Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.7% → 96.0%

Time: 4.3s

Alternatives: 7

Speedup: 0.6×

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: 84.7% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 2 \cdot 10^{+50}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (+ y z)) z) 2e+50) (+ x (* x (/ y z))) (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y + z)) / z) <= 2e+50) {
		tmp = x + (x * (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) <= 2d+50) then
        tmp = x + (x * (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) <= 2e+50) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y + z)) / z) <= 2e+50:
		tmp = x + (x * (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) <= 2e+50)
		tmp = Float64(x + Float64(x * 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) <= 2e+50)
		tmp = x + (x * (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], 2e+50], N[(x + N[(x * 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) < 2.0000000000000002e50

   1. Initial program 84.5%

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

      1. associate-*r/ 98.9%

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

      2. remove-double-neg 98.9%

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

      3. sub-neg 98.9%

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

      4. div-sub 98.9%

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

      5. distribute-frac-neg 98.9%

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

      6. *-inverses 98.9%

         \[\leadsto x \cdot \left(\frac{y}{z} - \left(-\color{blue}{1}\right)\right) \]

      7. metadata-eval 98.9%

         \[\leadsto x \cdot \left(\frac{y}{z} - \color{blue}{-1}\right) \]

      8. sub-neg 98.9%

         \[\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(--1\right)\right)} \]

      9. metadata-eval 98.9%

         \[\leadsto x \cdot \left(\frac{y}{z} + \color{blue}{1}\right) \]

      10. *-inverses 98.9%

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

      11. distribute-lft-out 98.9%

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

      12. *-inverses 98.9%

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

      13. *-rgt-identity 98.9%

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

      14. fma-def 98.9%

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

   3. Simplified 98.9%

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

      1. fma-udef 98.9%

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

   5. Applied egg-rr 98.9%

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

   if 2.0000000000000002e50 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 83.1%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 2 \cdot 10^{+50}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 89.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+180}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e+112) x (if (<= z 9.6e+180) (* (+ y z) (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+112) {
		tmp = x;
	} else if (z <= 9.6e+180) {
		tmp = (y + z) * (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 <= (-2.2d+112)) then
        tmp = x
    else if (z <= 9.6d+180) then
        tmp = (y + z) * (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 <= -2.2e+112) {
		tmp = x;
	} else if (z <= 9.6e+180) {
		tmp = (y + z) * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e+112:
		tmp = x
	elif z <= 9.6e+180:
		tmp = (y + z) * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e+112)
		tmp = x;
	elseif (z <= 9.6e+180)
		tmp = Float64(Float64(y + z) * Float64(x / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.2e+112)
		tmp = x;
	elseif (z <= 9.6e+180)
		tmp = (y + z) * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e+112], x, If[LessEqual[z, 9.6e+180], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e112 or 9.5999999999999994e180 < z

   1. Initial program 68.6%

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

      1. associate-*l/ 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in z around inf 89.5%

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

   if -2.1999999999999999e112 < z < 9.5999999999999994e180

   1. Initial program 88.9%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+180}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e-63) x (if (<= z 1.08e+46) (* x (/ y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e-63) {
		tmp = x;
	} else if (z <= 1.08e+46) {
		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 <= (-1.2d-63)) then
        tmp = x
    else if (z <= 1.08d+46) 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 <= -1.2e-63) {
		tmp = x;
	} else if (z <= 1.08e+46) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e-63:
		tmp = x
	elif z <= 1.08e+46:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e-63)
		tmp = x;
	elseif (z <= 1.08e+46)
		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 <= -1.2e-63)
		tmp = x;
	elseif (z <= 1.08e+46)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e-63], x, If[LessEqual[z, 1.08e+46], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-63 or 1.07999999999999994e46 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -1.2e-63 < z < 1.07999999999999994e46

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 75.9%

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

      1. associate-*r/ 69.5%

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

   6. Simplified 69.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e-63) x (if (<= z 5.2e+45) (* y (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e-63) {
		tmp = x;
	} else if (z <= 5.2e+45) {
		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 <= (-1.16d-63)) then
        tmp = x
    else if (z <= 5.2d+45) 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 <= -1.16e-63) {
		tmp = x;
	} else if (z <= 5.2e+45) {
		tmp = y * (x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e-63:
		tmp = x
	elif z <= 5.2e+45:
		tmp = y * (x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e-63)
		tmp = x;
	elseif (z <= 5.2e+45)
		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 <= -1.16e-63)
		tmp = x;
	elseif (z <= 5.2e+45)
		tmp = y * (x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e-63], x, If[LessEqual[z, 5.2e+45], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.16e-63 or 5.20000000000000014e45 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -1.16e-63 < z < 5.20000000000000014e45

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 75.9%

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

      1. associate-/l* 70.5%

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

      2. associate-/r/ 72.7%

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

   6. Applied egg-rr 72.7%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e-63) x (if (<= z 2.1e+47) (/ y (/ z x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-63) {
		tmp = x;
	} else if (z <= 2.1e+47) {
		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 <= (-1d-63)) then
        tmp = x
    else if (z <= 2.1d+47) 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 <= -1e-63) {
		tmp = x;
	} else if (z <= 2.1e+47) {
		tmp = y / (z / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e-63:
		tmp = x
	elif z <= 2.1e+47:
		tmp = y / (z / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e-63)
		tmp = x;
	elseif (z <= 2.1e+47)
		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 <= -1e-63)
		tmp = x;
	elseif (z <= 2.1e+47)
		tmp = y / (z / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e-63], x, If[LessEqual[z, 2.1e+47], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000007e-63 or 2.1e47 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -1.00000000000000007e-63 < z < 2.1e47

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 75.9%

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

      1. associate-*r/ 69.5%

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

   6. Simplified 69.5%

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

      1. associate-*r/ 75.9%

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

      2. *-commutative 75.9%

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

      3. associate-/l* 73.5%

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

   8. Applied egg-rr 73.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e-63) x (if (<= z 4.2e+45) (/ (* x y) z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e-63) {
		tmp = x;
	} else if (z <= 4.2e+45) {
		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 <= (-1.05d-63)) then
        tmp = x
    else if (z <= 4.2d+45) 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 <= -1.05e-63) {
		tmp = x;
	} else if (z <= 4.2e+45) {
		tmp = (x * y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e-63:
		tmp = x
	elif z <= 4.2e+45:
		tmp = (x * y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e-63)
		tmp = x;
	elseif (z <= 4.2e+45)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e-63)
		tmp = x;
	elseif (z <= 4.2e+45)
		tmp = (x * y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e-63], x, If[LessEqual[z, 4.2e+45], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-63 or 4.1999999999999999e45 < z

   1. Initial program 79.6%

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

      1. associate-*l/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -1.05e-63 < z < 4.1999999999999999e45

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   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 75.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+45}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 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 84.2%

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

   1. associate-*l/ 84.7%

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

3. Simplified 84.7%

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

4. Taylor expanded in z around inf 53.2%

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

5. Final simplification 53.2%

   \[\leadsto x \]

Developer target: 96.3% 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 2023336 
(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))