Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.0% → 96.0%

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: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.0× speedup

Math

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

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 85.0%

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

   1. associate-*l/ 83.0%

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

3. Simplified 83.0%

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

   1. associate-/r/ 96.6%

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

   2. +-commutative 96.6%

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

5. Applied egg-rr 96.6%

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

6. Final simplification 96.6%

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

Alternative 2: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-98}\right) \land \left(y \leq 1.8 \cdot 10^{-75} \lor \neg \left(y \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -32000000.0)
         (and (not (<= y 2.5e-98)) (or (<= y 1.8e-75) (not (<= y 4.1e-7)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32000000.0) || (!(y <= 2.5e-98) && ((y <= 1.8e-75) || !(y <= 4.1e-7)))) {
		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 <= (-32000000.0d0)) .or. (.not. (y <= 2.5d-98)) .and. (y <= 1.8d-75) .or. (.not. (y <= 4.1d-7))) 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 <= -32000000.0) || (!(y <= 2.5e-98) && ((y <= 1.8e-75) || !(y <= 4.1e-7)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -32000000.0) or (not (y <= 2.5e-98) and ((y <= 1.8e-75) or not (y <= 4.1e-7))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -32000000.0) || (!(y <= 2.5e-98) && ((y <= 1.8e-75) || !(y <= 4.1e-7))))
		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 <= -32000000.0) || (~((y <= 2.5e-98)) && ((y <= 1.8e-75) || ~((y <= 4.1e-7)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -32000000.0], And[N[Not[LessEqual[y, 2.5e-98]], $MachinePrecision], Or[LessEqual[y, 1.8e-75], N[Not[LessEqual[y, 4.1e-7]], $MachinePrecision]]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e7 or 2.50000000000000009e-98 < y < 1.8e-75 or 4.0999999999999999e-7 < y

   1. Initial program 84.9%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in z around 0 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-*r/ 74.5%

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

   6. Simplified 74.5%

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

   if -3.2e7 < y < 2.50000000000000009e-98 or 1.8e-75 < y < 4.0999999999999999e-7

   1. Initial program 85.1%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 80.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-98}\right) \land \left(y \leq 1.8 \cdot 10^{-75} \lor \neg \left(y \leq 4.1 \cdot 10^{-7}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -29:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -29.0)
     t_0
     (if (<= y 2.5e-98)
       x
       (if (<= y 7.4e-75) (* x (/ y z)) (if (<= y 2.7e-9) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -29.0) {
		tmp = t_0;
	} else if (y <= 2.5e-98) {
		tmp = x;
	} else if (y <= 7.4e-75) {
		tmp = x * (y / z);
	} else if (y <= 2.7e-9) {
		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 <= (-29.0d0)) then
        tmp = t_0
    else if (y <= 2.5d-98) then
        tmp = x
    else if (y <= 7.4d-75) then
        tmp = x * (y / z)
    else if (y <= 2.7d-9) 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 <= -29.0) {
		tmp = t_0;
	} else if (y <= 2.5e-98) {
		tmp = x;
	} else if (y <= 7.4e-75) {
		tmp = x * (y / z);
	} else if (y <= 2.7e-9) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -29.0:
		tmp = t_0
	elif y <= 2.5e-98:
		tmp = x
	elif y <= 7.4e-75:
		tmp = x * (y / z)
	elif y <= 2.7e-9:
		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 <= -29.0)
		tmp = t_0;
	elseif (y <= 2.5e-98)
		tmp = x;
	elseif (y <= 7.4e-75)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.7e-9)
		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 <= -29.0)
		tmp = t_0;
	elseif (y <= 2.5e-98)
		tmp = x;
	elseif (y <= 7.4e-75)
		tmp = x * (y / z);
	elseif (y <= 2.7e-9)
		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, -29.0], t$95$0, If[LessEqual[y, 2.5e-98], x, If[LessEqual[y, 7.4e-75], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-9], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -29 or 2.7000000000000002e-9 < y

   1. Initial program 84.1%

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

      1. associate-*l/ 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. associate-*r/ 75.6%

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

   6. Simplified 75.6%

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

   if -29 < y < 2.50000000000000009e-98 or 7.40000000000000047e-75 < y < 2.7000000000000002e-9

   1. Initial program 85.1%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 80.9%

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

   if 2.50000000000000009e-98 < y < 7.40000000000000047e-75

   1. Initial program 99.6%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -29:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -30500:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -30500.0)
   (/ (* x y) z)
   (if (<= y 1.25e-98)
     x
     (if (<= y 7.2e-74) (* x (/ y z)) (if (<= y 2.5e-11) x (* y (/ x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -30500.0) {
		tmp = (x * y) / z;
	} else if (y <= 1.25e-98) {
		tmp = x;
	} else if (y <= 7.2e-74) {
		tmp = x * (y / z);
	} else if (y <= 2.5e-11) {
		tmp = x;
	} else {
		tmp = y * (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 (y <= (-30500.0d0)) then
        tmp = (x * y) / z
    else if (y <= 1.25d-98) then
        tmp = x
    else if (y <= 7.2d-74) then
        tmp = x * (y / z)
    else if (y <= 2.5d-11) then
        tmp = x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -30500.0) {
		tmp = (x * y) / z;
	} else if (y <= 1.25e-98) {
		tmp = x;
	} else if (y <= 7.2e-74) {
		tmp = x * (y / z);
	} else if (y <= 2.5e-11) {
		tmp = x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -30500.0:
		tmp = (x * y) / z
	elif y <= 1.25e-98:
		tmp = x
	elif y <= 7.2e-74:
		tmp = x * (y / z)
	elif y <= 2.5e-11:
		tmp = x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -30500.0)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1.25e-98)
		tmp = x;
	elseif (y <= 7.2e-74)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 2.5e-11)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -30500.0)
		tmp = (x * y) / z;
	elseif (y <= 1.25e-98)
		tmp = x;
	elseif (y <= 7.2e-74)
		tmp = x * (y / z);
	elseif (y <= 2.5e-11)
		tmp = x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -30500.0], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.25e-98], x, If[LessEqual[y, 7.2e-74], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-11], x, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -30500

   1. Initial program 87.7%

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

      1. associate-*l/ 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in z around 0 69.8%

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

   if -30500 < y < 1.25000000000000005e-98 or 7.2000000000000005e-74 < y < 2.50000000000000009e-11

   1. Initial program 85.1%

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

      1. associate-*l/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 80.9%

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

   if 1.25000000000000005e-98 < y < 7.2000000000000005e-74

   1. Initial program 99.6%

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

      1. associate-*l/ 73.4%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

   if 2.50000000000000009e-11 < y

   1. Initial program 81.8%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 74.5%

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

      1. associate-*r/ 81.3%

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

   6. Simplified 81.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30500:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+205}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.7e+188) x (if (<= z 4.2e+205) (* (/ x z) (+ z y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+188) {
		tmp = x;
	} else if (z <= 4.2e+205) {
		tmp = (x / z) * (z + y);
	} 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 <= (-2.7d+188)) then
        tmp = x
    else if (z <= 4.2d+205) then
        tmp = (x / z) * (z + y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+188) {
		tmp = x;
	} else if (z <= 4.2e+205) {
		tmp = (x / z) * (z + y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.7e+188:
		tmp = x
	elif z <= 4.2e+205:
		tmp = (x / z) * (z + y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.7e+188)
		tmp = x;
	elseif (z <= 4.2e+205)
		tmp = Float64(Float64(x / z) * Float64(z + y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.7e+188)
		tmp = x;
	elseif (z <= 4.2e+205)
		tmp = (x / z) * (z + y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.7e+188], x, If[LessEqual[z, 4.2e+205], N[(N[(x / z), $MachinePrecision] * N[(z + y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e188 or 4.2000000000000001e205 < z

   1. Initial program 63.5%

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

      1. associate-*l/ 51.2%

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

   3. Simplified 51.2%

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

   4. Taylor expanded in z around inf 95.9%

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

   if -2.7e188 < z < 4.2000000000000001e205

   1. Initial program 90.1%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+205}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.1% 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 85.0%

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

   1. associate-*l/ 83.0%

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

3. Simplified 83.0%

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

4. Taylor expanded in z around inf 47.8%

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

5. Final simplification 47.8%

   \[\leadsto x \]

Developer target: 96.0% 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 2023257 
(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))