Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.3% → 96.0%

Time: 4.3s

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: 84.3% 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, 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 81.6%

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

   1. remove-double-neg 81.6%

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

   2. distribute-lft-neg-out 81.6%

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

   3. *-commutative 81.6%

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

   4. distribute-lft-neg-in 81.6%

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

   5. associate-/l* 89.7%

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

   6. distribute-neg-in 89.7%

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

   7. unsub-neg 89.7%

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

   8. div-sub 87.0%

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

   9. distribute-frac-neg 87.0%

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

   10. associate-/r/ 85.5%

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

   11. distribute-rgt-neg-out 85.5%

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

   12. remove-double-neg 85.5%

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

   13. associate-/r/ 96.6%

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

   14. *-inverses 96.6%

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

   15. *-lft-identity 96.6%

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

   16. *-commutative 96.6%

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

   17. fma-neg 96.6%

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

   18. remove-double-neg 96.6%

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

3. Simplified 96.6%

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

   1. fma-udef 96.6%

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

6. Applied egg-rr 96.6%

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

7. Final simplification 96.6%

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

Alternative 2: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.12e-18) x (if (<= z 5.5e-79) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.12e-18) {
		tmp = x;
	} else if (z <= 5.5e-79) {
		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 <= (-1.12d-18)) then
        tmp = x
    else if (z <= 5.5d-79) 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 <= -1.12e-18) {
		tmp = x;
	} else if (z <= 5.5e-79) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.12e-18:
		tmp = x
	elif z <= 5.5e-79:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.12e-18)
		tmp = x;
	elseif (z <= 5.5e-79)
		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 <= -1.12e-18)
		tmp = x;
	elseif (z <= 5.5e-79)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.12e-18], x, If[LessEqual[z, 5.5e-79], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000001e-18 or 5.4999999999999997e-79 < z

   1. Initial program 74.3%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around 0 72.7%

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

   if -1.12000000000000001e-18 < z < 5.4999999999999997e-79

   1. Initial program 91.9%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   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-*r/ 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e-15) x (if (<= z 2.3e-78) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e-15) {
		tmp = x;
	} else if (z <= 2.3e-78) {
		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 <= (-5d-15)) then
        tmp = x
    else if (z <= 2.3d-78) 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 <= -5e-15) {
		tmp = x;
	} else if (z <= 2.3e-78) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e-15:
		tmp = x
	elif z <= 2.3e-78:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e-15)
		tmp = x;
	elseif (z <= 2.3e-78)
		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 <= -5e-15)
		tmp = x;
	elseif (z <= 2.3e-78)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e-15], x, If[LessEqual[z, 2.3e-78], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999999e-15 or 2.3000000000000002e-78 < z

   1. Initial program 74.3%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around 0 72.7%

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

   if -4.99999999999999999e-15 < z < 2.3000000000000002e-78

   1. Initial program 91.9%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   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* 75.1%

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

      2. associate-/r/ 79.7%

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

   7. Applied egg-rr 79.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.72e-19) x (if (<= z 2.1e-78) (/ y (/ z x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.72e-19) {
		tmp = x;
	} else if (z <= 2.1e-78) {
		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 <= (-1.72d-19)) then
        tmp = x
    else if (z <= 2.1d-78) 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 <= -1.72e-19) {
		tmp = x;
	} else if (z <= 2.1e-78) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.72e-19:
		tmp = x
	elif z <= 2.1e-78:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.72e-19)
		tmp = x;
	elseif (z <= 2.1e-78)
		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 <= -1.72e-19)
		tmp = x;
	elseif (z <= 2.1e-78)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.72e-19], x, If[LessEqual[z, 2.1e-78], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.72000000000000004e-19 or 2.1000000000000001e-78 < z

   1. Initial program 74.3%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around 0 72.7%

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

   if -1.72000000000000004e-19 < z < 2.1000000000000001e-78

   1. Initial program 91.9%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   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-*r/ 75.2%

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

   7. Simplified 75.2%

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

      1. associate-*r/ 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-/l* 80.7%

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

   9. Applied egg-rr 80.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.72 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{+200}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 5.8e+200) (* (+ y z) (/ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.8e+200) {
		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 <= 5.8d+200) 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 <= 5.8e+200) {
		tmp = (y + z) * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5.8e+200:
		tmp = (y + z) * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5.8e+200)
		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 <= 5.8e+200)
		tmp = (y + z) * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5.8e+200], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 5.7999999999999998e200

   1. Initial program 85.2%

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

      1. associate-*l/ 89.8%

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

      2. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   if 5.7999999999999998e200 < z

   1. Initial program 43.9%

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

      1. associate-*l/ 74.8%

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

      2. *-commutative 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in y around 0 95.1%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.8 \cdot 10^{+200}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

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 81.6%

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

   1. associate-*l/ 88.5%

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

   2. *-commutative 88.5%

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

3. Simplified 88.5%

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

5. Taylor expanded in y around 0 50.5%

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

6. Final simplification 50.5%

   \[\leadsto x \]
7. Add Preprocessing

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 2024018 
(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))