Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.0% → 95.6%

Time: 6.3s

Alternatives: 7

Speedup: 1.0×

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: 85.0% 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: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \frac{y}{z}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-*l/ 86.0%

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

   2. distribute-lft-in 81.1%

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

   3. associate-*l/ 76.2%

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

   4. associate-*r/ 80.4%

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

   5. fma-undefine 80.4%

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

   6. remove-double-neg 80.4%

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

   7. distribute-rgt-neg-out 80.4%

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

   8. distribute-lft-neg-out 80.4%

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

   9. distribute-frac-neg2 80.4%

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

   10. associate-*l/ 84.1%

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

   11. associate-/l* 97.3%

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

   12. *-inverses 97.3%

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

   13. *-rgt-identity 97.3%

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

3. Simplified 97.3%

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

Alternative 2: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e+22) x (if (<= z 2.2e-77) (/ y (/ z x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e+22) {
		tmp = x;
	} else if (z <= 2.2e-77) {
		tmp = y / (z / x);
	} 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 <= (-4.2d+22)) then
        tmp = x
    else if (z <= 2.2d-77) then
        tmp = y / (z / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e+22) {
		tmp = x;
	} else if (z <= 2.2e-77) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e+22:
		tmp = x
	elif z <= 2.2e-77:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e+22)
		tmp = x;
	elseif (z <= 2.2e-77)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.2e+22)
		tmp = x;
	elseif (z <= 2.2e-77)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e+22], x, If[LessEqual[z, 2.2e-77], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999996e22 or 2.20000000000000007e-77 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.5%

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

   if -4.1999999999999996e22 < z < 2.20000000000000007e-77

   1. Initial program 94.0%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

   5. Simplified 77.8%

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

      1. associate-*l/ 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. associate-*l/ 77.8%

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

      2. associate-*r/ 79.2%

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

      3. clear-num 79.2%

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

      4. un-div-inv 79.6%

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

   9. Applied egg-rr 79.6%

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

Alternative 3: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.6e+19) x (if (<= z 2.5e-77) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.6e+19) {
		tmp = x;
	} else if (z <= 2.5e-77) {
		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 <= (-6.6d+19)) then
        tmp = x
    else if (z <= 2.5d-77) 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 <= -6.6e+19) {
		tmp = x;
	} else if (z <= 2.5e-77) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.6e+19:
		tmp = x
	elif z <= 2.5e-77:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.6e+19)
		tmp = x;
	elseif (z <= 2.5e-77)
		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 (z <= -6.6e+19)
		tmp = x;
	elseif (z <= 2.5e-77)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.6e+19], x, If[LessEqual[z, 2.5e-77], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e19 or 2.49999999999999982e-77 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.5%

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

   if -6.6e19 < z < 2.49999999999999982e-77

   1. Initial program 94.0%

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

      1. associate-/l* 94.0%

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

      2. remove-double-neg 94.0%

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

      3. unsub-neg 94.0%

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

      4. div-sub 94.0%

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

      5. remove-double-neg 94.0%

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

      6. distribute-frac-neg2 94.0%

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

      7. *-inverses 94.0%

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

      8. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around inf 77.8%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

   7. Simplified 79.2%

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

Alternative 4: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.1e+22) x (if (<= z 4e-77) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.1e+22) {
		tmp = x;
	} else if (z <= 4e-77) {
		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 <= (-6.1d+22)) then
        tmp = x
    else if (z <= 4d-77) 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 <= -6.1e+22) {
		tmp = x;
	} else if (z <= 4e-77) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.1e+22:
		tmp = x
	elif z <= 4e-77:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.1e+22)
		tmp = x;
	elseif (z <= 4e-77)
		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 <= -6.1e+22)
		tmp = x;
	elseif (z <= 4e-77)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.1e+22], x, If[LessEqual[z, 4e-77], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0999999999999998e22 or 3.9999999999999997e-77 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 78.5%

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

   if -6.0999999999999998e22 < z < 3.9999999999999997e-77

   1. Initial program 94.0%

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

      1. associate-/l* 94.0%

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

      2. remove-double-neg 94.0%

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

      3. unsub-neg 94.0%

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

      4. div-sub 94.0%

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

      5. remove-double-neg 94.0%

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

      6. distribute-frac-neg2 94.0%

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

      7. *-inverses 94.0%

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

      8. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around inf 76.2%

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

Alternative 5: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-/l* 97.3%

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

   2. remove-double-neg 97.3%

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

   3. unsub-neg 97.3%

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

   4. div-sub 97.3%

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

   5. remove-double-neg 97.3%

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

   6. distribute-frac-neg2 97.3%

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

   7. *-inverses 97.3%

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

   8. metadata-eval 97.3%

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

3. Simplified 97.3%

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

   1. sub-neg 97.3%

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

   2. metadata-eval 97.3%

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

   3. distribute-rgt-in 97.3%

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

   4. *-un-lft-identity 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

   \[\leadsto x + x \cdot \frac{y}{z} \]
8. Add Preprocessing

Alternative 6: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - -1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- (/ y z) -1.0)))

C

double code(double x, double y, double z) {
	return x * ((y / z) - -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 = x * ((y / z) - (-1.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x * ((y / z) - -1.0);
}

Python

def code(x, y, z):
	return x * ((y / z) - -1.0)

Julia

function code(x, y, z)
	return Float64(x * Float64(Float64(y / z) - -1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * ((y / z) - -1.0);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.8%

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

   1. associate-/l* 97.3%

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

   2. remove-double-neg 97.3%

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

   3. unsub-neg 97.3%

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

   4. div-sub 97.3%

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

   5. remove-double-neg 97.3%

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

   6. distribute-frac-neg2 97.3%

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

   7. *-inverses 97.3%

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

   8. metadata-eval 97.3%

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

3. Simplified 97.3%

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

Alternative 7: 50.5% 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 83.8%

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

   1. associate-/l* 97.3%

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

   2. remove-double-neg 97.3%

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

   3. unsub-neg 97.3%

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

   4. div-sub 97.3%

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

   5. remove-double-neg 97.3%

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

   6. distribute-frac-neg2 97.3%

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

   7. *-inverses 97.3%

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

   8. metadata-eval 97.3%

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

3. Simplified 97.3%

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

5. Taylor expanded in y around 0 52.1%

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

Developer Target 1: 95.9% 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 2024186 
(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))