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

Percentage Accurate: 99.9% → 99.9%

Time: 10.9s

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: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(x, 0.5, (y * (1.0 + (log(z) - z))));
}

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * 0.5 + N[(y * N[(1.0 + N[(N[Log[z], $MachinePrecision] - 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. Step-by-step derivation

   1. cancel-sign-sub 99.9%

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

   2. fma-neg 99.9%

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

   3. distribute-lft-neg-in 99.9%

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

   4. remove-double-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+r- 99.9%

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

   7. +-commutative 99.9%

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

   8. associate--l+ 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 84.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -2 \cdot 10^{-146} \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -2e-146) (not (<= (* x 0.5) 2e-36)))
   (- (* 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) <= -2e-146) || !((x * 0.5) <= 2e-36)) {
		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) <= (-2d-146)) .or. (.not. ((x * 0.5d0) <= 2d-36))) 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) <= -2e-146) || !((x * 0.5) <= 2e-36)) {
		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) <= -2e-146) or not ((x * 0.5) <= 2e-36):
		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) <= -2e-146) || !(Float64(x * 0.5) <= 2e-36))
		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) <= -2e-146) || ~(((x * 0.5) <= 2e-36)))
		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], -2e-146], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-36]], $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)) < -2.00000000000000005e-146 or 1.9999999999999999e-36 < (*.f64 x #s(literal 1/2 binary64))

   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 85.6%

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

      1. associate-*r* 85.6%

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

      2. mul-1-neg 85.6%

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

   5. Simplified 85.6%

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

   if -2.00000000000000005e-146 < (*.f64 x #s(literal 1/2 binary64)) < 1.9999999999999999e-36

   1. Initial program 99.7%

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

      1. cancel-sign-sub 99.7%

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

      2. fma-neg 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

      4. remove-double-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+r- 99.7%

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

      7. +-commutative 99.7%

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

      8. associate--l+ 99.7%

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

   3. Simplified 99.7%

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

      1. fma-undefine 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+l+ 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-lft-in 99.7%

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

      9. associate-+r+ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 92.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -2 \cdot 10^{-146} \lor \neg \left(x \cdot 0.5 \leq 2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.0295:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.0295)
   (+ (* x 0.5) (* y (+ 1.0 (log z))))
   (fma y (- z) (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0295) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = fma(y, -z, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.0295)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.0295], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.029499999999999998

   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 98.4%

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

   if 0.029499999999999998 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.5%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.5%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-z}, x \cdot 0.5\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-258}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, -z, x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.8e-258) (* y (+ 1.0 (log z))) (fma y (- z) (* x 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.8e-258) {
		tmp = y * (1.0 + log(z));
	} else {
		tmp = fma(y, -z, (x * 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.8e-258)
		tmp = Float64(y * Float64(1.0 + log(z)));
	else
		tmp = fma(y, Float64(-z), Float64(x * 0.5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.8e-258], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * (-z) + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7999999999999998e-258

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in x around 0 63.9%

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

   if 3.7999999999999998e-258 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.3%

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

      1. neg-mul-1 79.3%

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

   7. Simplified 79.3%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-z}, x \cdot 0.5\right) \]
3. Recombined 2 regimes into one program.
4. 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: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7.5e-259) (* y (+ 1.0 (log z))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e-259) {
		tmp = 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 <= 7.5d-259) then
        tmp = 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 <= 7.5e-259) {
		tmp = 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 <= 7.5e-259:
		tmp = 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 <= 7.5e-259)
		tmp = 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 <= 7.5e-259)
		tmp = 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, 7.5e-259], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.50000000000000052e-259

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in x around 0 63.9%

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

   if 7.50000000000000052e-259 < z

   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 79.2%

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

      1. associate-*r* 79.2%

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

      2. mul-1-neg 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{+25} \lor \neg \left(z \leq 1.18 \cdot 10^{+176}\right) \land z \leq 7.6 \cdot 10^{+191}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 8.5e+25) (and (not (<= z 1.18e+176)) (<= z 7.6e+191)))
   (* x 0.5)
   (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 8.5e+25) || (!(z <= 1.18e+176) && (z <= 7.6e+191))) {
		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 <= 8.5d+25) .or. (.not. (z <= 1.18d+176)) .and. (z <= 7.6d+191)) 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 <= 8.5e+25) || (!(z <= 1.18e+176) && (z <= 7.6e+191))) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 8.5e+25) or (not (z <= 1.18e+176) and (z <= 7.6e+191)):
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 8.5e+25) || (!(z <= 1.18e+176) && (z <= 7.6e+191)))
		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 <= 8.5e+25) || (~((z <= 1.18e+176)) && (z <= 7.6e+191)))
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 8.5e+25], And[N[Not[LessEqual[z, 1.18e+176]], $MachinePrecision], LessEqual[z, 7.6e+191]]], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.5000000000000007e25 or 1.18000000000000006e176 < z < 7.5999999999999996e191

   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 x around inf 55.5%

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

   if 8.5000000000000007e25 < z < 1.18000000000000006e176 or 7.5999999999999996e191 < z

   1. Initial program 100.0%

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

      1. cancel-sign-sub 100.0%

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

      2. fma-neg 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. remove-double-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r- 100.0%

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

      7. +-commutative 100.0%

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

      8. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+l+ 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-lft-in 100.0%

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

      9. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

   9. Simplified 74.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{+25} \lor \neg \left(z \leq 1.18 \cdot 10^{+176}\right) \land z \leq 7.6 \cdot 10^{+191}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% 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 74.3%

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

   1. associate-*r* 74.3%

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

   2. mul-1-neg 74.3%

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

5. Simplified 74.3%

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

6. Final simplification 74.3%

   \[\leadsto x \cdot 0.5 - y \cdot z \]
7. Add Preprocessing

Alternative 9: 39.1% 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 x around inf 45.4%

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

4. Final simplification 45.4%

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

Developer target: 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 2024087 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

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