Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.2% → 96.2%

Time: 4.1s

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: 85.2% 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: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (z + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 2: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54} \lor \neg \left(z \leq 5.2 \cdot 10^{-17}\right) \land z \leq 1.25 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+51)
   x
   (if (or (<= z 9e-54) (and (not (<= z 5.2e-17)) (<= z 1.25e+109)))
     (* x (/ y z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+51) {
		tmp = x;
	} else if ((z <= 9e-54) || (!(z <= 5.2e-17) && (z <= 1.25e+109))) {
		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 <= (-4.4d+51)) then
        tmp = x
    else if ((z <= 9d-54) .or. (.not. (z <= 5.2d-17)) .and. (z <= 1.25d+109)) 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 <= -4.4e+51) {
		tmp = x;
	} else if ((z <= 9e-54) || (!(z <= 5.2e-17) && (z <= 1.25e+109))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+51:
		tmp = x
	elif (z <= 9e-54) or (not (z <= 5.2e-17) and (z <= 1.25e+109)):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e+51)
		tmp = x;
	elseif ((z <= 9e-54) || (!(z <= 5.2e-17) && (z <= 1.25e+109)))
		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 <= -4.4e+51)
		tmp = x;
	elseif ((z <= 9e-54) || (~((z <= 5.2e-17)) && (z <= 1.25e+109)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e+51], x, If[Or[LessEqual[z, 9e-54], And[N[Not[LessEqual[z, 5.2e-17]], $MachinePrecision], LessEqual[z, 1.25e+109]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999984e51 or 8.9999999999999997e-54 < z < 5.20000000000000006e-17 or 1.25e109 < z

   1. Initial program 72.9%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 86.0%

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

   if -4.39999999999999984e51 < z < 8.9999999999999997e-54 or 5.20000000000000006e-17 < z < 1.25e109

   1. Initial program 91.8%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 74.0%

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

      1. associate-*r/ 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-54} \lor \neg \left(z \leq 5.2 \cdot 10^{-17}\right) \land z \leq 1.25 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e+51)
   x
   (if (<= z 2.85e-52)
     (/ x (/ z y))
     (if (<= z 5.2e-17) x (if (<= z 9.8e+107) (* x (/ y z)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e+51) {
		tmp = x;
	} else if (z <= 2.85e-52) {
		tmp = x / (z / y);
	} else if (z <= 5.2e-17) {
		tmp = x;
	} else if (z <= 9.8e+107) {
		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 <= (-4.2d+51)) then
        tmp = x
    else if (z <= 2.85d-52) then
        tmp = x / (z / y)
    else if (z <= 5.2d-17) then
        tmp = x
    else if (z <= 9.8d+107) 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 <= -4.2e+51) {
		tmp = x;
	} else if (z <= 2.85e-52) {
		tmp = x / (z / y);
	} else if (z <= 5.2e-17) {
		tmp = x;
	} else if (z <= 9.8e+107) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e+51:
		tmp = x
	elif z <= 2.85e-52:
		tmp = x / (z / y)
	elif z <= 5.2e-17:
		tmp = x
	elif z <= 9.8e+107:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e+51)
		tmp = x;
	elseif (z <= 2.85e-52)
		tmp = Float64(x / Float64(z / y));
	elseif (z <= 5.2e-17)
		tmp = x;
	elseif (z <= 9.8e+107)
		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 <= -4.2e+51)
		tmp = x;
	elseif (z <= 2.85e-52)
		tmp = x / (z / y);
	elseif (z <= 5.2e-17)
		tmp = x;
	elseif (z <= 9.8e+107)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e+51], x, If[LessEqual[z, 2.85e-52], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-17], x, If[LessEqual[z, 9.8e+107], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000002e51 or 2.8499999999999999e-52 < z < 5.20000000000000006e-17 or 9.8000000000000003e107 < z

   1. Initial program 72.9%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 86.0%

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

   if -4.2000000000000002e51 < z < 2.8499999999999999e-52

   1. Initial program 91.4%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-/l* 76.4%

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

   6. Simplified 76.4%

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

   if 5.20000000000000006e-17 < z < 9.8000000000000003e107

   1. Initial program 94.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.3%

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

      1. associate-*r/ 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+51)
   x
   (if (<= z 1.5e-52)
     (/ y (/ z x))
     (if (<= z 7.4e-17) x (if (<= z 1.2e+110) (* x (/ y z)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+51) {
		tmp = x;
	} else if (z <= 1.5e-52) {
		tmp = y / (z / x);
	} else if (z <= 7.4e-17) {
		tmp = x;
	} else if (z <= 1.2e+110) {
		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 <= (-4.4d+51)) then
        tmp = x
    else if (z <= 1.5d-52) then
        tmp = y / (z / x)
    else if (z <= 7.4d-17) then
        tmp = x
    else if (z <= 1.2d+110) 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 <= -4.4e+51) {
		tmp = x;
	} else if (z <= 1.5e-52) {
		tmp = y / (z / x);
	} else if (z <= 7.4e-17) {
		tmp = x;
	} else if (z <= 1.2e+110) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+51:
		tmp = x
	elif z <= 1.5e-52:
		tmp = y / (z / x)
	elif z <= 7.4e-17:
		tmp = x
	elif z <= 1.2e+110:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e+51)
		tmp = x;
	elseif (z <= 1.5e-52)
		tmp = Float64(y / Float64(z / x));
	elseif (z <= 7.4e-17)
		tmp = x;
	elseif (z <= 1.2e+110)
		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 <= -4.4e+51)
		tmp = x;
	elseif (z <= 1.5e-52)
		tmp = y / (z / x);
	elseif (z <= 7.4e-17)
		tmp = x;
	elseif (z <= 1.2e+110)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e+51], x, If[LessEqual[z, 1.5e-52], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-17], x, If[LessEqual[z, 1.2e+110], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999984e51 or 1.5e-52 < z < 7.3999999999999995e-17 or 1.20000000000000006e110 < z

   1. Initial program 72.9%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 86.0%

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

   if -4.39999999999999984e51 < z < 1.5e-52

   1. Initial program 91.4%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 76.0%

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

   6. Simplified 76.0%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-/l* 79.8%

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

   8. Applied egg-rr 79.8%

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

   if 7.3999999999999995e-17 < z < 1.20000000000000006e110

   1. Initial program 94.7%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 61.3%

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

      1. associate-*r/ 66.4%

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

   6. Simplified 66.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 95.8% accurate, 1.0× speedup

Math

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

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(Float64(z + y) / z))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Final simplification 97.0%

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

Alternative 6: 50.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 84.2%

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

   1. associate-*r/ 97.0%

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

3. Simplified 97.0%

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

4. Taylor expanded in y around 0 48.0%

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

5. Final simplification 48.0%

   \[\leadsto x \]

Developer target: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (z / (y + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(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))