Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 85.3% → 96.1%

Time: 4.6s

Alternatives: 6

Speedup: 0.8×

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: 85.3% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+196) (* (/ x z) (+ y z)) (/ x (/ z (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+196) {
		tmp = (x / z) * (y + z);
	} else {
		tmp = x / (z / (y + 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 <= (-1.05d+196)) then
        tmp = (x / z) * (y + z)
    else
        tmp = x / (z / (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+196) {
		tmp = (x / z) * (y + z);
	} else {
		tmp = x / (z / (y + z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+196:
		tmp = (x / z) * (y + z)
	else:
		tmp = x / (z / (y + z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+196)
		tmp = Float64(Float64(x / z) * Float64(y + z));
	else
		tmp = Float64(x / Float64(z / Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+196)
		tmp = (x / z) * (y + z);
	else
		tmp = x / (z / (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+196], N[(N[(x / z), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000007e196

   1. Initial program 92.6%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   if -1.05000000000000007e196 < y

   1. Initial program 78.7%

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

      1. associate-*l/ 86.1%

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

   3. Simplified 86.1%

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

      1. associate-/r/ 97.6%

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

      2. +-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \]

Alternative 2: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -300000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-42} \lor \neg \left(z \leq -2.4 \cdot 10^{-130}\right) \land z \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -300000000000.0)
   x
   (if (or (<= z -9.5e-42) (and (not (<= z -2.4e-130)) (<= z 4.6e-26)))
     (* x (/ y z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -300000000000.0) {
		tmp = x;
	} else if ((z <= -9.5e-42) || (!(z <= -2.4e-130) && (z <= 4.6e-26))) {
		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 (z <= (-300000000000.0d0)) then
        tmp = x
    else if ((z <= (-9.5d-42)) .or. (.not. (z <= (-2.4d-130))) .and. (z <= 4.6d-26)) 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 (z <= -300000000000.0) {
		tmp = x;
	} else if ((z <= -9.5e-42) || (!(z <= -2.4e-130) && (z <= 4.6e-26))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -300000000000.0:
		tmp = x
	elif (z <= -9.5e-42) or (not (z <= -2.4e-130) and (z <= 4.6e-26)):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -300000000000.0)
		tmp = x;
	elseif ((z <= -9.5e-42) || (!(z <= -2.4e-130) && (z <= 4.6e-26)))
		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 (z <= -300000000000.0)
		tmp = x;
	elseif ((z <= -9.5e-42) || (~((z <= -2.4e-130)) && (z <= 4.6e-26)))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -300000000000.0], x, If[Or[LessEqual[z, -9.5e-42], And[N[Not[LessEqual[z, -2.4e-130]], $MachinePrecision], LessEqual[z, 4.6e-26]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3e11 or -9.49999999999999948e-42 < z < -2.39999999999999997e-130 or 4.60000000000000018e-26 < z

   1. Initial program 71.4%

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

      1. associate-*l/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in z around inf 80.1%

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

   if -3e11 < z < -9.49999999999999948e-42 or -2.39999999999999997e-130 < z < 4.60000000000000018e-26

   1. Initial program 90.9%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*r/ 74.0%

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

   6. Simplified 74.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -300000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-42} \lor \neg \left(z \leq -2.4 \cdot 10^{-130}\right) \land z \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -280000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-82} \lor \neg \left(z \leq -2.4 \cdot 10^{-130}\right) \land z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -280000000000.0)
   x
   (if (or (<= z -1.65e-82) (and (not (<= z -2.4e-130)) (<= z 6e-25)))
     (* y (/ x z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -280000000000.0) {
		tmp = x;
	} else if ((z <= -1.65e-82) || (!(z <= -2.4e-130) && (z <= 6e-25))) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-280000000000.0d0)) then
        tmp = x
    else if ((z <= (-1.65d-82)) .or. (.not. (z <= (-2.4d-130))) .and. (z <= 6d-25)) then
        tmp = y * (x / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -280000000000.0) {
		tmp = x;
	} else if ((z <= -1.65e-82) || (!(z <= -2.4e-130) && (z <= 6e-25))) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -280000000000.0:
		tmp = x
	elif (z <= -1.65e-82) or (not (z <= -2.4e-130) and (z <= 6e-25)):
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -280000000000.0)
		tmp = x;
	elseif ((z <= -1.65e-82) || (!(z <= -2.4e-130) && (z <= 6e-25)))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -280000000000.0)
		tmp = x;
	elseif ((z <= -1.65e-82) || (~((z <= -2.4e-130)) && (z <= 6e-25)))
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -280000000000.0], x, If[Or[LessEqual[z, -1.65e-82], And[N[Not[LessEqual[z, -2.4e-130]], $MachinePrecision], LessEqual[z, 6e-25]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e11 or -1.65000000000000011e-82 < z < -2.39999999999999997e-130 or 5.9999999999999995e-25 < z

   1. Initial program 68.7%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 83.2%

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

   if -2.8e11 < z < -1.65000000000000011e-82 or -2.39999999999999997e-130 < z < 5.9999999999999995e-25

   1. Initial program 91.7%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 76.1%

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

      1. associate-*r/ 76.4%

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

   6. Simplified 76.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -280000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-82} \lor \neg \left(z \leq -2.4 \cdot 10^{-130}\right) \land z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -250000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -250000000000.0)
   x
   (if (<= z -5.2e-83)
     (* y (/ x z))
     (if (<= z -2.4e-130) x (if (<= z 4.6e-26) (/ y (/ z x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -250000000000.0) {
		tmp = x;
	} else if (z <= -5.2e-83) {
		tmp = y * (x / z);
	} else if (z <= -2.4e-130) {
		tmp = x;
	} else if (z <= 4.6e-26) {
		tmp = y / (z / x);
	} 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 <= (-250000000000.0d0)) then
        tmp = x
    else if (z <= (-5.2d-83)) then
        tmp = y * (x / z)
    else if (z <= (-2.4d-130)) then
        tmp = x
    else if (z <= 4.6d-26) then
        tmp = y / (z / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -250000000000.0) {
		tmp = x;
	} else if (z <= -5.2e-83) {
		tmp = y * (x / z);
	} else if (z <= -2.4e-130) {
		tmp = x;
	} else if (z <= 4.6e-26) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -250000000000.0:
		tmp = x
	elif z <= -5.2e-83:
		tmp = y * (x / z)
	elif z <= -2.4e-130:
		tmp = x
	elif z <= 4.6e-26:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -250000000000.0)
		tmp = x;
	elseif (z <= -5.2e-83)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= -2.4e-130)
		tmp = x;
	elseif (z <= 4.6e-26)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -250000000000.0)
		tmp = x;
	elseif (z <= -5.2e-83)
		tmp = y * (x / z);
	elseif (z <= -2.4e-130)
		tmp = x;
	elseif (z <= 4.6e-26)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -250000000000.0], x, If[LessEqual[z, -5.2e-83], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-130], x, If[LessEqual[z, 4.6e-26], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e11 or -5.20000000000000018e-83 < z < -2.39999999999999997e-130 or 4.60000000000000018e-26 < z

   1. Initial program 68.7%

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

      1. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 83.2%

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

   if -2.5e11 < z < -5.20000000000000018e-83

   1. Initial program 99.7%

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

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

   4. Taylor expanded in z around 0 62.3%

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

      1. associate-*r/ 62.5%

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

   6. Simplified 62.5%

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

   if -2.39999999999999997e-130 < z < 4.60000000000000018e-26

   1. Initial program 89.7%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around 0 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*r/ 74.4%

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

   6. Simplified 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/r/ 80.9%

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

   8. Applied egg-rr 80.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -250000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.66e+114) x (if (<= z 2.35e+151) (* (/ x z) (+ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.66e+114) {
		tmp = x;
	} else if (z <= 2.35e+151) {
		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 <= (-1.66d+114)) then
        tmp = x
    else if (z <= 2.35d+151) 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 <= -1.66e+114) {
		tmp = x;
	} else if (z <= 2.35e+151) {
		tmp = (x / z) * (y + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.66e+114:
		tmp = x
	elif z <= 2.35e+151:
		tmp = (x / z) * (y + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.66e+114)
		tmp = x;
	elseif (z <= 2.35e+151)
		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 <= -1.66e+114)
		tmp = x;
	elseif (z <= 2.35e+151)
		tmp = (x / z) * (y + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.66e+114], x, If[LessEqual[z, 2.35e+151], N[(N[(x / z), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.66000000000000008e114 or 2.34999999999999995e151 < z

   1. Initial program 53.4%

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

      1. associate-*l/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 92.5%

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

   if -1.66000000000000008e114 < z < 2.34999999999999995e151

   1. Initial program 90.4%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.3% 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 80.1%

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

   1. associate-*l/ 86.9%

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

3. Simplified 86.9%

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

4. Taylor expanded in z around inf 52.6%

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

5. Final simplification 52.6%

   \[\leadsto x \]

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 2023208 
(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))