System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Percentage Accurate: 99.9% → 99.7%

Time: 10.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + \left(y \cdot \left(1 + \log z\right) - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (* x 0.5) (- (* y (+ 1.0 (log z))) (* y z))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + ((y * (1.0 + log(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 * 0.5d0) + ((y * (1.0d0 + log(z))) - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + ((y * (1.0 + Math.log(z))) - (y * z));
}

Python

def code(x, y, z):
	return (x * 0.5) + ((y * (1.0 + math.log(z))) - (y * z))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(Float64(y * Float64(1.0 + log(z))) - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + ((y * (1.0 + log(z))) - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

   2. associate-+r- 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + 1\right) - z\right)} \]

4. Applied egg-rr 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + 1\right) - z\right)} \]
5. Step-by-step derivation

   1. sub-neg 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + 1\right) + \left(-z\right)\right)} \]

   2. distribute-rgt-in 99.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z + 1\right) \cdot y + \left(-z\right) \cdot y\right)} \]

6. Applied egg-rr 99.9%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z + 1\right) \cdot y + \left(-z\right) \cdot y\right)} \]
7. Step-by-step derivation

   1. fma-define 99.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{\mathsf{fma}\left(\log z + 1, y, \left(-z\right) \cdot y\right)} \]

   2. distribute-lft-neg-out 99.9%

      \[\leadsto x \cdot 0.5 + \mathsf{fma}\left(\log z + 1, y, \color{blue}{-z \cdot y}\right) \]

   3. fmm-undef 99.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(\log z + 1\right) \cdot y - z \cdot y\right)} \]

   4. *-commutative 99.9%

      \[\leadsto x \cdot 0.5 + \left(\color{blue}{y \cdot \left(\log z + 1\right)} - z \cdot y\right) \]

   5. +-commutative 99.9%

      \[\leadsto x \cdot 0.5 + \left(y \cdot \color{blue}{\left(1 + \log z\right)} - z \cdot y\right) \]

8. Applied egg-rr 99.9%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 + \log z\right) - z \cdot y\right)} \]

9. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1 + \log z\right) - y \cdot z\right) \]
10. Add Preprocessing

Alternative 2: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -0.0002 \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -0.0002) (not (<= (* x 0.5) 2e-100)))
   (- (* x 0.5) (* y z))
   (* y (- (+ 1.0 (log z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -0.0002) || !((x * 0.5) <= 2e-100)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 + log(z)) - 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 * 0.5d0) <= (-0.0002d0)) .or. (.not. ((x * 0.5d0) <= 2d-100))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * ((1.0d0 + log(z)) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -0.0002) || !((x * 0.5) <= 2e-100)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 + Math.log(z)) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -0.0002) or not ((x * 0.5) <= 2e-100):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * ((1.0 + math.log(z)) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -0.0002) || !(Float64(x * 0.5) <= 2e-100))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(Float64(1.0 + log(z)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -0.0002) || ~(((x * 0.5) <= 2e-100)))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * ((1.0 + log(z)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -0.0002], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-100]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 1/2 binary64)) < -2.0000000000000001e-4 or 2e-100 < (*.f64 x #s(literal 1/2 binary64))

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

   5. Simplified 89.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-out 89.7%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. unsub-neg 89.7%

         \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

   7. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

   if -2.0000000000000001e-4 < (*.f64 x #s(literal 1/2 binary64)) < 2e-100

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cbrt-cube 74.9%

         \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\sqrt[3]{\left(\left(\left(1 - z\right) + \log z\right) \cdot \left(\left(1 - z\right) + \log z\right)\right) \cdot \left(\left(1 - z\right) + \log z\right)}} \]

      2. pow3 74.8%

         \[\leadsto x \cdot 0.5 + y \cdot \sqrt[3]{\color{blue}{{\left(\left(1 - z\right) + \log z\right)}^{3}}} \]

   4. Applied egg-rr 74.8%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\sqrt[3]{{\left(\left(1 - z\right) + \log z\right)}^{3}}} \]

   5. Taylor expanded in x around inf 71.5%

      \[\leadsto \color{blue}{x \cdot \left(0.5 + \frac{y \cdot \left(\left(1 + \log z\right) - z\right)}{x}\right)} \]
   6. Step-by-step derivation

      1. associate-/l* 62.0%

         \[\leadsto x \cdot \left(0.5 + \color{blue}{y \cdot \frac{\left(1 + \log z\right) - z}{x}}\right) \]

      2. associate-+r- 62.0%

         \[\leadsto x \cdot \left(0.5 + y \cdot \frac{\color{blue}{1 + \left(\log z - z\right)}}{x}\right) \]

   7. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(0.5 + y \cdot \frac{1 + \left(\log z - z\right)}{x}\right)} \]

   8. Taylor expanded in x around 0 92.5%

      \[\leadsto \color{blue}{y \cdot \left(\left(1 + \log z\right) - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -0.0002 \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.28) (+ (* x 0.5) (* y (+ 1.0 (log z)))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.28) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = (x * 0.5) - (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 (z <= 0.28d0) then
        tmp = (x * 0.5d0) + (y * (1.0d0 + log(z)))
    else
        tmp = (x * 0.5d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.28) {
		tmp = (x * 0.5) + (y * (1.0 + Math.log(z)));
	} else {
		tmp = (x * 0.5) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.28:
		tmp = (x * 0.5) + (y * (1.0 + math.log(z)))
	else:
		tmp = (x * 0.5) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.28)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.28)
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	else
		tmp = (x * 0.5) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.28], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.28000000000000003

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 98.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 + \log z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(1 + \log z\right) \cdot y} \]

   5. Simplified 98.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(1 + \log z\right) \cdot y} \]

   if 0.28000000000000003 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 99.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 99.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

   5. Simplified 99.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-out 99.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. unsub-neg 99.0%

         \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

   7. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 + \log z\right) - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (- (+ 1.0 (log z)) z))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 + log(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 * 0.5d0) + (y * ((1.0d0 + log(z)) - z))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 + Math.log(z)) - z));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 + math.log(z)) - z))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 + log(z)) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 + log(z)) - z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\log z + \left(1 - z\right)\right)} \]

   2. associate-+r- 99.9%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + 1\right) - z\right)} \]

4. Applied egg-rr 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\log z + 1\right) - z\right)} \]

5. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 + \log z\right) - z\right) \]
6. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\log z + \left(1 - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (log z) (- 1.0 z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * (log(z) + (1.0 - 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 * 0.5d0) + (y * (log(z) + (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * (Math.log(z) + (1.0 - z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * (math.log(z) + (1.0 - z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(log(z) + Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * (log(z) + (1.0 - z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[Log[z], $MachinePrecision] + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \left(\log z + \left(1 - z\right)\right) \]
4. Add Preprocessing

Alternative 6: 60.9% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 2.7e+22) (* x 0.5) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.7e+22) {
		tmp = x * 0.5;
	} else {
		tmp = 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 (z <= 2.7d+22) then
        tmp = x * 0.5d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.7e+22) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.7e+22:
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.7e+22)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.7e+22)
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.7e+22], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.7000000000000002e22

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 57.4%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 57.4%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 57.4%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

   5. Simplified 57.4%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]

   6. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 2.7000000000000002e22 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

      2. mul-1-neg 100.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

   5. Simplified 100.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot y + 0.5 \cdot \frac{x}{z}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto z \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + -1 \cdot y\right)} \]

      2. mul-1-neg 99.9%

         \[\leadsto z \cdot \left(0.5 \cdot \frac{x}{z} + \color{blue}{\left(-y\right)}\right) \]

      3. unsub-neg 99.9%

         \[\leadsto z \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} - y\right)} \]

      4. associate-*r/ 99.9%

         \[\leadsto z \cdot \left(\color{blue}{\frac{0.5 \cdot x}{z}} - y\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{0.5 \cdot x}{z} - y\right)} \]

   9. Taylor expanded in x around 0 72.3%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.7 \cdot 10^{+22}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 - y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x 0.5) (* y z)))

C

double code(double x, double y, double z) {
	return (x * 0.5) - (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 * 0.5d0) - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) - (y * z);
}

Python

def code(x, y, z):
	return (x * 0.5) - (y * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) - Float64(y * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) - (y * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. associate-*r* 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

   2. mul-1-neg 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

5. Simplified 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]
6. Step-by-step derivation

   1. distribute-lft-neg-out 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

   2. unsub-neg 77.7%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

7. Applied egg-rr 77.7%

   \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
8. Add Preprocessing

Alternative 8: 41.5% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 0.5))

C

double code(double x, double y, double z) {
	return x * 0.5;
}

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 * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 0.5;
}

Python

def code(x, y, z):
	return x * 0.5

Julia

function code(x, y, z)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. associate-*r* 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

   2. mul-1-neg 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

5. Simplified 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]

6. Taylor expanded in x around inf 42.1%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

7. Final simplification 42.1%

   \[\leadsto x \cdot 0.5 \]
8. Add Preprocessing

Alternative 9: 2.2% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -0.5))

C

double code(double x, double y, double z) {
	return x * -0.5;
}

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 * (-0.5d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -0.5;
}

Python

def code(x, y, z):
	return x * -0.5

Julia

function code(x, y, z)
	return Float64(x * -0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -0.5;
end

Wolfram

code[x_, y_, z_] := N[(x * -0.5), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. associate-*r* 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

   2. mul-1-neg 77.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right)} \cdot z \]

5. Simplified 77.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y\right) \cdot z} \]

6. Taylor expanded in z around inf 68.9%

   \[\leadsto \color{blue}{z \cdot \left(-1 \cdot y + 0.5 \cdot \frac{x}{z}\right)} \]
7. Step-by-step derivation

   1. +-commutative 68.9%

      \[\leadsto z \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + -1 \cdot y\right)} \]

   2. mul-1-neg 68.9%

      \[\leadsto z \cdot \left(0.5 \cdot \frac{x}{z} + \color{blue}{\left(-y\right)}\right) \]

   3. unsub-neg 68.9%

      \[\leadsto z \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} - y\right)} \]

   4. associate-*r/ 68.9%

      \[\leadsto z \cdot \left(\color{blue}{\frac{0.5 \cdot x}{z}} - y\right) \]

8. Simplified 68.9%

   \[\leadsto \color{blue}{z \cdot \left(\frac{0.5 \cdot x}{z} - y\right)} \]
9. Step-by-step derivation

   1. frac-2neg 68.9%

      \[\leadsto z \cdot \left(\color{blue}{\frac{-0.5 \cdot x}{-z}} - y\right) \]

   2. div-inv 68.8%

      \[\leadsto z \cdot \left(\color{blue}{\left(-0.5 \cdot x\right) \cdot \frac{1}{-z}} - y\right) \]

   3. *-commutative 68.8%

      \[\leadsto z \cdot \left(\left(-\color{blue}{x \cdot 0.5}\right) \cdot \frac{1}{-z} - y\right) \]

   4. distribute-rgt-neg-in 68.8%

      \[\leadsto z \cdot \left(\color{blue}{\left(x \cdot \left(-0.5\right)\right)} \cdot \frac{1}{-z} - y\right) \]

   5. metadata-eval 68.8%

      \[\leadsto z \cdot \left(\left(x \cdot \color{blue}{-0.5}\right) \cdot \frac{1}{-z} - y\right) \]

   6. add-sqr-sqrt 0.0%

      \[\leadsto z \cdot \left(\left(x \cdot -0.5\right) \cdot \frac{1}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - y\right) \]

   7. sqrt-unprod 37.1%

      \[\leadsto z \cdot \left(\left(x \cdot -0.5\right) \cdot \frac{1}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - y\right) \]

   8. sqr-neg 37.1%

      \[\leadsto z \cdot \left(\left(x \cdot -0.5\right) \cdot \frac{1}{\sqrt{\color{blue}{z \cdot z}}} - y\right) \]

   9. sqrt-unprod 37.1%

      \[\leadsto z \cdot \left(\left(x \cdot -0.5\right) \cdot \frac{1}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - y\right) \]

   10. add-sqr-sqrt 37.1%

       \[\leadsto z \cdot \left(\left(x \cdot -0.5\right) \cdot \frac{1}{\color{blue}{z}} - y\right) \]

10. Applied egg-rr 37.1%

    \[\leadsto z \cdot \left(\color{blue}{\left(x \cdot -0.5\right) \cdot \frac{1}{z}} - y\right) \]
11. Step-by-step derivation

    1. associate-*l* 37.1%

       \[\leadsto z \cdot \left(\color{blue}{x \cdot \left(-0.5 \cdot \frac{1}{z}\right)} - y\right) \]

    2. associate-*r/ 37.1%

       \[\leadsto z \cdot \left(x \cdot \color{blue}{\frac{-0.5 \cdot 1}{z}} - y\right) \]

    3. metadata-eval 37.1%

       \[\leadsto z \cdot \left(x \cdot \frac{\color{blue}{-0.5}}{z} - y\right) \]

12. Simplified 37.1%

    \[\leadsto z \cdot \left(\color{blue}{x \cdot \frac{-0.5}{z}} - y\right) \]

13. Taylor expanded in z around 0 2.4%

    \[\leadsto \color{blue}{-0.5 \cdot x} \]

14. Final simplification 2.4%

    \[\leadsto x \cdot -0.5 \]
15. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (* 0.5 x)) (* y (- z (log z)))))

C

double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - log(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 = (y + (0.5d0 * x)) - (y * (z - log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - Math.log(z)));
}

Python

def code(x, y, z):
	return (y + (0.5 * x)) - (y * (z - math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(0.5 * x)) - Float64(y * Float64(z - log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (0.5 * x)) - (y * (z - log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(z - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024177 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (* 1/2 x)) (* y (- z (log z)))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))