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

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

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

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

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

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

Java

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

Python

def code(x, y, z):
	return (x - y) / (z - y)

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]

2. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+34)
   1.0
   (if (<= y 2e-40)
     (/ x z)
     (if (<= y 4.8e-9)
       (/ (- y) z)
       (if (<= y 7.5e+28) 1.0 (if (<= y 6.8e+155) (/ (- x) y) 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+34) {
		tmp = 1.0;
	} else if (y <= 2e-40) {
		tmp = x / z;
	} else if (y <= 4.8e-9) {
		tmp = -y / z;
	} else if (y <= 7.5e+28) {
		tmp = 1.0;
	} else if (y <= 6.8e+155) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.35d+34)) then
        tmp = 1.0d0
    else if (y <= 2d-40) then
        tmp = x / z
    else if (y <= 4.8d-9) then
        tmp = -y / z
    else if (y <= 7.5d+28) then
        tmp = 1.0d0
    else if (y <= 6.8d+155) then
        tmp = -x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+34) {
		tmp = 1.0;
	} else if (y <= 2e-40) {
		tmp = x / z;
	} else if (y <= 4.8e-9) {
		tmp = -y / z;
	} else if (y <= 7.5e+28) {
		tmp = 1.0;
	} else if (y <= 6.8e+155) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+34:
		tmp = 1.0
	elif y <= 2e-40:
		tmp = x / z
	elif y <= 4.8e-9:
		tmp = -y / z
	elif y <= 7.5e+28:
		tmp = 1.0
	elif y <= 6.8e+155:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+34)
		tmp = 1.0;
	elseif (y <= 2e-40)
		tmp = Float64(x / z);
	elseif (y <= 4.8e-9)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 7.5e+28)
		tmp = 1.0;
	elseif (y <= 6.8e+155)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+34)
		tmp = 1.0;
	elseif (y <= 2e-40)
		tmp = x / z;
	elseif (y <= 4.8e-9)
		tmp = -y / z;
	elseif (y <= 7.5e+28)
		tmp = 1.0;
	elseif (y <= 6.8e+155)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+34], 1.0, If[LessEqual[y, 2e-40], N[(x / z), $MachinePrecision], If[LessEqual[y, 4.8e-9], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 7.5e+28], 1.0, If[LessEqual[y, 6.8e+155], N[((-x) / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35e34 or 4.8e-9 < y < 7.4999999999999998e28 or 6.8000000000000002e155 < y

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-/r/ 99.9%

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

      4. associate-/l* 99.8%

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

      5. neg-mul-1 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. distribute-neg-out 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. associate-/l* 99.9%

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

      12. neg-mul-1 99.9%

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

      13. sub-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. distribute-neg-out 99.9%

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

      16. remove-double-neg 99.9%

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

      17. 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. Taylor expanded in y around inf 71.8%

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

   if -1.35e34 < y < 1.9999999999999999e-40

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in y around 0 61.7%

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

   if 1.9999999999999999e-40 < y < 4.8e-9

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.6%

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

      5. neg-mul-1 99.6%

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

      6. sub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-neg-out 99.6%

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

      9. remove-double-neg 99.6%

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

      10. sub-neg 99.6%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around 0 86.5%

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

   5. Taylor expanded in y around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

   if 7.4999999999999998e28 < y < 6.8000000000000002e155

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.6%

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

      5. neg-mul-1 99.6%

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

      6. sub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-neg-out 99.6%

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

      9. remove-double-neg 99.6%

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

      10. sub-neg 99.6%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around inf 53.9%

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

      1. neg-mul-1 53.9%

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

      2. distribute-neg-frac 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around inf 50.2%

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

      1. associate-*r/ 50.2%

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

      2. mul-1-neg 50.2%

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

   9. Simplified 50.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-48} \lor \neg \left(x \leq 2.35 \cdot 10^{-46} \lor \neg \left(x \leq 2020000000000\right) \land x \leq 2.15 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-48)
         (not
          (or (<= x 2.35e-46)
              (and (not (<= x 2020000000000.0)) (<= x 2.15e+36)))))
   (/ x (- z y))
   (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-48) || !((x <= 2.35e-46) || (!(x <= 2020000000000.0) && (x <= 2.15e+36)))) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.5d-48)) .or. (.not. (x <= 2.35d-46) .or. (.not. (x <= 2020000000000.0d0)) .and. (x <= 2.15d+36))) then
        tmp = x / (z - y)
    else
        tmp = y / (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-48) || !((x <= 2.35e-46) || (!(x <= 2020000000000.0) && (x <= 2.15e+36)))) {
		tmp = x / (z - y);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-48) or not ((x <= 2.35e-46) or (not (x <= 2020000000000.0) and (x <= 2.15e+36))):
		tmp = x / (z - y)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-48) || !((x <= 2.35e-46) || (!(x <= 2020000000000.0) && (x <= 2.15e+36))))
		tmp = Float64(x / Float64(z - y));
	else
		tmp = Float64(y / Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e-48) || ~(((x <= 2.35e-46) || (~((x <= 2020000000000.0)) && (x <= 2.15e+36)))))
		tmp = x / (z - y);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-48], N[Not[Or[LessEqual[x, 2.35e-46], And[N[Not[LessEqual[x, 2020000000000.0]], $MachinePrecision], LessEqual[x, 2.15e+36]]]], $MachinePrecision]], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e-48 or 2.34999999999999983e-46 < x < 2.02e12 or 2.15000000000000002e36 < x

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.7%

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

      4. associate-/l* 99.6%

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

      5. neg-mul-1 99.6%

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

      6. sub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-neg-out 99.6%

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

      9. remove-double-neg 99.6%

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

      10. sub-neg 99.6%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around inf 80.3%

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

      1. neg-mul-1 80.3%

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

      2. distribute-neg-frac 80.3%

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

   6. Simplified 80.3%

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

      1. frac-2neg 80.3%

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

      2. div-inv 79.9%

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

      3. remove-double-neg 79.9%

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

   8. Applied egg-rr 79.9%

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

   9. Taylor expanded in x around 0 80.3%

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

   if -1.5e-48 < x < 2.34999999999999983e-46 or 2.02e12 < x < 2.15000000000000002e36

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.9%

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

      4. associate-/l* 99.8%

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

      5. neg-mul-1 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. distribute-neg-out 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around 0 86.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-48} \lor \neg \left(x \leq 2.35 \cdot 10^{-46} \lor \neg \left(x \leq 2020000000000\right) \land x \leq 2.15 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 4: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 225000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -7.2e-40)
     t_0
     (if (<= y 1.7e-41) (/ x z) (if (<= y 225000.0) (/ (- y) z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -7.2e-40) {
		tmp = t_0;
	} else if (y <= 1.7e-41) {
		tmp = x / z;
	} else if (y <= 225000.0) {
		tmp = -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 <= (-7.2d-40)) then
        tmp = t_0
    else if (y <= 1.7d-41) then
        tmp = x / z
    else if (y <= 225000.0d0) then
        tmp = -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 <= -7.2e-40) {
		tmp = t_0;
	} else if (y <= 1.7e-41) {
		tmp = x / z;
	} else if (y <= 225000.0) {
		tmp = -y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -7.2e-40:
		tmp = t_0
	elif y <= 1.7e-41:
		tmp = x / z
	elif y <= 225000.0:
		tmp = -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 <= -7.2e-40)
		tmp = t_0;
	elseif (y <= 1.7e-41)
		tmp = Float64(x / z);
	elseif (y <= 225000.0)
		tmp = Float64(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 <= -7.2e-40)
		tmp = t_0;
	elseif (y <= 1.7e-41)
		tmp = x / z;
	elseif (y <= 225000.0)
		tmp = -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, -7.2e-40], t$95$0, If[LessEqual[y, 1.7e-41], N[(x / z), $MachinePrecision], If[LessEqual[y, 225000.0], N[((-y) / z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e-40 or 225000 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in z around 0 76.7%

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

      1. div-sub 76.7%

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

      2. *-inverses 76.7%

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

   6. Simplified 76.7%

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

   if -7.2e-40 < y < 1.6999999999999999e-41

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in y around 0 64.9%

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

   if 1.6999999999999999e-41 < y < 225000

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around 0 80.7%

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

   5. Taylor expanded in y around 0 70.8%

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

      1. associate-*r/ 70.8%

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

      2. neg-mul-1 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-40}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 225000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 225000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -9e+34)
     t_0
     (if (<= y 8e-39) (/ x (- z y)) (if (<= y 225000.0) (/ (- y) z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -9e+34) {
		tmp = t_0;
	} else if (y <= 8e-39) {
		tmp = x / (z - y);
	} else if (y <= 225000.0) {
		tmp = -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 <= (-9d+34)) then
        tmp = t_0
    else if (y <= 8d-39) then
        tmp = x / (z - y)
    else if (y <= 225000.0d0) then
        tmp = -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 <= -9e+34) {
		tmp = t_0;
	} else if (y <= 8e-39) {
		tmp = x / (z - y);
	} else if (y <= 225000.0) {
		tmp = -y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -9e+34:
		tmp = t_0
	elif y <= 8e-39:
		tmp = x / (z - y)
	elif y <= 225000.0:
		tmp = -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 <= -9e+34)
		tmp = t_0;
	elseif (y <= 8e-39)
		tmp = Float64(x / Float64(z - y));
	elseif (y <= 225000.0)
		tmp = Float64(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 <= -9e+34)
		tmp = t_0;
	elseif (y <= 8e-39)
		tmp = x / (z - y);
	elseif (y <= 225000.0)
		tmp = -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, -9e+34], t$95$0, If[LessEqual[y, 8e-39], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 225000.0], N[((-y) / z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000001e34 or 225000 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in z around 0 81.2%

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

      1. div-sub 81.2%

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

      2. *-inverses 81.2%

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

   6. Simplified 81.2%

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

   if -9.0000000000000001e34 < y < 7.99999999999999943e-39

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around inf 75.7%

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

      1. neg-mul-1 75.7%

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

      2. distribute-neg-frac 75.7%

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

   6. Simplified 75.7%

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

      1. frac-2neg 75.7%

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

      2. div-inv 75.4%

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

      3. remove-double-neg 75.4%

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

   8. Applied egg-rr 75.4%

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

   9. Taylor expanded in x around 0 75.7%

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

   if 7.99999999999999943e-39 < y < 225000

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around 0 80.7%

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

   5. Taylor expanded in y around 0 70.8%

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

      1. associate-*r/ 70.8%

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

      2. neg-mul-1 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+34}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 225000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 6: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+33)
   1.0
   (if (<= y 2.9e+28) (/ x z) (if (<= y 6.8e+155) (/ (- x) y) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+33) {
		tmp = 1.0;
	} else if (y <= 2.9e+28) {
		tmp = x / z;
	} else if (y <= 6.8e+155) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.2d+33)) then
        tmp = 1.0d0
    else if (y <= 2.9d+28) then
        tmp = x / z
    else if (y <= 6.8d+155) then
        tmp = -x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+33) {
		tmp = 1.0;
	} else if (y <= 2.9e+28) {
		tmp = x / z;
	} else if (y <= 6.8e+155) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+33:
		tmp = 1.0
	elif y <= 2.9e+28:
		tmp = x / z
	elif y <= 6.8e+155:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+33)
		tmp = 1.0;
	elseif (y <= 2.9e+28)
		tmp = Float64(x / z);
	elseif (y <= 6.8e+155)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.2e+33)
		tmp = 1.0;
	elseif (y <= 2.9e+28)
		tmp = x / z;
	elseif (y <= 6.8e+155)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+33], 1.0, If[LessEqual[y, 2.9e+28], N[(x / z), $MachinePrecision], If[LessEqual[y, 6.8e+155], N[((-x) / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2000000000000005e33 or 6.8000000000000002e155 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.9%

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

      4. associate-/l* 99.8%

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

      5. neg-mul-1 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. distribute-neg-out 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in y around inf 75.7%

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

   if -7.2000000000000005e33 < y < 2.9000000000000001e28

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 99.9%

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

      12. neg-mul-1 99.9%

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

      13. sub-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. distribute-neg-out 99.9%

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

      16. remove-double-neg 99.9%

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

      17. 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. Taylor expanded in y around 0 57.7%

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

   if 2.9000000000000001e28 < y < 6.8000000000000002e155

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.6%

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

      5. neg-mul-1 99.6%

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

      6. sub-neg 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-neg-out 99.6%

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

      9. remove-double-neg 99.6%

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

      10. sub-neg 99.6%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in x around inf 53.9%

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

      1. neg-mul-1 53.9%

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

      2. distribute-neg-frac 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around inf 50.2%

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

      1. associate-*r/ 50.2%

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

      2. mul-1-neg 50.2%

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

   9. Simplified 50.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+155}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+37) 1.0 (if (<= y 900000000.0) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+37) {
		tmp = 1.0;
	} else if (y <= 900000000.0) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.05d+37)) then
        tmp = 1.0d0
    else if (y <= 900000000.0d0) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+37) {
		tmp = 1.0;
	} else if (y <= 900000000.0) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+37:
		tmp = 1.0
	elif y <= 900000000.0:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+37)
		tmp = 1.0;
	elseif (y <= 900000000.0)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+37)
		tmp = 1.0;
	elseif (y <= 900000000.0)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+37], 1.0, If[LessEqual[y, 900000000.0], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e37 or 9e8 < y

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in y around inf 60.9%

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

   if -1.0500000000000001e37 < y < 9e8

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-/r/ 99.8%

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

      4. associate-/l* 99.7%

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

      5. neg-mul-1 99.7%

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

      6. sub-neg 99.7%

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

      7. +-commutative 99.7%

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

      8. distribute-neg-out 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. associate-/l* 100.0%

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

      12. neg-mul-1 100.0%

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

      13. sub-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-out 100.0%

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

      16. remove-double-neg 100.0%

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

      17. 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. Taylor expanded in y around 0 59.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 35.4% 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. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. associate-/r/ 99.8%

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

   4. associate-/l* 99.7%

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

   5. neg-mul-1 99.7%

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

   6. sub-neg 99.7%

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

   7. +-commutative 99.7%

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

   8. distribute-neg-out 99.7%

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

   9. remove-double-neg 99.7%

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

   10. sub-neg 99.7%

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

   11. associate-/l* 100.0%

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

   12. neg-mul-1 100.0%

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

   13. sub-neg 100.0%

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

   14. +-commutative 100.0%

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

   15. distribute-neg-out 100.0%

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

   16. remove-double-neg 100.0%

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

   17. 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. Taylor expanded in y around inf 32.8%

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

5. Final simplification 32.8%

   \[\leadsto 1 \]

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 2023336 
(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)))