Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.7% → 95.5%

Time: 5.5s

Alternatives: 9

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: 84.7% 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: 95.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+73) (/ (* x (+ y z)) z) (fma x (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+73) {
		tmp = (x * (y + z)) / z;
	} else {
		tmp = fma(x, (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+73)
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	else
		tmp = fma(x, Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+73], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e73

   1. Initial program 97.2%

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

   if -1.95e73 < y

   1. Initial program 87.8%

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

      1. associate-*l/ 81.1%

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

      2. distribute-rgt-in 76.8%

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

      3. associate-*r/ 72.6%

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

      4. *-commutative 72.6%

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

      5. associate-*r/ 76.1%

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

      6. associate-*r/ 89.3%

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

      7. associate-/l* 76.4%

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

      8. associate-/r/ 97.7%

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

      9. *-inverses 97.7%

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

      10. *-lft-identity 97.7%

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

      11. fma-def 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \end{array} \]

Alternative 2: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-42} \lor \neg \left(y \leq 2.8 \cdot 10^{-86} \lor \neg \left(y \leq 5.1 \cdot 10^{-46}\right) \land y \leq 3800\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e-42)
         (not (or (<= y 2.8e-86) (and (not (<= y 5.1e-46)) (<= y 3800.0)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e-42) || !((y <= 2.8e-86) || (!(y <= 5.1e-46) && (y <= 3800.0)))) {
		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 ((y <= (-1.1d-42)) .or. (.not. (y <= 2.8d-86) .or. (.not. (y <= 5.1d-46)) .and. (y <= 3800.0d0))) 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 ((y <= -1.1e-42) || !((y <= 2.8e-86) || (!(y <= 5.1e-46) && (y <= 3800.0)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e-42) or not ((y <= 2.8e-86) or (not (y <= 5.1e-46) and (y <= 3800.0))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e-42) || !((y <= 2.8e-86) || (!(y <= 5.1e-46) && (y <= 3800.0))))
		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 ((y <= -1.1e-42) || ~(((y <= 2.8e-86) || (~((y <= 5.1e-46)) && (y <= 3800.0)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e-42], N[Not[Or[LessEqual[y, 2.8e-86], And[N[Not[LessEqual[y, 5.1e-46]], $MachinePrecision], LessEqual[y, 3800.0]]]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000003e-42 or 2.80000000000000009e-86 < y < 5.0999999999999997e-46 or 3800 < y

   1. Initial program 95.1%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 80.0%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if -1.10000000000000003e-42 < y < 2.80000000000000009e-86 or 5.0999999999999997e-46 < y < 3800

   1. Initial program 82.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 78.9%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-42} \lor \neg \left(y \leq 2.8 \cdot 10^{-86} \lor \neg \left(y \leq 5.1 \cdot 10^{-46}\right) \land y \leq 3800\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-41} \lor \neg \left(y \leq 2.7 \cdot 10^{-80} \lor \neg \left(y \leq 8.5 \cdot 10^{-45}\right) \land y \leq 6600\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-41)
         (not (or (<= y 2.7e-80) (and (not (<= y 8.5e-45)) (<= y 6600.0)))))
   (/ (* y x) z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-41) || !((y <= 2.7e-80) || (!(y <= 8.5e-45) && (y <= 6600.0)))) {
		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 ((y <= (-3.4d-41)) .or. (.not. (y <= 2.7d-80) .or. (.not. (y <= 8.5d-45)) .and. (y <= 6600.0d0))) 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 ((y <= -3.4e-41) || !((y <= 2.7e-80) || (!(y <= 8.5e-45) && (y <= 6600.0)))) {
		tmp = (y * x) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-41) or not ((y <= 2.7e-80) or (not (y <= 8.5e-45) and (y <= 6600.0))):
		tmp = (y * x) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-41) || !((y <= 2.7e-80) || (!(y <= 8.5e-45) && (y <= 6600.0))))
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-41) || ~(((y <= 2.7e-80) || (~((y <= 8.5e-45)) && (y <= 6600.0)))))
		tmp = (y * x) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-41], N[Not[Or[LessEqual[y, 2.7e-80], And[N[Not[LessEqual[y, 8.5e-45]], $MachinePrecision], LessEqual[y, 6600.0]]]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.3999999999999998e-41 or 2.7000000000000002e-80 < y < 8.50000000000000041e-45 or 6600 < y

   1. Initial program 95.1%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 80.0%

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

   if -3.3999999999999998e-41 < y < 2.7000000000000002e-80 or 8.50000000000000041e-45 < y < 6600

   1. Initial program 82.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 78.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-41} \lor \neg \left(y \leq 2.7 \cdot 10^{-80} \lor \neg \left(y \leq 8.5 \cdot 10^{-45}\right) \land y \leq 6600\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 9500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -3.3e-43)
     t_0
     (if (<= y 2.2e-78)
       x
       (if (<= y 4.2e-46) (* x (/ y z)) (if (<= y 9500.0) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -3.3e-43) {
		tmp = t_0;
	} else if (y <= 2.2e-78) {
		tmp = x;
	} else if (y <= 4.2e-46) {
		tmp = x * (y / z);
	} else if (y <= 9500.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (y <= (-3.3d-43)) then
        tmp = t_0
    else if (y <= 2.2d-78) then
        tmp = x
    else if (y <= 4.2d-46) then
        tmp = x * (y / z)
    else if (y <= 9500.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -3.3e-43) {
		tmp = t_0;
	} else if (y <= 2.2e-78) {
		tmp = x;
	} else if (y <= 4.2e-46) {
		tmp = x * (y / z);
	} else if (y <= 9500.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -3.3e-43:
		tmp = t_0
	elif y <= 2.2e-78:
		tmp = x
	elif y <= 4.2e-46:
		tmp = x * (y / z)
	elif y <= 9500.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -3.3e-43)
		tmp = t_0;
	elseif (y <= 2.2e-78)
		tmp = x;
	elseif (y <= 4.2e-46)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 9500.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -3.3e-43)
		tmp = t_0;
	elseif (y <= 2.2e-78)
		tmp = x;
	elseif (y <= 4.2e-46)
		tmp = x * (y / z);
	elseif (y <= 9500.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-43], t$95$0, If[LessEqual[y, 2.2e-78], x, If[LessEqual[y, 4.2e-46], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9500.0], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000016e-43 or 9500 < y

   1. Initial program 94.8%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 77.1%

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

   6. Simplified 77.1%

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

   if -3.30000000000000016e-43 < y < 2.1999999999999999e-78 or 4.19999999999999975e-46 < y < 9500

   1. Initial program 82.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 78.9%

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

   if 2.1999999999999999e-78 < y < 4.19999999999999975e-46

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 88.1%

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

      1. associate-*r/ 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 9500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 14500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.8e-41)
   (* y (/ x z))
   (if (<= y 2.45e-79)
     x
     (if (<= y 3.4e-45) (* x (/ y z)) (if (<= y 14500.0) x (/ y (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e-41) {
		tmp = y * (x / z);
	} else if (y <= 2.45e-79) {
		tmp = x;
	} else if (y <= 3.4e-45) {
		tmp = x * (y / z);
	} else if (y <= 14500.0) {
		tmp = x;
	} else {
		tmp = y / (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 (y <= (-7.8d-41)) then
        tmp = y * (x / z)
    else if (y <= 2.45d-79) then
        tmp = x
    else if (y <= 3.4d-45) then
        tmp = x * (y / z)
    else if (y <= 14500.0d0) then
        tmp = x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e-41) {
		tmp = y * (x / z);
	} else if (y <= 2.45e-79) {
		tmp = x;
	} else if (y <= 3.4e-45) {
		tmp = x * (y / z);
	} else if (y <= 14500.0) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.8e-41:
		tmp = y * (x / z)
	elif y <= 2.45e-79:
		tmp = x
	elif y <= 3.4e-45:
		tmp = x * (y / z)
	elif y <= 14500.0:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.8e-41)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 2.45e-79)
		tmp = x;
	elseif (y <= 3.4e-45)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 14500.0)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.8e-41)
		tmp = y * (x / z);
	elseif (y <= 2.45e-79)
		tmp = x;
	elseif (y <= 3.4e-45)
		tmp = x * (y / z);
	elseif (y <= 14500.0)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.8e-41], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e-79], x, If[LessEqual[y, 3.4e-45], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 14500.0], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.79999999999999982e-41

   1. Initial program 96.6%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r/ 79.0%

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

   6. Simplified 79.0%

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

   if -7.79999999999999982e-41 < y < 2.45e-79 or 3.40000000000000004e-45 < y < 14500

   1. Initial program 82.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 78.9%

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

   if 2.45e-79 < y < 3.40000000000000004e-45

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 88.1%

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

      1. associate-*r/ 87.9%

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

   6. Simplified 87.9%

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

   if 14500 < y

   1. Initial program 93.2%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-*r/ 75.5%

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

   6. Simplified 75.5%

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

      1. clear-num 75.4%

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

      2. un-div-inv 75.5%

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

   8. Applied egg-rr 75.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 14500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.55e+73) (/ (* x (+ y z)) z) (* x (/ (+ y z) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e+73) {
		tmp = (x * (y + z)) / z;
	} else {
		tmp = x * ((y + z) / 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 <= (-2.55d+73)) then
        tmp = (x * (y + z)) / z
    else
        tmp = x * ((y + z) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e+73) {
		tmp = (x * (y + z)) / z;
	} else {
		tmp = x * ((y + z) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.55e+73:
		tmp = (x * (y + z)) / z
	else:
		tmp = x * ((y + z) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.55e+73)
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	else
		tmp = Float64(x * Float64(Float64(y + z) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.55e+73)
		tmp = (x * (y + z)) / z;
	else
		tmp = x * ((y + z) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.55e+73], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55000000000000012e73

   1. Initial program 97.2%

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

   if -2.55000000000000012e73 < y

   1. Initial program 87.8%

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

      1. associate-*r/ 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternative 7: 95.8% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

   1. associate-*r/ 95.4%

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

3. Simplified 95.4%

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

4. Final simplification 95.4%

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

Alternative 8: 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]

Derivation

1. Initial program 89.2%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

4. Final simplification 95.5%

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

Alternative 9: 51.0% 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 89.2%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

4. Taylor expanded in z around inf 46.5%

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

5. Final simplification 46.5%

   \[\leadsto x \]

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 2023301 
(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))