Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.1% → 95.7%

Time: 4.0s

Alternatives: 7

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: 84.1% 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: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \frac{y}{z}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. associate-*l/ 83.0%

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

   2. distribute-rgt-in 80.9%

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

   3. *-commutative 80.9%

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

   4. associate-/r/ 93.9%

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

   5. *-inverses 93.9%

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

   6. /-rgt-identity 93.9%

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

   7. associate-*r/ 95.1%

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

   8. *-commutative 95.1%

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

   9. associate-*r/ 97.3%

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

   10. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+44} \lor \neg \left(y \leq 1.1 \cdot 10^{+23}\right) \land \left(y \leq 1.3 \cdot 10^{+69} \lor \neg \left(y \leq 2.8 \cdot 10^{+127}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.45e+44)
         (and (not (<= y 1.1e+23)) (or (<= y 1.3e+69) (not (<= y 2.8e+127)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.45e+44) || (!(y <= 1.1e+23) && ((y <= 1.3e+69) || !(y <= 2.8e+127)))) {
		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 <= (-1.45d+44)) .or. (.not. (y <= 1.1d+23)) .and. (y <= 1.3d+69) .or. (.not. (y <= 2.8d+127))) 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 <= -1.45e+44) || (!(y <= 1.1e+23) && ((y <= 1.3e+69) || !(y <= 2.8e+127)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.45e+44) or (not (y <= 1.1e+23) and ((y <= 1.3e+69) or not (y <= 2.8e+127))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.45e+44) || (!(y <= 1.1e+23) && ((y <= 1.3e+69) || !(y <= 2.8e+127))))
		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 <= -1.45e+44) || (~((y <= 1.1e+23)) && ((y <= 1.3e+69) || ~((y <= 2.8e+127)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.45e+44], And[N[Not[LessEqual[y, 1.1e+23]], $MachinePrecision], Or[LessEqual[y, 1.3e+69], N[Not[LessEqual[y, 2.8e+127]], $MachinePrecision]]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e44 or 1.10000000000000004e23 < y < 1.3000000000000001e69 or 2.8000000000000002e127 < y

   1. Initial program 92.0%

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

      1. associate-*l/ 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-*r/ 79.2%

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

   6. Simplified 79.2%

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

   if -1.4500000000000001e44 < y < 1.10000000000000004e23 or 1.3000000000000001e69 < y < 2.8000000000000002e127

   1. Initial program 82.0%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 75.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+44} \lor \neg \left(y \leq 1.1 \cdot 10^{+23}\right) \land \left(y \leq 1.3 \cdot 10^{+69} \lor \neg \left(y \leq 2.8 \cdot 10^{+127}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+69}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -5e+49)
     t_0
     (if (<= y 1.1e+23)
       x
       (if (<= y 1e+69) (* x (/ y z)) (if (<= y 6.8e+127) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -5e+49) {
		tmp = t_0;
	} else if (y <= 1.1e+23) {
		tmp = x;
	} else if (y <= 1e+69) {
		tmp = x * (y / z);
	} else if (y <= 6.8e+127) {
		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 <= (-5d+49)) then
        tmp = t_0
    else if (y <= 1.1d+23) then
        tmp = x
    else if (y <= 1d+69) then
        tmp = x * (y / z)
    else if (y <= 6.8d+127) 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 <= -5e+49) {
		tmp = t_0;
	} else if (y <= 1.1e+23) {
		tmp = x;
	} else if (y <= 1e+69) {
		tmp = x * (y / z);
	} else if (y <= 6.8e+127) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -5e+49:
		tmp = t_0
	elif y <= 1.1e+23:
		tmp = x
	elif y <= 1e+69:
		tmp = x * (y / z)
	elif y <= 6.8e+127:
		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 <= -5e+49)
		tmp = t_0;
	elseif (y <= 1.1e+23)
		tmp = x;
	elseif (y <= 1e+69)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 6.8e+127)
		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 <= -5e+49)
		tmp = t_0;
	elseif (y <= 1.1e+23)
		tmp = x;
	elseif (y <= 1e+69)
		tmp = x * (y / z);
	elseif (y <= 6.8e+127)
		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, -5e+49], t$95$0, If[LessEqual[y, 1.1e+23], x, If[LessEqual[y, 1e+69], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+127], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000004e49 or 6.79999999999999955e127 < y

   1. Initial program 90.6%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 78.9%

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

   6. Simplified 78.9%

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

   if -5.0000000000000004e49 < y < 1.10000000000000004e23 or 1.0000000000000001e69 < y < 6.79999999999999955e127

   1. Initial program 82.0%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 75.9%

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

   if 1.10000000000000004e23 < y < 1.0000000000000001e69

   1. Initial program 99.8%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*r/ 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+69}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z)))
   (if (<= y -1.65e+43)
     t_0
     (if (<= y 1.28e+23)
       x
       (if (<= y 9.5e+68) (* x (/ y z)) (if (<= y 3e+127) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (y <= -1.65e+43) {
		tmp = t_0;
	} else if (y <= 1.28e+23) {
		tmp = x;
	} else if (y <= 9.5e+68) {
		tmp = x * (y / z);
	} else if (y <= 3e+127) {
		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 * y) / z
    if (y <= (-1.65d+43)) then
        tmp = t_0
    else if (y <= 1.28d+23) then
        tmp = x
    else if (y <= 9.5d+68) then
        tmp = x * (y / z)
    else if (y <= 3d+127) 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 * y) / z;
	double tmp;
	if (y <= -1.65e+43) {
		tmp = t_0;
	} else if (y <= 1.28e+23) {
		tmp = x;
	} else if (y <= 9.5e+68) {
		tmp = x * (y / z);
	} else if (y <= 3e+127) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if y <= -1.65e+43:
		tmp = t_0
	elif y <= 1.28e+23:
		tmp = x
	elif y <= 9.5e+68:
		tmp = x * (y / z)
	elif y <= 3e+127:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (y <= -1.65e+43)
		tmp = t_0;
	elseif (y <= 1.28e+23)
		tmp = x;
	elseif (y <= 9.5e+68)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 3e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	tmp = 0.0;
	if (y <= -1.65e+43)
		tmp = t_0;
	elseif (y <= 1.28e+23)
		tmp = x;
	elseif (y <= 9.5e+68)
		tmp = x * (y / z);
	elseif (y <= 3e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.65e+43], t$95$0, If[LessEqual[y, 1.28e+23], x, If[LessEqual[y, 9.5e+68], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+127], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6500000000000001e43 or 3.0000000000000002e127 < y

   1. Initial program 90.6%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around 0 80.2%

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

   if -1.6500000000000001e43 < y < 1.28e23 or 9.50000000000000069e68 < y < 3.0000000000000002e127

   1. Initial program 82.0%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 75.9%

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

   if 1.28e23 < y < 9.50000000000000069e68

   1. Initial program 99.8%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*r/ 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+43}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 5: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.7e+144) x (if (<= z 1.95e+93) (* (/ x z) (+ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+144) {
		tmp = x;
	} else if (z <= 1.95e+93) {
		tmp = (x / z) * (y + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.7d+144)) then
        tmp = x
    else if (z <= 1.95d+93) then
        tmp = (x / z) * (y + z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+144) {
		tmp = x;
	} else if (z <= 1.95e+93) {
		tmp = (x / z) * (y + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.7e+144:
		tmp = x
	elif z <= 1.95e+93:
		tmp = (x / z) * (y + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.7e+144)
		tmp = x;
	elseif (z <= 1.95e+93)
		tmp = Float64(Float64(x / z) * Float64(y + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.7e+144)
		tmp = x;
	elseif (z <= 1.95e+93)
		tmp = (x / z) * (y + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.7e+144], x, If[LessEqual[z, 1.95e+93], N[(N[(x / z), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.70000000000000015e144 or 1.9500000000000001e93 < z

   1. Initial program 72.4%

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

      1. associate-*l/ 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in z around inf 87.9%

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

   if -2.70000000000000015e144 < z < 1.9500000000000001e93

   1. Initial program 91.8%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. associate-*l/ 83.0%

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

   2. distribute-rgt-in 80.9%

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

   3. *-commutative 80.9%

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

   4. associate-/r/ 93.9%

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

   5. *-inverses 93.9%

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

   6. /-rgt-identity 93.9%

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

   7. associate-*r/ 95.1%

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

   8. *-commutative 95.1%

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

   9. associate-*r/ 97.3%

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

   10. fma-def 97.3%

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

3. Simplified 97.3%

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

   1. fma-udef 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 7: 51.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 85.8%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
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 53.9%

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

5. Final simplification 53.9%

   \[\leadsto x \]

Developer target: 96.1% 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 2023185 
(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))