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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

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. Final simplification 100.0%

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

Alternative 2: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.3 \cdot 10^{-23} \lor \neg \left(x \leq 4 \cdot 10^{+32}\right) \land x \leq 1.12 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{-x}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-5)
         (not (or (<= x 1.3e-23) (and (not (<= x 4e+32)) (<= x 1.12e+70)))))
   (/ (- x) (- y z))
   (/ y (- y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-5) || !((x <= 1.3e-23) || (!(x <= 4e+32) && (x <= 1.12e+70)))) {
		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 <= (-1.5d-5)) .or. (.not. (x <= 1.3d-23) .or. (.not. (x <= 4d+32)) .and. (x <= 1.12d+70))) 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 <= -1.5e-5) || !((x <= 1.3e-23) || (!(x <= 4e+32) && (x <= 1.12e+70)))) {
		tmp = -x / (y - z);
	} else {
		tmp = y / (y - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-5) or not ((x <= 1.3e-23) or (not (x <= 4e+32) and (x <= 1.12e+70))):
		tmp = -x / (y - z)
	else:
		tmp = y / (y - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-5) || !((x <= 1.3e-23) || (!(x <= 4e+32) && (x <= 1.12e+70))))
		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 <= -1.5e-5) || ~(((x <= 1.3e-23) || (~((x <= 4e+32)) && (x <= 1.12e+70)))))
		tmp = -x / (y - z);
	else
		tmp = y / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-5], N[Not[Or[LessEqual[x, 1.3e-23], And[N[Not[LessEqual[x, 4e+32]], $MachinePrecision], LessEqual[x, 1.12e+70]]]], $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 < -1.50000000000000004e-5 or 1.3e-23 < x < 4.00000000000000021e32 or 1.11999999999999993e70 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.9%

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

      1. neg-mul-1 80.9%

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

      2. distribute-neg-frac 80.9%

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

   6. Simplified 80.9%

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

   if -1.50000000000000004e-5 < x < 1.3e-23 or 4.00000000000000021e32 < x < 1.11999999999999993e70

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 82.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.3 \cdot 10^{-23} \lor \neg \left(x \leq 4 \cdot 10^{+32}\right) \land x \leq 1.12 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{-x}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 3: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-91}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+21}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+42)
   1.0
   (if (<= y 1e-91)
     (/ x z)
     (if (<= y 8e+21) (/ (- y) z) (if (<= y 4.3e+40) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+42) {
		tmp = 1.0;
	} else if (y <= 1e-91) {
		tmp = x / z;
	} else if (y <= 8e+21) {
		tmp = -y / z;
	} else if (y <= 4.3e+40) {
		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 <= (-1.65d+42)) then
        tmp = 1.0d0
    else if (y <= 1d-91) then
        tmp = x / z
    else if (y <= 8d+21) then
        tmp = -y / z
    else if (y <= 4.3d+40) 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 <= -1.65e+42) {
		tmp = 1.0;
	} else if (y <= 1e-91) {
		tmp = x / z;
	} else if (y <= 8e+21) {
		tmp = -y / z;
	} else if (y <= 4.3e+40) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+42:
		tmp = 1.0
	elif y <= 1e-91:
		tmp = x / z
	elif y <= 8e+21:
		tmp = -y / z
	elif y <= 4.3e+40:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+42)
		tmp = 1.0;
	elseif (y <= 1e-91)
		tmp = Float64(x / z);
	elseif (y <= 8e+21)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 4.3e+40)
		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 <= -1.65e+42)
		tmp = 1.0;
	elseif (y <= 1e-91)
		tmp = x / z;
	elseif (y <= 8e+21)
		tmp = -y / z;
	elseif (y <= 4.3e+40)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+42], 1.0, If[LessEqual[y, 1e-91], N[(x / z), $MachinePrecision], If[LessEqual[y, 8e+21], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 4.3e+40], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e42 or 4.3000000000000002e40 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 71.1%

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

   if -1.6499999999999999e42 < y < 1.00000000000000002e-91 or 8e21 < y < 4.3000000000000002e40

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 66.3%

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

   if 1.00000000000000002e-91 < y < 8e21

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 55.1%

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

   5. Taylor expanded in y around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. distribute-neg-frac 35.3%

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

   7. Simplified 35.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-91}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+21}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;1 + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+42)
   (+ 1.0 (/ z y))
   (if (<= y 1.02e-91)
     (/ x z)
     (if (<= y 2.8e+21) (/ (- y) z) (if (<= y 9.5e+40) (/ x z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+42) {
		tmp = 1.0 + (z / y);
	} else if (y <= 1.02e-91) {
		tmp = x / z;
	} else if (y <= 2.8e+21) {
		tmp = -y / z;
	} else if (y <= 9.5e+40) {
		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+42)) then
        tmp = 1.0d0 + (z / y)
    else if (y <= 1.02d-91) then
        tmp = x / z
    else if (y <= 2.8d+21) then
        tmp = -y / z
    else if (y <= 9.5d+40) 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+42) {
		tmp = 1.0 + (z / y);
	} else if (y <= 1.02e-91) {
		tmp = x / z;
	} else if (y <= 2.8e+21) {
		tmp = -y / z;
	} else if (y <= 9.5e+40) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+42:
		tmp = 1.0 + (z / y)
	elif y <= 1.02e-91:
		tmp = x / z
	elif y <= 2.8e+21:
		tmp = -y / z
	elif y <= 9.5e+40:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+42)
		tmp = Float64(1.0 + Float64(z / y));
	elseif (y <= 1.02e-91)
		tmp = Float64(x / z);
	elseif (y <= 2.8e+21)
		tmp = Float64(Float64(-y) / z);
	elseif (y <= 9.5e+40)
		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+42)
		tmp = 1.0 + (z / y);
	elseif (y <= 1.02e-91)
		tmp = x / z;
	elseif (y <= 2.8e+21)
		tmp = -y / z;
	elseif (y <= 9.5e+40)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+42], N[(1.0 + N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-91], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.8e+21], N[((-y) / z), $MachinePrecision], If[LessEqual[y, 9.5e+40], N[(x / z), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.04999999999999998e42

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 79.1%

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

   5. Taylor expanded in y around inf 67.4%

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

   if -1.04999999999999998e42 < y < 1.01999999999999994e-91 or 2.8e21 < y < 9.5000000000000003e40

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 66.3%

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

   if 1.01999999999999994e-91 < y < 2.8e21

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 55.1%

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

   5. Taylor expanded in y around 0 35.3%

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

      1. mul-1-neg 35.3%

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

      2. distribute-neg-frac 35.3%

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

   7. Simplified 35.3%

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

   if 9.5000000000000003e40 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 74.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;1 + \frac{z}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (- y z))))
   (if (<= y -3.5e-31)
     t_0
     (if (<= y 2.85e-92) (/ x z) (if (<= y 9.2e+59) t_0 (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double tmp;
	if (y <= -3.5e-31) {
		tmp = t_0;
	} else if (y <= 2.85e-92) {
		tmp = x / z;
	} else if (y <= 9.2e+59) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (y - z)
    if (y <= (-3.5d-31)) then
        tmp = t_0
    else if (y <= 2.85d-92) then
        tmp = x / z
    else if (y <= 9.2d+59) then
        tmp = t_0
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (y - z);
	double tmp;
	if (y <= -3.5e-31) {
		tmp = t_0;
	} else if (y <= 2.85e-92) {
		tmp = x / z;
	} else if (y <= 9.2e+59) {
		tmp = t_0;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (y - z)
	tmp = 0
	if y <= -3.5e-31:
		tmp = t_0
	elif y <= 2.85e-92:
		tmp = x / z
	elif y <= 9.2e+59:
		tmp = t_0
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(y - z))
	tmp = 0.0
	if (y <= -3.5e-31)
		tmp = t_0;
	elseif (y <= 2.85e-92)
		tmp = Float64(x / z);
	elseif (y <= 9.2e+59)
		tmp = t_0;
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (y - z);
	tmp = 0.0;
	if (y <= -3.5e-31)
		tmp = t_0;
	elseif (y <= 2.85e-92)
		tmp = x / z;
	elseif (y <= 9.2e+59)
		tmp = t_0;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-31], t$95$0, If[LessEqual[y, 2.85e-92], N[(x / z), $MachinePrecision], If[LessEqual[y, 9.2e+59], t$95$0, N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999985e-31 or 2.85000000000000004e-92 < y < 9.20000000000000032e59

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 65.9%

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

   if -3.49999999999999985e-31 < y < 2.85000000000000004e-92

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 70.4%

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

   if 9.20000000000000032e59 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 92.2%

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

      1. div-sub 92.3%

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

      2. *-inverses 92.3%

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

   6. Simplified 92.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 6: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+41} \lor \neg \left(y \leq 6 \cdot 10^{-86}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e+41) (not (<= y 6e-86))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+41) || !(y <= 6e-86)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.5d+41)) .or. (.not. (y <= 6d-86))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e+41) || !(y <= 6e-86)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e+41) or not (y <= 6e-86):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e+41) || !(y <= 6e-86))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e+41) || ~((y <= 6e-86)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e+41], N[Not[LessEqual[y, 6e-86]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000072e41 or 6.0000000000000002e-86 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. div-sub 73.9%

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

      2. *-inverses 73.9%

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

   6. Simplified 73.9%

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

   if -7.50000000000000072e41 < y < 6.0000000000000002e-86

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 67.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+41} \lor \neg \left(y \leq 6 \cdot 10^{-86}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 7: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-75} \lor \neg \left(z \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e-75) (not (<= z 1.8e-22))) (/ (- x y) z) (- 1.0 (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-75) || !(z <= 1.8e-22)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.2d-75)) .or. (.not. (z <= 1.8d-22))) then
        tmp = (x - y) / z
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-75) || !(z <= 1.8e-22)) {
		tmp = (x - y) / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e-75) or not (z <= 1.8e-22):
		tmp = (x - y) / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e-75) || !(z <= 1.8e-22))
		tmp = Float64(Float64(x - y) / z);
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e-75) || ~((z <= 1.8e-22)))
		tmp = (x - y) / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e-75], N[Not[LessEqual[z, 1.8e-22]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e-75 or 1.7999999999999999e-22 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 72.7%

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

      1. associate-*r/ 72.7%

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

      2. neg-mul-1 72.7%

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

      3. neg-sub0 72.7%

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

      4. associate--r- 72.7%

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

      5. neg-sub0 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in y around 0 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. sub-neg 72.7%

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

      4. div-sub 72.7%

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

   9. Simplified 72.7%

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

   if -5.2e-75 < z < 1.7999999999999999e-22

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 84.0%

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

      1. div-sub 84.0%

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

      2. *-inverses 84.0%

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

   6. Simplified 84.0%

      \[\leadsto \color{blue}{1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-75} \lor \neg \left(z \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 8: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+46) 1.0 (if (<= y 4.8e+40) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+46) {
		tmp = 1.0;
	} else if (y <= 4.8e+40) {
		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 <= (-2d+46)) then
        tmp = 1.0d0
    else if (y <= 4.8d+40) 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 <= -2e+46) {
		tmp = 1.0;
	} else if (y <= 4.8e+40) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+46:
		tmp = 1.0
	elif y <= 4.8e+40:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+46)
		tmp = 1.0;
	elseif (y <= 4.8e+40)
		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 <= -2e+46)
		tmp = 1.0;
	elseif (y <= 4.8e+40)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+46], 1.0, If[LessEqual[y, 4.8e+40], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2e46 or 4.8e40 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 71.1%

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

   if -2e46 < y < 4.8e40

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 56.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 34.6% 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%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

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

   4. associate-+l- 100.0%

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

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. sub-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. neg-sub0 100.0%

      \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + z} \]

   10. associate-+l- 100.0%

       \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - z\right)}} \]

   11. sub0-neg 100.0%

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

   12. neg-mul-1 100.0%

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

   13. times-frac 100.0%

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

   14. metadata-eval 100.0%

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

   15. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around inf 35.8%

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

5. Final simplification 35.8%

   \[\leadsto 1 \]

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 2023185 
(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)))