Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.9% → 96.1%

Time: 3.9s

Alternatives: 8

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: 84.9% 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: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-68} \lor \neg \left(z \leq 0.002\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-68) (not (<= z 0.002)))
   (* x (/ (+ y z) z))
   (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-68) || !(z <= 0.002)) {
		tmp = x * ((y + z) / z);
	} else {
		tmp = (y + z) * (x / 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 ((z <= (-1.7d-68)) .or. (.not. (z <= 0.002d0))) then
        tmp = x * ((y + z) / z)
    else
        tmp = (y + z) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-68) || !(z <= 0.002)) {
		tmp = x * ((y + z) / z);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-68) or not (z <= 0.002):
		tmp = x * ((y + z) / z)
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-68) || !(z <= 0.002))
		tmp = Float64(x * Float64(Float64(y + z) / z));
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.7e-68) || ~((z <= 0.002)))
		tmp = x * ((y + z) / z);
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-68], N[Not[LessEqual[z, 0.002]], $MachinePrecision]], N[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000009e-68 or 2e-3 < z

   1. Initial program 82.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -1.70000000000000009e-68 < z < 2e-3

   1. Initial program 90.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-68} \lor \neg \left(z \leq 0.002\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ y z)) z) 5e-18) (/ x (/ z (+ y z))) (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 5e-18) {
		tmp = x / (z / (y + z));
	} else {
		tmp = (y + z) * (x / 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 (((x * (y + z)) / z) <= 5d-18) then
        tmp = x / (z / (y + z))
    else
        tmp = (y + z) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 5e-18) {
		tmp = x / (z / (y + z));
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y + z)) / z) <= 5e-18:
		tmp = x / (z / (y + z))
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y + z)) / z) <= 5e-18)
		tmp = Float64(x / Float64(z / Float64(y + z)));
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * (y + z)) / z) <= 5e-18)
		tmp = x / (z / (y + z));
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 5e-18], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 5.00000000000000036e-18

   1. Initial program 88.4%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   if 5.00000000000000036e-18 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 82.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+26} \lor \neg \left(y \leq 5.5 \cdot 10^{-147}\right) \land \left(y \leq 7.2 \cdot 10^{-124} \lor \neg \left(y \leq 2 \cdot 10^{+40}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+26)
         (and (not (<= y 5.5e-147)) (or (<= y 7.2e-124) (not (<= y 2e+40)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+26) || (!(y <= 5.5e-147) && ((y <= 7.2e-124) || !(y <= 2e+40)))) {
		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+26)) .or. (.not. (y <= 5.5d-147)) .and. (y <= 7.2d-124) .or. (.not. (y <= 2d+40))) 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+26) || (!(y <= 5.5e-147) && ((y <= 7.2e-124) || !(y <= 2e+40)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+26) or (not (y <= 5.5e-147) and ((y <= 7.2e-124) or not (y <= 2e+40))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+26) || (!(y <= 5.5e-147) && ((y <= 7.2e-124) || !(y <= 2e+40))))
		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+26) || (~((y <= 5.5e-147)) && ((y <= 7.2e-124) || ~((y <= 2e+40)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+26], And[N[Not[LessEqual[y, 5.5e-147]], $MachinePrecision], Or[LessEqual[y, 7.2e-124], N[Not[LessEqual[y, 2e+40]], $MachinePrecision]]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000004e26 or 5.5e-147 < y < 7.20000000000000019e-124 or 2.00000000000000006e40 < y

   1. Initial program 91.6%

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

      1. associate-*r/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around inf 79.6%

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

      1. associate-*r/ 74.2%

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

   6. Simplified 74.2%

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

   if -1.10000000000000004e26 < y < 5.5e-147 or 7.20000000000000019e-124 < y < 2.00000000000000006e40

   1. Initial program 81.4%

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

      1. associate-*r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 76.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+26} \lor \neg \left(y \leq 5.5 \cdot 10^{-147}\right) \land \left(y \leq 7.2 \cdot 10^{-124} \lor \neg \left(y \leq 2 \cdot 10^{+40}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 70.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.55 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -1.7e+26)
     t_0
     (if (<= y 4.55e-147)
       x
       (if (<= y 6.5e-125) (* x (/ y z)) (if (<= y 2e-99) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -1.7e+26) {
		tmp = t_0;
	} else if (y <= 4.55e-147) {
		tmp = x;
	} else if (y <= 6.5e-125) {
		tmp = x * (y / z);
	} else if (y <= 2e-99) {
		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 <= (-1.7d+26)) then
        tmp = t_0
    else if (y <= 4.55d-147) then
        tmp = x
    else if (y <= 6.5d-125) then
        tmp = x * (y / z)
    else if (y <= 2d-99) 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 <= -1.7e+26) {
		tmp = t_0;
	} else if (y <= 4.55e-147) {
		tmp = x;
	} else if (y <= 6.5e-125) {
		tmp = x * (y / z);
	} else if (y <= 2e-99) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -1.7e+26:
		tmp = t_0
	elif y <= 4.55e-147:
		tmp = x
	elif y <= 6.5e-125:
		tmp = x * (y / z)
	elif y <= 2e-99:
		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 <= -1.7e+26)
		tmp = t_0;
	elseif (y <= 4.55e-147)
		tmp = x;
	elseif (y <= 6.5e-125)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2e-99)
		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 <= -1.7e+26)
		tmp = t_0;
	elseif (y <= 4.55e-147)
		tmp = x;
	elseif (y <= 6.5e-125)
		tmp = x * (y / z);
	elseif (y <= 2e-99)
		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, -1.7e+26], t$95$0, If[LessEqual[y, 4.55e-147], x, If[LessEqual[y, 6.5e-125], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-99], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e26 or 2e-99 < y

   1. Initial program 90.9%

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

      1. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. associate-*l/ 75.2%

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

   6. Applied egg-rr 75.2%

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

   if -1.7000000000000001e26 < y < 4.54999999999999977e-147 or 6.4999999999999999e-125 < y < 2e-99

   1. Initial program 79.8%

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

      1. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 81.7%

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

   if 4.54999999999999977e-147 < y < 6.4999999999999999e-125

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 85.6%

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

      1. associate-*r/ 85.6%

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

   6. Simplified 85.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.55 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (/ z x))))
   (if (<= y -1.15e+26)
     t_0
     (if (<= y 5.5e-147)
       x
       (if (<= y 6.5e-125) (* x (/ y z)) (if (<= y 2.5e-98) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (z / x);
	double tmp;
	if (y <= -1.15e+26) {
		tmp = t_0;
	} else if (y <= 5.5e-147) {
		tmp = x;
	} else if (y <= 6.5e-125) {
		tmp = x * (y / z);
	} else if (y <= 2.5e-98) {
		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 / (z / x)
    if (y <= (-1.15d+26)) then
        tmp = t_0
    else if (y <= 5.5d-147) then
        tmp = x
    else if (y <= 6.5d-125) then
        tmp = x * (y / z)
    else if (y <= 2.5d-98) 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 / (z / x);
	double tmp;
	if (y <= -1.15e+26) {
		tmp = t_0;
	} else if (y <= 5.5e-147) {
		tmp = x;
	} else if (y <= 6.5e-125) {
		tmp = x * (y / z);
	} else if (y <= 2.5e-98) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (z / x)
	tmp = 0
	if y <= -1.15e+26:
		tmp = t_0
	elif y <= 5.5e-147:
		tmp = x
	elif y <= 6.5e-125:
		tmp = x * (y / z)
	elif y <= 2.5e-98:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (y <= -1.15e+26)
		tmp = t_0;
	elseif (y <= 5.5e-147)
		tmp = x;
	elseif (y <= 6.5e-125)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.5e-98)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (z / x);
	tmp = 0.0;
	if (y <= -1.15e+26)
		tmp = t_0;
	elseif (y <= 5.5e-147)
		tmp = x;
	elseif (y <= 6.5e-125)
		tmp = x * (y / z);
	elseif (y <= 2.5e-98)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+26], t$95$0, If[LessEqual[y, 5.5e-147], x, If[LessEqual[y, 6.5e-125], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-98], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e26 or 2.50000000000000009e-98 < y

   1. Initial program 90.9%

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

      1. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around inf 74.2%

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

      1. associate-*r/ 69.4%

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

   6. Simplified 69.4%

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

      1. associate-*r/ 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-/l* 75.2%

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

   8. Applied egg-rr 75.2%

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

   if -1.15e26 < y < 5.5e-147 or 6.4999999999999999e-125 < y < 2.50000000000000009e-98

   1. Initial program 79.8%

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

      1. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 81.7%

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

   if 5.5e-147 < y < 6.4999999999999999e-125

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 85.6%

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

      1. associate-*r/ 85.6%

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

   6. Simplified 85.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e+26)
   (/ (* x y) z)
   (if (<= y 5.5e-147)
     x
     (if (<= y 1.05e-123)
       (* x (/ y z))
       (if (<= y 1.32e-98) x (/ y (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e+26) {
		tmp = (x * y) / z;
	} else if (y <= 5.5e-147) {
		tmp = x;
	} else if (y <= 1.05e-123) {
		tmp = x * (y / z);
	} else if (y <= 1.32e-98) {
		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 <= (-1.15d+26)) then
        tmp = (x * y) / z
    else if (y <= 5.5d-147) then
        tmp = x
    else if (y <= 1.05d-123) then
        tmp = x * (y / z)
    else if (y <= 1.32d-98) 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 <= -1.15e+26) {
		tmp = (x * y) / z;
	} else if (y <= 5.5e-147) {
		tmp = x;
	} else if (y <= 1.05e-123) {
		tmp = x * (y / z);
	} else if (y <= 1.32e-98) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e+26:
		tmp = (x * y) / z
	elif y <= 5.5e-147:
		tmp = x
	elif y <= 1.05e-123:
		tmp = x * (y / z)
	elif y <= 1.32e-98:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e+26)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 5.5e-147)
		tmp = x;
	elseif (y <= 1.05e-123)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 1.32e-98)
		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 <= -1.15e+26)
		tmp = (x * y) / z;
	elseif (y <= 5.5e-147)
		tmp = x;
	elseif (y <= 1.05e-123)
		tmp = x * (y / z);
	elseif (y <= 1.32e-98)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e+26], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 5.5e-147], x, If[LessEqual[y, 1.05e-123], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-98], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.15e26

   1. Initial program 91.6%

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

      1. associate-*r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 77.9%

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

   if -1.15e26 < y < 5.5e-147 or 1.05e-123 < y < 1.31999999999999995e-98

   1. Initial program 79.8%

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

      1. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 81.7%

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

   if 5.5e-147 < y < 1.05e-123

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 85.6%

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

      1. associate-*r/ 85.6%

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

   6. Simplified 85.6%

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

   if 1.31999999999999995e-98 < y

   1. Initial program 90.3%

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

      1. associate-*r/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 71.6%

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

      1. associate-*r/ 69.8%

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

   6. Simplified 69.8%

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

      1. associate-*r/ 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-/l* 76.3%

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

   8. Applied egg-rr 76.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+26}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

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 86.4%

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

   1. associate-*r/ 94.1%

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

3. Simplified 94.1%

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

4. Final simplification 94.1%

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

Alternative 8: 50.5% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.4%

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

   1. associate-*r/ 94.1%

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

3. Simplified 94.1%

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

4. Taylor expanded in y around 0 47.0%

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

5. Final simplification 47.0%

   \[\leadsto x \]

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 2023290 
(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))