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

Percentage Accurate: 99.9% → 99.9%

Time: 8.4s

Alternatives: 7

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, 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]

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-23} \lor \neg \left(x \cdot 0.5 \leq 10^{-157} \lor \neg \left(x \cdot 0.5 \leq 4 \cdot 10^{-120}\right) \land x \cdot 0.5 \leq 10^{-63}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e-23)
         (not
          (or (<= (* x 0.5) 1e-157)
              (and (not (<= (* x 0.5) 4e-120)) (<= (* x 0.5) 1e-63)))))
   (- (* x 0.5) (* y z))
   (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-23) || !(((x * 0.5) <= 1e-157) || (!((x * 0.5) <= 4e-120) && ((x * 0.5) <= 1e-63)))) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 - z) + log(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) <= (-5d-23)) .or. (.not. ((x * 0.5d0) <= 1d-157) .or. (.not. ((x * 0.5d0) <= 4d-120)) .and. ((x * 0.5d0) <= 1d-63))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * ((1.0d0 - z) + log(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e-23) || !(((x * 0.5) <= 1e-157) || (!((x * 0.5) <= 4e-120) && ((x * 0.5) <= 1e-63)))) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 - z) + Math.log(z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -5e-23) or not (((x * 0.5) <= 1e-157) or (not ((x * 0.5) <= 4e-120) and ((x * 0.5) <= 1e-63))):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * ((1.0 - z) + math.log(z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -5e-23) || !((Float64(x * 0.5) <= 1e-157) || (!(Float64(x * 0.5) <= 4e-120) && (Float64(x * 0.5) <= 1e-63))))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(Float64(1.0 - z) + log(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -5e-23) || ~((((x * 0.5) <= 1e-157) || (~(((x * 0.5) <= 4e-120)) && ((x * 0.5) <= 1e-63)))))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * ((1.0 - z) + log(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -5e-23], N[Not[Or[LessEqual[N[(x * 0.5), $MachinePrecision], 1e-157], And[N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 4e-120]], $MachinePrecision], LessEqual[N[(x * 0.5), $MachinePrecision], 1e-63]]]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 1/2) < -5.0000000000000002e-23 or 9.99999999999999943e-158 < (*.f64 x 1/2) < 3.99999999999999991e-120 or 1.00000000000000007e-63 < (*.f64 x 1/2)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. distribute-rgt-neg-out 85.5%

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

   4. Simplified 85.5%

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

      1. distribute-rgt-neg-out 85.5%

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

      2. unsub-neg 85.5%

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

   6. Applied egg-rr 85.5%

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

   if -5.0000000000000002e-23 < (*.f64 x 1/2) < 9.99999999999999943e-158 or 3.99999999999999991e-120 < (*.f64 x 1/2) < 1.00000000000000007e-63

   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. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. distribute-lft-in 99.7%

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

      4. *-rgt-identity 99.7%

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

      5. associate-+r+ 99.7%

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

      6. fma-def 99.7%

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

      7. +-commutative 99.7%

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

      8. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-in 90.1%

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

      3. sub-neg 90.1%

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

      4. mul-1-neg 90.1%

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

      5. sub-neg 90.1%

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

      6. +-commutative 90.1%

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

      7. distribute-neg-in 90.1%

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

      8. remove-double-neg 90.1%

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

      9. sub-neg 90.1%

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

      10. metadata-eval 90.1%

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

      11. +-commutative 90.1%

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

   6. Simplified 90.1%

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

      1. distribute-neg-in 90.1%

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

      2. metadata-eval 90.1%

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

      3. sub-neg 90.1%

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

      4. associate-+l- 90.1%

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

      5. distribute-lft-out 89.9%

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

   8. Applied egg-rr 89.9%

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

      1. distribute-lft-out 90.1%

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

      2. *-commutative 90.1%

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

      3. +-commutative 90.1%

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

   10. Applied egg-rr 90.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-23} \lor \neg \left(x \cdot 0.5 \leq 10^{-157} \lor \neg \left(x \cdot 0.5 \leq 4 \cdot 10^{-120}\right) \land x \cdot 0.5 \leq 10^{-63}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \end{array} \]

Alternative 3: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.00044:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.00044) (+ (* 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 <= 0.00044) {
		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 <= 0.00044d0) 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 <= 0.00044) {
		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 <= 0.00044:
		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 <= 0.00044)
		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 <= 0.00044)
		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, 0.00044], 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 < 4.40000000000000016e-4

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.0%

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

   if 4.40000000000000016e-4 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-rgt-neg-out 97.8%

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

   4. Simplified 97.8%

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

      1. distribute-rgt-neg-out 97.8%

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

      2. unsub-neg 97.8%

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

   6. Applied egg-rr 97.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.00044:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 4: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+198) (* y (+ 1.0 (log z))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+198) {
		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 (y <= (-8.5d+198)) 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 (y <= -8.5e+198) {
		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 y <= -8.5e+198:
		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 (y <= -8.5e+198)
		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 (y <= -8.5e+198)
		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[y, -8.5e+198], 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 y < -8.5000000000000001e198

   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. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. distribute-lft-in 99.5%

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

      4. *-rgt-identity 99.5%

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

      5. associate-+r+ 99.4%

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

      6. fma-def 99.4%

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

      7. +-commutative 99.4%

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

      8. unsub-neg 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around -inf 94.2%

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

      1. mul-1-neg 94.2%

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

      2. distribute-rgt-neg-in 94.2%

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

      3. sub-neg 94.2%

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

      4. mul-1-neg 94.2%

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

      5. sub-neg 94.2%

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

      6. +-commutative 94.2%

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

      7. distribute-neg-in 94.2%

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

      8. remove-double-neg 94.2%

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

      9. sub-neg 94.2%

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

      10. metadata-eval 94.2%

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

      11. +-commutative 94.2%

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

   6. Simplified 94.2%

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

   7. Taylor expanded in z around 0 78.8%

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

   if -8.5000000000000001e198 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-out 76.7%

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

   4. Simplified 76.7%

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

      1. distribute-rgt-neg-out 76.7%

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

      2. unsub-neg 76.7%

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

   6. Applied egg-rr 76.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 5: 60.9% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 50000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+41}\right) \land z \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 50000000.0) (and (not (<= z 4.2e+41)) (<= z 1.5e+58)))
   (* x 0.5)
   (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 50000000.0) || (!(z <= 4.2e+41) && (z <= 1.5e+58))) {
		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 <= 50000000.0d0) .or. (.not. (z <= 4.2d+41)) .and. (z <= 1.5d+58)) 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 <= 50000000.0) || (!(z <= 4.2e+41) && (z <= 1.5e+58))) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 50000000.0) or (not (z <= 4.2e+41) and (z <= 1.5e+58)):
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 50000000.0) || (!(z <= 4.2e+41) && (z <= 1.5e+58)))
		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 <= 50000000.0) || (~((z <= 4.2e+41)) && (z <= 1.5e+58)))
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 50000000.0], And[N[Not[LessEqual[z, 4.2e+41]], $MachinePrecision], LessEqual[z, 1.5e+58]]], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5e7 or 4.1999999999999999e41 < z < 1.5000000000000001e58

   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. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. distribute-lft-in 99.7%

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

      4. *-rgt-identity 99.7%

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

      5. associate-+r+ 99.7%

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

      6. fma-def 99.7%

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

      7. +-commutative 99.7%

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

      8. unsub-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 51.9%

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

   if 5e7 < z < 4.1999999999999999e41 or 1.5000000000000001e58 < 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. sub-neg 100.0%

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

      2. associate-+l+ 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. *-rgt-identity 100.0%

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

      5. associate-+r+ 100.0%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around -inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-rgt-neg-in 80.1%

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

      3. sub-neg 80.1%

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

      4. mul-1-neg 80.1%

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

      5. sub-neg 80.1%

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

      6. +-commutative 80.1%

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

      7. distribute-neg-in 80.1%

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

      8. remove-double-neg 80.1%

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

      9. sub-neg 80.1%

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

      10. metadata-eval 80.1%

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

      11. +-commutative 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in z around inf 79.0%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 50000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+41}\right) \land z \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 75.7% 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. Taylor expanded in z around inf 72.5%

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

   1. mul-1-neg 72.5%

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

   2. distribute-rgt-neg-out 72.5%

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

4. Simplified 72.5%

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

   1. distribute-rgt-neg-out 72.5%

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

   2. unsub-neg 72.5%

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

6. Applied egg-rr 72.5%

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

7. Final simplification 72.5%

   \[\leadsto x \cdot 0.5 - y \cdot z \]

Alternative 7: 39.3% 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. Step-by-step derivation

   1. sub-neg 99.9%

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

   2. associate-+l+ 99.9%

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

   3. distribute-lft-in 99.8%

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

   4. *-rgt-identity 99.8%

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

   5. associate-+r+ 99.8%

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

   6. fma-def 99.8%

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

   7. +-commutative 99.8%

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

   8. unsub-neg 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 39.7%

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

5. Final simplification 39.7%

   \[\leadsto x \cdot 0.5 \]

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 2023230 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

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