Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.5% → 96.0%

Time: 7.9s

Alternatives: 6

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: 84.5% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{\frac{z}{z + y}}{x}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ 1.0 (/ (/ z (+ z y)) x)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.6%

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

   1. *-commutative 73.6%

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

   2. associate-/l* 87.3%

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

3. Simplified 87.3%

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

   1. add-cube-cbrt 86.1%

      \[\leadsto \left(y + z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{x}{z}} \cdot \sqrt[3]{\frac{x}{z}}\right) \cdot \sqrt[3]{\frac{x}{z}}\right)} \]

   2. pow3 86.1%

      \[\leadsto \left(y + z\right) \cdot \color{blue}{{\left(\sqrt[3]{\frac{x}{z}}\right)}^{3}} \]

6. Applied egg-rr 86.1%

   \[\leadsto \left(y + z\right) \cdot \color{blue}{{\left(\sqrt[3]{\frac{x}{z}}\right)}^{3}} \]
7. Step-by-step derivation

   1. rem-cube-cbrt 87.3%

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

   2. clear-num 87.1%

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

   3. div-inv 87.7%

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

   4. div-inv 87.5%

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

   5. associate-/r* 96.4%

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

   6. +-commutative 96.4%

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

8. Applied egg-rr 96.4%

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

   1. clear-num 96.4%

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

   2. inv-pow 96.4%

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

   3. div-inv 96.3%

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

   4. clear-num 96.6%

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

10. Applied egg-rr 96.6%

    \[\leadsto \color{blue}{{\left(\frac{1}{x} \cdot \frac{z}{z + y}\right)}^{-1}} \]
11. Step-by-step derivation

    1. unpow-1 96.6%

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

    2. associate-*l/ 96.6%

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

    3. *-lft-identity 96.6%

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

    4. +-commutative 96.6%

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

12. Simplified 96.6%

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

13. Final simplification 96.6%

    \[\leadsto \frac{1}{\frac{\frac{z}{z + y}}{x}} \]
14. Add Preprocessing

Alternative 2: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.25e-10) x (if (<= z 170000.0) (/ y (/ z x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.25e-10) {
		tmp = x;
	} else if (z <= 170000.0) {
		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 <= (-2.25d-10)) then
        tmp = x
    else if (z <= 170000.0d0) 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 <= -2.25e-10) {
		tmp = x;
	} else if (z <= 170000.0) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.25e-10:
		tmp = x
	elif z <= 170000.0:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.25e-10)
		tmp = x;
	elseif (z <= 170000.0)
		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 <= -2.25e-10)
		tmp = x;
	elseif (z <= 170000.0)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.25e-10], x, If[LessEqual[z, 170000.0], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e-10 or 1.7e5 < z

   1. Initial program 59.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 83.5%

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

   if -2.25e-10 < z < 1.7e5

   1. Initial program 87.1%

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

      1. associate-/l* 93.4%

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

      2. remove-double-neg 93.4%

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

      3. unsub-neg 93.4%

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

      4. div-sub 93.4%

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

      5. remove-double-neg 93.4%

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

      6. distribute-frac-neg2 93.4%

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

      7. *-inverses 93.4%

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

      8. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. associate-*l/ 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

      1. clear-num 71.1%

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

      2. un-div-inv 71.3%

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

   9. Applied egg-rr 71.3%

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

Alternative 3: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 25000:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-11) x (if (<= z 25000.0) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-11) {
		tmp = x;
	} else if (z <= 25000.0) {
		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 <= (-7.5d-11)) then
        tmp = x
    else if (z <= 25000.0d0) 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 <= -7.5e-11) {
		tmp = x;
	} else if (z <= 25000.0) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-11:
		tmp = x
	elif z <= 25000.0:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-11)
		tmp = x;
	elseif (z <= 25000.0)
		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 <= -7.5e-11)
		tmp = x;
	elseif (z <= 25000.0)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-11], x, If[LessEqual[z, 25000.0], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-11 or 25000 < z

   1. Initial program 59.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 83.5%

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

   if -7.5e-11 < z < 25000

   1. Initial program 87.1%

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

      1. associate-/l* 93.4%

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

      2. remove-double-neg 93.4%

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

      3. unsub-neg 93.4%

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

      4. div-sub 93.4%

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

      5. remove-double-neg 93.4%

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

      6. distribute-frac-neg2 93.4%

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

      7. *-inverses 93.4%

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

      8. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. associate-*l/ 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

Alternative 4: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 30000000:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e-10) x (if (<= z 30000000.0) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e-10) {
		tmp = x;
	} else if (z <= 30000000.0) {
		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 <= (-2.4d-10)) then
        tmp = x
    else if (z <= 30000000.0d0) 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 <= -2.4e-10) {
		tmp = x;
	} else if (z <= 30000000.0) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.4e-10:
		tmp = x
	elif z <= 30000000.0:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e-10)
		tmp = x;
	elseif (z <= 30000000.0)
		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 <= -2.4e-10)
		tmp = x;
	elseif (z <= 30000000.0)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.4e-10], x, If[LessEqual[z, 30000000.0], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e-10 or 3e7 < z

   1. Initial program 59.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 83.5%

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

   if -2.4e-10 < z < 3e7

   1. Initial program 87.1%

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

      1. associate-/l* 93.4%

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

      2. remove-double-neg 93.4%

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

      3. unsub-neg 93.4%

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

      4. div-sub 93.4%

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

      5. remove-double-neg 93.4%

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

      6. distribute-frac-neg2 93.4%

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

      7. *-inverses 93.4%

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

      8. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in y around inf 67.0%

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

Alternative 5: 95.9% 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 73.6%

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

   1. associate-/l* 96.5%

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

   2. remove-double-neg 96.5%

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

   3. unsub-neg 96.5%

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

   4. div-sub 96.5%

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

   5. remove-double-neg 96.5%

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

   6. distribute-frac-neg2 96.5%

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

   7. *-inverses 96.5%

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

   8. metadata-eval 96.5%

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

3. Simplified 96.5%

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

Alternative 6: 50.6% 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 73.6%

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

   1. associate-/l* 96.5%

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

   2. remove-double-neg 96.5%

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

   3. unsub-neg 96.5%

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

   4. div-sub 96.5%

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

   5. remove-double-neg 96.5%

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

   6. distribute-frac-neg2 96.5%

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

   7. *-inverses 96.5%

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

   8. metadata-eval 96.5%

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

3. Simplified 96.5%

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

5. Taylor expanded in y around 0 54.8%

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

Developer Target 1: 96.1% 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 2024181 
(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))