Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.3% → 96.0%

Time: 3.8s

Alternatives: 6

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: 96.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 4 \cdot 10^{-37}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + z}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ y z)) z) 4e-37) (+ x (* x (/ y z))) (/ (+ y z) (/ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 4e-37) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (y + z) / (z / 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 (((x * (y + z)) / z) <= 4d-37) then
        tmp = x + (x * (y / z))
    else
        tmp = (y + z) / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 4e-37) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (y + z) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y + z)) / z) <= 4e-37:
		tmp = x + (x * (y / z))
	else:
		tmp = (y + z) / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y + z)) / z) <= 4e-37)
		tmp = Float64(x + Float64(x * Float64(y / z)));
	else
		tmp = Float64(Float64(y + z) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * (y + z)) / z) <= 4e-37)
		tmp = x + (x * (y / z));
	else
		tmp = (y + z) / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 4e-37], N[(x + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 4.00000000000000027e-37

   1. Initial program 87.4%

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

      1. associate-*l/ 75.2%

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

      2. distribute-rgt-in 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-/r/ 95.4%

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

      5. *-inverses 95.4%

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

      6. /-rgt-identity 95.4%

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

      7. associate-*r/ 95.2%

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

      8. *-commutative 95.2%

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

      9. associate-*r/ 99.9%

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

      10. fma-def 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   if 4.00000000000000027e-37 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 85.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

      1. *-commutative 96.7%

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

      2. clear-num 96.5%

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

      3. un-div-inv 96.8%

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

      4. +-commutative 96.8%

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

   5. Applied egg-rr 96.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 4 \cdot 10^{-37}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + z}{\frac{z}{x}}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 500000000000:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ y z)) z) 500000000000.0)
   (+ x (* x (/ y z)))
   (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 500000000000.0) {
		tmp = x + (x * (y / z));
	} 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 (((x * (y + z)) / z) <= 500000000000.0d0) then
        tmp = x + (x * (y / z))
    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 (((x * (y + z)) / z) <= 500000000000.0) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y + z)) / z) <= 500000000000.0:
		tmp = x + (x * (y / z))
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y + z)) / z) <= 500000000000.0)
		tmp = Float64(x + Float64(x * Float64(y / z)));
	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 (((x * (y + z)) / z) <= 500000000000.0)
		tmp = x + (x * (y / z));
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 500000000000.0], N[(x + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 5e11

   1. Initial program 88.1%

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

      1. associate-*l/ 76.4%

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

      2. distribute-rgt-in 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-/r/ 95.7%

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

      5. *-inverses 95.7%

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

      6. /-rgt-identity 95.7%

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

      7. associate-*r/ 95.5%

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

      8. *-commutative 95.5%

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

      9. associate-*r/ 99.9%

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

      10. fma-def 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
   4. Step-by-step derivation

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   if 5e11 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 83.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 500000000000:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+132}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.4e+208) x (if (<= z 1.15e+132) (* (+ y z) (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.4e+208) {
		tmp = x;
	} else if (z <= 1.15e+132) {
		tmp = (y + z) * (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 <= (-6.4d+208)) then
        tmp = x
    else if (z <= 1.15d+132) then
        tmp = (y + z) * (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 <= -6.4e+208) {
		tmp = x;
	} else if (z <= 1.15e+132) {
		tmp = (y + z) * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.4e+208:
		tmp = x
	elif z <= 1.15e+132:
		tmp = (y + z) * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.4e+208)
		tmp = x;
	elseif (z <= 1.15e+132)
		tmp = Float64(Float64(y + z) * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.4e+208)
		tmp = x;
	elseif (z <= 1.15e+132)
		tmp = (y + z) * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.4e+208], x, If[LessEqual[z, 1.15e+132], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4000000000000002e208 or 1.1500000000000001e132 < z

   1. Initial program 71.1%

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

      1. associate-*l/ 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in z around inf 89.3%

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

   if -6.4000000000000002e208 < z < 1.1500000000000001e132

   1. Initial program 91.6%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+208}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+132}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-39} \lor \neg \left(y \leq 3.8 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e-39) (not (<= y 3.8e-20))) (* x (/ y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e-39) || !(y <= 3.8e-20)) {
		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 ((y <= (-1.25d-39)) .or. (.not. (y <= 3.8d-20))) 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 ((y <= -1.25e-39) || !(y <= 3.8e-20)) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e-39) or not (y <= 3.8e-20):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e-39) || !(y <= 3.8e-20))
		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 ((y <= -1.25e-39) || ~((y <= 3.8e-20)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e-39], N[Not[LessEqual[y, 3.8e-20]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e-39 or 3.7999999999999998e-20 < y

   1. Initial program 88.8%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*r/ 71.4%

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

   6. Simplified 71.4%

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

   if -1.25e-39 < y < 3.7999999999999998e-20

   1. Initial program 84.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 81.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-39} \lor \neg \left(y \leq 3.8 \cdot 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e-41) (* x (/ y z)) (if (<= y 6.2e-18) x (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e-41) {
		tmp = x * (y / z);
	} else if (y <= 6.2e-18) {
		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 <= (-3d-41)) then
        tmp = x * (y / z)
    else if (y <= 6.2d-18) 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 <= -3e-41) {
		tmp = x * (y / z);
	} else if (y <= 6.2e-18) {
		tmp = x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e-41:
		tmp = x * (y / z)
	elif y <= 6.2e-18:
		tmp = x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e-41)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 6.2e-18)
		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 <= -3e-41)
		tmp = x * (y / z);
	elseif (y <= 6.2e-18)
		tmp = x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e-41], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-18], x, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999989e-41

   1. Initial program 85.7%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r/ 72.3%

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

   6. Simplified 72.3%

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

   if -2.99999999999999989e-41 < y < 6.20000000000000014e-18

   1. Initial program 84.5%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 81.6%

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

   if 6.20000000000000014e-18 < y

   1. Initial program 92.2%

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

      1. associate-*l/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around 0 76.4%

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

      1. associate-*r/ 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6: 50.8% 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 86.7%

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

   1. associate-*l/ 82.8%

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

3. Simplified 82.8%

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

4. Taylor expanded in z around inf 53.2%

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

5. Final simplification 53.2%

   \[\leadsto x \]

Developer target: 96.3% 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 2023242 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

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

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