ((x <= (-2200.0d0)) .or. (.not. (x <= 0.0006d0))) 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 ((x <= -2200.0) || !(x <= 0.0006)) {
		tmp = -x / (y - z);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2200.0) or not (x <= 0.0006):
		tmp = -x / (y - z)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2200.0) || !(x <= 0.0006))
		tmp = Float64(Float64(-x) / Float64(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 ((x <= -2200.0) || ~((x <= 0.0006)))
		tmp = -x / (y - z);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2200.0], N[Not[LessEqual[x, 0.0006]], $MachinePrecision]], N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2200 or 5.99999999999999947e-4 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.8%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 78.3%

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

      1. neg-mul-1 78.3%

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

      2. distribute-neg-frac 78.3%

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

   7. Simplified 78.3%

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

   if -2200 < x < 5.99999999999999947e-4

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 100.0%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 82.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2200 \lor \neg \left(x \leq 0.0006\right):\\ \;\;\;\;\frac{-x}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-91} \lor \neg \left(y \leq 7.6 \cdot 10^{+47}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-91) (not (<= y 7.6e+47))) (- 1.0 (/ x y)) (/ (- x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-91) || !(y <= 7.6e+47)) {
		tmp = 1.0 - (x / y);
	} 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 <= (-3.4d-91)) .or. (.not. (y <= 7.6d+47))) then
        tmp = 1.0d0 - (x / y)
    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 <= -3.4e-91) || !(y <= 7.6e+47)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = (x - y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-91) or not (y <= 7.6e+47):
		tmp = 1.0 - (x / y)
	else:
		tmp = (x - y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-91) || !(y <= 7.6e+47))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(Float64(x - y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-91) || ~((y <= 7.6e+47)))
		tmp = 1.0 - (x / y);
	else
		tmp = (x - y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-91], N[Not[LessEqual[y, 7.6e+47]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000027e-91 or 7.6000000000000007e47 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 74.7%

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

      1. div-sub 74.7%

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

      2. *-inverses 74.7%

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

   7. Simplified 74.7%

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

   if -3.40000000000000027e-91 < y < 7.6000000000000007e47

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 86.6%

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

      1. associate-*r/ 86.6%

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

      2. sub-neg 86.6%

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

      3. mul-1-neg 86.6%

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

      4. distribute-lft-in 86.6%

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

      5. neg-mul-1 86.6%

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

      6. neg-mul-1 86.6%

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

      7. mul-1-neg 86.6%

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

      8. remove-double-neg 86.6%

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

      9. +-commutative 86.6%

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

      10. unsub-neg 86.6%

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

   9. Simplified 86.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-91} \lor \neg \left(y \leq 7.6 \cdot 10^{+47}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.4e+36) 1.0 (if (<= y 1.26e+35) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.4e+36) {
		tmp = 1.0;
	} else if (y <= 1.26e+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 <= (-5.4d+36)) then
        tmp = 1.0d0
    else if (y <= 1.26d+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 <= -5.4e+36) {
		tmp = 1.0;
	} else if (y <= 1.26e+35) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.4e+36:
		tmp = 1.0
	elif y <= 1.26e+35:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.4e+36)
		tmp = 1.0;
	elseif (y <= 1.26e+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 <= -5.4e+36)
		tmp = 1.0;
	elseif (y <= 1.26e+35)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.4e+36], 1.0, If[LessEqual[y, 1.26e+35], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4000000000000002e36 or 1.26e35 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.8%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 60.7%

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

   if -5.4000000000000002e36 < y < 1.26e35

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. remove-double-neg 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. sub-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-/r* 100.0%

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

      8. div-sub 100.0%

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

      9. remove-double-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. associate-/l* 99.9%

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

      12. associate-/r/ 100.0%

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

      13. metadata-eval 100.0%

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

      14. *-lft-identity 100.0%

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

      15. remove-double-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

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

      20. *-lft-identity 100.0%

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

      21. unsub-neg 100.0%

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

      22. remove-double-neg 100.0%

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

      23. +-commutative 100.0%

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

      24. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 65.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 100.0%

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

   2. remove-double-neg 100.0%

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

   3. distribute-neg-in 100.0%

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

   4. +-commutative 100.0%

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

   5. sub-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-/r* 100.0%

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

   8. div-sub 100.0%

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

   9. remove-double-neg 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate-/l* 99.9%

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

   12. associate-/r/ 100.0%

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

   13. metadata-eval 100.0%

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

   14. *-lft-identity 100.0%

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

   15. remove-double-neg 100.0%

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

   16. neg-mul-1 100.0%

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

   17. associate-/l* 99.9%

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

   18. associate-/r/ 100.0%

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

   19. metadata-eval 100.0%

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

   20. *-lft-identity 100.0%

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

   21. unsub-neg 100.0%

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

   22. remove-double-neg 100.0%

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

   23. +-commutative 100.0%

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

   24. sub-neg 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 33.4%

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

6. Final simplification 33.4%

   \[\leadsto 1 \]
7. 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 2024020 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

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