Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.3% → 95.4%

Time: 7.7s

Alternatives: 8

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

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

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)) / z
end function

Java

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

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

C

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

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)) / z
end function

Java

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

Python

def code(x, y, z):
	return (x * (y + z)) / z

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.5e+64) (fma x (/ y z) x) (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e+64) {
		tmp = fma(x, (y / z), x);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.5e+64)
		tmp = fma(x, Float64(y / z), x);
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.5e+64], N[(x * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5000000000000001e64

   1. Initial program 82.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.7%

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

      2. remove-double-neg 80.7%

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

      3. unsub-neg 80.7%

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

      4. distribute-rgt-out-- 76.4%

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

      5. associate-*r/ 73.9%

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

      6. *-commutative 73.9%

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

      7. associate-*r/ 74.6%

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

      8. associate-*r/ 80.9%

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

      9. distribute-lft-neg-out 80.9%

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

      10. distribute-frac-neg 80.9%

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

      11. distribute-frac-neg2 80.9%

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

      12. fma-neg 80.9%

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

      13. distribute-frac-neg 80.9%

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

      14. distribute-lft-neg-out 80.9%

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

      15. *-commutative 80.9%

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

      16. associate-/l* 97.5%

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

      17. *-inverses 97.5%

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

      18. *-rgt-identity 97.5%

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

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
   4. Add Preprocessing

   if 1.5000000000000001e64 < y

   1. Initial program 88.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

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

      2. associate-/l* 98.2%

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

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-13} \lor \neg \left(y \leq 1.32 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.02e-13) (not (<= y 1.32e-86))) (* y (/ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e-13) || !(y <= 1.32e-86)) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	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 <= (-1.02d-13)) .or. (.not. (y <= 1.32d-86))) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.02e-13) || !(y <= 1.32e-86)) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.02e-13) or not (y <= 1.32e-86):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.02e-13) || !(y <= 1.32e-86))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.02e-13) || ~((y <= 1.32e-86)))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.02e-13], N[Not[LessEqual[y, 1.32e-86]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.0199999999999999e-13 or 1.32e-86 < y

   1. Initial program 86.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.1%

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

      2. remove-double-neg 92.1%

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

      3. distribute-frac-neg2 92.1%

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

      4. neg-sub0 92.1%

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

      5. remove-double-neg 92.1%

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

      6. unsub-neg 92.1%

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

      7. div-sub 92.1%

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

      8. *-inverses 92.1%

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

      9. metadata-eval 92.1%

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

      10. associate--r- 92.1%

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

      11. neg-sub0 92.1%

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

      12. distribute-frac-neg2 92.1%

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

      13. remove-double-neg 92.1%

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

      14. sub-neg 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around inf 69.6%

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

      1. associate-*l/ 71.4%

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

      2. *-commutative 71.4%

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

   7. Simplified 71.4%

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

   if -1.0199999999999999e-13 < y < 1.32e-86

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

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

      5. remove-double-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. div-sub 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r- 100.0%

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

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 80.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-13} \lor \neg \left(y \leq 1.32 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e+30) x (if (<= z 3e-89) (/ (* y x) z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+30) {
		tmp = x;
	} else if (z <= 3e-89) {
		tmp = (y * x) / z;
	} else {
		tmp = x;
	}
	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 <= (-3.8d+30)) then
        tmp = x
    else if (z <= 3d-89) then
        tmp = (y * x) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+30) {
		tmp = x;
	} else if (z <= 3e-89) {
		tmp = (y * x) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e+30:
		tmp = x
	elif z <= 3e-89:
		tmp = (y * x) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e+30)
		tmp = x;
	elseif (z <= 3e-89)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.8e+30)
		tmp = x;
	elseif (z <= 3e-89)
		tmp = (y * x) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e+30], x, If[LessEqual[z, 3e-89], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000001e30 or 2.9999999999999999e-89 < z

   1. Initial program 74.9%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

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

      2. remove-double-neg 99.2%

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

      3. distribute-frac-neg2 99.2%

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

      4. neg-sub0 99.2%

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

      5. remove-double-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. div-sub 99.2%

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

      8. *-inverses 99.2%

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

      9. metadata-eval 99.2%

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

      10. associate--r- 99.2%

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

      11. neg-sub0 99.2%

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

      12. distribute-frac-neg2 99.2%

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

      13. remove-double-neg 99.2%

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

      14. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 76.3%

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

   if -3.8000000000000001e30 < z < 2.9999999999999999e-89

   1. Initial program 94.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.9%

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

      2. remove-double-neg 90.9%

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

      3. distribute-frac-neg2 90.9%

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

      4. neg-sub0 90.9%

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

      5. remove-double-neg 90.9%

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

      6. unsub-neg 90.9%

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

      7. div-sub 91.0%

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

      8. *-inverses 91.0%

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

      9. metadata-eval 91.0%

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

      10. associate--r- 91.0%

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

      11. neg-sub0 91.0%

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

      12. distribute-frac-neg2 91.0%

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

      13. remove-double-neg 91.0%

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

      14. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 78.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-14) (/ y (/ z x)) (if (<= y 1.18e-86) x (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-14) {
		tmp = y / (z / x);
	} else if (y <= 1.18e-86) {
		tmp = x;
	} else {
		tmp = y * (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 <= (-5d-14)) then
        tmp = y / (z / x)
    else if (y <= 1.18d-86) then
        tmp = x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-14) {
		tmp = y / (z / x);
	} else if (y <= 1.18e-86) {
		tmp = x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-14:
		tmp = y / (z / x)
	elif y <= 1.18e-86:
		tmp = x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-14)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 1.18e-86)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-14)
		tmp = y / (z / x);
	elseif (y <= 1.18e-86)
		tmp = x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-14], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e-86], x, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e-14

   1. Initial program 83.2%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.4%

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

      2. remove-double-neg 91.4%

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

      3. distribute-frac-neg2 91.4%

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

      4. neg-sub0 91.4%

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

      5. remove-double-neg 91.4%

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

      6. unsub-neg 91.4%

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

      7. div-sub 91.5%

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

      8. *-inverses 91.5%

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

      9. metadata-eval 91.5%

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

      10. associate--r- 91.5%

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

      11. neg-sub0 91.5%

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

      12. distribute-frac-neg2 91.5%

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

      13. remove-double-neg 91.5%

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

      14. sub-neg 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in y around inf 63.1%

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

      1. associate-*l/ 63.0%

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

      2. *-commutative 63.0%

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

   7. Simplified 63.0%

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

      1. clear-num 63.0%

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

      2. un-div-inv 63.2%

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

   9. Applied egg-rr 63.2%

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

   if -5.0000000000000002e-14 < y < 1.1799999999999999e-86

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. distribute-frac-neg2 99.9%

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

      4. neg-sub0 99.9%

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

      5. remove-double-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. div-sub 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r- 100.0%

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

      11. neg-sub0 100.0%

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

      12. distribute-frac-neg2 100.0%

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

      13. remove-double-neg 100.0%

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

      14. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 80.7%

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

   if 1.1799999999999999e-86 < y

   1. Initial program 88.5%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.5%

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

      2. remove-double-neg 92.5%

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

      3. distribute-frac-neg2 92.5%

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

      4. neg-sub0 92.5%

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

      5. remove-double-neg 92.5%

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

      6. unsub-neg 92.5%

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

      7. div-sub 92.5%

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

      8. *-inverses 92.5%

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

      9. metadata-eval 92.5%

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

      10. associate--r- 92.5%

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

      11. neg-sub0 92.5%

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

      12. distribute-frac-neg2 92.5%

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

      13. remove-double-neg 92.5%

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

      14. sub-neg 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in y around inf 73.7%

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

      1. associate-*l/ 76.8%

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

      2. *-commutative 76.8%

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

   7. Simplified 76.8%

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

Alternative 5: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+30) x (if (<= z 2.55e-89) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+30) {
		tmp = x;
	} else if (z <= 2.55e-89) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	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 <= (-3.3d+30)) then
        tmp = x
    else if (z <= 2.55d-89) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+30) {
		tmp = x;
	} else if (z <= 2.55e-89) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+30:
		tmp = x
	elif z <= 2.55e-89:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+30)
		tmp = x;
	elseif (z <= 2.55e-89)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+30)
		tmp = x;
	elseif (z <= 2.55e-89)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+30], x, If[LessEqual[z, 2.55e-89], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000026e30 or 2.55000000000000002e-89 < z

   1. Initial program 74.9%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

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

      2. remove-double-neg 99.2%

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

      3. distribute-frac-neg2 99.2%

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

      4. neg-sub0 99.2%

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

      5. remove-double-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. div-sub 99.2%

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

      8. *-inverses 99.2%

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

      9. metadata-eval 99.2%

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

      10. associate--r- 99.2%

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

      11. neg-sub0 99.2%

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

      12. distribute-frac-neg2 99.2%

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

      13. remove-double-neg 99.2%

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

      14. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 76.3%

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

   if -3.30000000000000026e30 < z < 2.55000000000000002e-89

   1. Initial program 94.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.9%

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

      2. remove-double-neg 90.9%

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

      3. distribute-frac-neg2 90.9%

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

      4. neg-sub0 90.9%

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

      5. remove-double-neg 90.9%

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

      6. unsub-neg 90.9%

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

      7. div-sub 91.0%

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

      8. *-inverses 91.0%

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

      9. metadata-eval 91.0%

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

      10. associate--r- 91.0%

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

      11. neg-sub0 91.0%

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

      12. distribute-frac-neg2 91.0%

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

      13. remove-double-neg 91.0%

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

      14. sub-neg 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 70.4%

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

Alternative 6: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.75 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.75e+64) (* x (- (/ y z) -1.0)) (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.75e+64) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = (y + z) * (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 <= 3.75d+64) then
        tmp = x * ((y / z) - (-1.0d0))
    else
        tmp = (y + z) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.75e+64) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.75e+64:
		tmp = x * ((y / z) - -1.0)
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.75e+64)
		tmp = Float64(x * Float64(Float64(y / z) - -1.0));
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.75e+64)
		tmp = x * ((y / z) - -1.0);
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.75e+64], N[(x * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.7500000000000003e64

   1. Initial program 82.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 97.5%

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

      2. remove-double-neg 97.5%

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

      3. distribute-frac-neg2 97.5%

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

      4. neg-sub0 97.5%

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

      5. remove-double-neg 97.5%

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

      6. unsub-neg 97.5%

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

      7. div-sub 97.5%

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

      8. *-inverses 97.5%

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

      9. metadata-eval 97.5%

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

      10. associate--r- 97.5%

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

      11. neg-sub0 97.5%

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

      12. distribute-frac-neg2 97.5%

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

      13. remove-double-neg 97.5%

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

      14. sub-neg 97.5%

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

   3. Simplified 97.5%

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

   if 3.7500000000000003e64 < y

   1. Initial program 88.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

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

      2. associate-/l* 98.2%

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

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.9 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.9e+175) (* x (- (/ y z) -1.0)) (* y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.9e+175) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = y * (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 <= 5.9d+175) then
        tmp = x * ((y / z) - (-1.0d0))
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.9e+175) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.9e+175:
		tmp = x * ((y / z) - -1.0)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.9e+175)
		tmp = Float64(x * Float64(Float64(y / z) - -1.0));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.9e+175)
		tmp = x * ((y / z) - -1.0);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.9e+175], N[(x * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.9000000000000003e175

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

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

      2. remove-double-neg 96.8%

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

      3. distribute-frac-neg2 96.8%

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

      4. neg-sub0 96.8%

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

      5. remove-double-neg 96.8%

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

      6. unsub-neg 96.8%

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

      7. div-sub 96.9%

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

      8. *-inverses 96.9%

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

      9. metadata-eval 96.9%

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

      10. associate--r- 96.9%

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

      11. neg-sub0 96.9%

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

      12. distribute-frac-neg2 96.9%

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

      13. remove-double-neg 96.9%

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

      14. sub-neg 96.9%

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

   3. Simplified 96.9%

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

   if 5.9000000000000003e175 < y

   1. Initial program 89.9%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.1%

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

      2. remove-double-neg 87.1%

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

      3. distribute-frac-neg2 87.1%

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

      4. neg-sub0 87.1%

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

      5. remove-double-neg 87.1%

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

      6. unsub-neg 87.1%

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

      7. div-sub 87.1%

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

      8. *-inverses 87.1%

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

      9. metadata-eval 87.1%

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

      10. associate--r- 87.1%

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

      11. neg-sub0 87.1%

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

      12. distribute-frac-neg2 87.1%

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

      13. remove-double-neg 87.1%

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

      14. sub-neg 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in y around inf 89.9%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

   7. Simplified 99.8%

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

Alternative 8: 50.0% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 84.0%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 95.4%

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

   2. remove-double-neg 95.4%

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

   3. distribute-frac-neg2 95.4%

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

   4. neg-sub0 95.4%

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

   5. remove-double-neg 95.4%

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

   6. unsub-neg 95.4%

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

   7. div-sub 95.5%

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

   8. *-inverses 95.5%

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

   9. metadata-eval 95.5%

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

   10. associate--r- 95.5%

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

   11. neg-sub0 95.5%

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

   12. distribute-frac-neg2 95.5%

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

   13. remove-double-neg 95.5%

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

   14. sub-neg 95.5%

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

3. Simplified 95.5%

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

5. Taylor expanded in y around 0 51.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ z (+ y z))))

  (/ (* x (+ y z)) z))