Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.8% → 96.4%

Time: 3.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% 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: 96.4% 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 83.9%

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

   1. associate-*l/ 88.6%

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

3. Simplified 88.6%

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

   1. associate-/r/ 98.0%

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

   2. +-commutative 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-25} \lor \neg \left(y \leq -1.05 \cdot 10^{-63}\right) \land \left(y \leq -2.6 \cdot 10^{-116} \lor \neg \left(y \leq 5.3 \cdot 10^{-99}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-25)
         (and (not (<= y -1.05e-63))
              (or (<= y -2.6e-116) (not (<= y 5.3e-99)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-25) || (!(y <= -1.05e-63) && ((y <= -2.6e-116) || !(y <= 5.3e-99)))) {
		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 <= (-4d-25)) .or. (.not. (y <= (-1.05d-63))) .and. (y <= (-2.6d-116)) .or. (.not. (y <= 5.3d-99))) 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 <= -4e-25) || (!(y <= -1.05e-63) && ((y <= -2.6e-116) || !(y <= 5.3e-99)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-25) or (not (y <= -1.05e-63) and ((y <= -2.6e-116) or not (y <= 5.3e-99))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-25) || (!(y <= -1.05e-63) && ((y <= -2.6e-116) || !(y <= 5.3e-99))))
		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 <= -4e-25) || (~((y <= -1.05e-63)) && ((y <= -2.6e-116) || ~((y <= 5.3e-99)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-25], And[N[Not[LessEqual[y, -1.05e-63]], $MachinePrecision], Or[LessEqual[y, -2.6e-116], N[Not[LessEqual[y, 5.3e-99]], $MachinePrecision]]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000015e-25 or -1.05e-63 < y < -2.6e-116 or 5.3000000000000003e-99 < y

   1. Initial program 86.2%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around 0 70.8%

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

      1. associate-*r/ 72.9%

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

   6. Simplified 72.9%

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

   if -4.00000000000000015e-25 < y < -1.05e-63 or -2.6e-116 < y < 5.3000000000000003e-99

   1. Initial program 79.8%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in z around inf 83.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-25} \lor \neg \left(y \leq -1.05 \cdot 10^{-63}\right) \land \left(y \leq -2.6 \cdot 10^{-116} \lor \neg \left(y \leq 5.3 \cdot 10^{-99}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ z y))))
   (if (<= y -1.8e-27)
     t_0
     (if (<= y -8.5e-64)
       x
       (if (<= y -1.7e-115) (* x (/ y z)) (if (<= y 6.3e-102) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (z / y);
	double tmp;
	if (y <= -1.8e-27) {
		tmp = t_0;
	} else if (y <= -8.5e-64) {
		tmp = x;
	} else if (y <= -1.7e-115) {
		tmp = x * (y / z);
	} else if (y <= 6.3e-102) {
		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 = x / (z / y)
    if (y <= (-1.8d-27)) then
        tmp = t_0
    else if (y <= (-8.5d-64)) then
        tmp = x
    else if (y <= (-1.7d-115)) then
        tmp = x * (y / z)
    else if (y <= 6.3d-102) 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 = x / (z / y);
	double tmp;
	if (y <= -1.8e-27) {
		tmp = t_0;
	} else if (y <= -8.5e-64) {
		tmp = x;
	} else if (y <= -1.7e-115) {
		tmp = x * (y / z);
	} else if (y <= 6.3e-102) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (z / y)
	tmp = 0
	if y <= -1.8e-27:
		tmp = t_0
	elif y <= -8.5e-64:
		tmp = x
	elif y <= -1.7e-115:
		tmp = x * (y / z)
	elif y <= 6.3e-102:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(z / y))
	tmp = 0.0
	if (y <= -1.8e-27)
		tmp = t_0;
	elseif (y <= -8.5e-64)
		tmp = x;
	elseif (y <= -1.7e-115)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 6.3e-102)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (z / y);
	tmp = 0.0;
	if (y <= -1.8e-27)
		tmp = t_0;
	elseif (y <= -8.5e-64)
		tmp = x;
	elseif (y <= -1.7e-115)
		tmp = x * (y / z);
	elseif (y <= 6.3e-102)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e-27], t$95$0, If[LessEqual[y, -8.5e-64], x, If[LessEqual[y, -1.7e-115], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.3e-102], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e-27 or 6.29999999999999999e-102 < y

   1. Initial program 87.0%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

      1. associate-/r/ 96.8%

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

      2. +-commutative 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in z around 0 71.6%

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

      1. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

   if -1.7999999999999999e-27 < y < -8.49999999999999996e-64 or -1.6999999999999999e-115 < y < 6.29999999999999999e-102

   1. Initial program 79.8%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in z around inf 83.7%

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

   if -8.49999999999999996e-64 < y < -1.6999999999999999e-115

   1. Initial program 76.1%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in z around 0 60.5%

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

      1. associate-*r/ 84.2%

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

   6. Simplified 84.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e-29)
   (/ (* x y) z)
   (if (<= y -7.2e-64)
     x
     (if (<= y -1.95e-115) (* x (/ y z)) (if (<= y 5e-99) x (/ x (/ z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e-29) {
		tmp = (x * y) / z;
	} else if (y <= -7.2e-64) {
		tmp = x;
	} else if (y <= -1.95e-115) {
		tmp = x * (y / z);
	} else if (y <= 5e-99) {
		tmp = x;
	} else {
		tmp = x / (z / y);
	}
	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 <= (-3.1d-29)) then
        tmp = (x * y) / z
    else if (y <= (-7.2d-64)) then
        tmp = x
    else if (y <= (-1.95d-115)) then
        tmp = x * (y / z)
    else if (y <= 5d-99) then
        tmp = x
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e-29) {
		tmp = (x * y) / z;
	} else if (y <= -7.2e-64) {
		tmp = x;
	} else if (y <= -1.95e-115) {
		tmp = x * (y / z);
	} else if (y <= 5e-99) {
		tmp = x;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e-29:
		tmp = (x * y) / z
	elif y <= -7.2e-64:
		tmp = x
	elif y <= -1.95e-115:
		tmp = x * (y / z)
	elif y <= 5e-99:
		tmp = x
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e-29)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= -7.2e-64)
		tmp = x;
	elseif (y <= -1.95e-115)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 5e-99)
		tmp = x;
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e-29)
		tmp = (x * y) / z;
	elseif (y <= -7.2e-64)
		tmp = x;
	elseif (y <= -1.95e-115)
		tmp = x * (y / z);
	elseif (y <= 5e-99)
		tmp = x;
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e-29], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -7.2e-64], x, If[LessEqual[y, -1.95e-115], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-99], x, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.10000000000000026e-29

   1. Initial program 88.5%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 75.0%

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

   if -3.10000000000000026e-29 < y < -7.1999999999999996e-64 or -1.9499999999999999e-115 < y < 4.99999999999999969e-99

   1. Initial program 79.8%

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

      1. associate-*l/ 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in z around inf 83.7%

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

   if -7.1999999999999996e-64 < y < -1.9499999999999999e-115

   1. Initial program 76.1%

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

      1. associate-*l/ 79.8%

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

   3. Simplified 79.8%

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

   4. Taylor expanded in z around 0 60.5%

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

      1. associate-*r/ 84.2%

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

   6. Simplified 84.2%

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

   if 4.99999999999999969e-99 < y

   1. Initial program 86.0%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

      1. associate-/r/ 97.7%

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

      2. +-commutative 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in z around 0 69.1%

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

      1. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{z} \cdot \left(z + y\right) \end{array} \]

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.9%

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

   1. associate-*l/ 88.6%

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

3. Simplified 88.6%

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

4. Final simplification 88.6%

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

Alternative 6: 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 83.9%

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

   1. associate-*l/ 88.6%

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

3. Simplified 88.6%

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

4. Taylor expanded in z around inf 46.7%

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

5. Final simplification 46.7%

   \[\leadsto x \]

Developer target: 96.4% 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 2023318 
(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))