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

Percentage Accurate: 99.9% → 99.9%

Time: 12.0s

Alternatives: 10

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

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((log(z) + (1.0d0 - z)) * y) + (0.5d0 * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\log z + \left(1 - z\right)\right) \cdot y\\ t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ (log z) (- 1.0 z)) y)) (t_1 (* (- z) y)))
   (if (<= t_0 -1e+85) t_1 (if (<= t_0 5e+142) (* 0.5 x) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (log(z) + (1.0 - z)) * y;
	double t_1 = -z * y;
	double tmp;
	if (t_0 <= -1e+85) {
		tmp = t_1;
	} else if (t_0 <= 5e+142) {
		tmp = 0.5 * x;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (log(z) + (1.0d0 - z)) * y
    t_1 = -z * y
    if (t_0 <= (-1d+85)) then
        tmp = t_1
    else if (t_0 <= 5d+142) then
        tmp = 0.5d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.log(z) + (1.0 - z)) * y;
	double t_1 = -z * y;
	double tmp;
	if (t_0 <= -1e+85) {
		tmp = t_1;
	} else if (t_0 <= 5e+142) {
		tmp = 0.5 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.log(z) + (1.0 - z)) * y
	t_1 = -z * y
	tmp = 0
	if t_0 <= -1e+85:
		tmp = t_1
	elif t_0 <= 5e+142:
		tmp = 0.5 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(log(z) + Float64(1.0 - z)) * y)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (t_0 <= -1e+85)
		tmp = t_1;
	elseif (t_0 <= 5e+142)
		tmp = Float64(0.5 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (log(z) + (1.0 - z)) * y;
	t_1 = -z * y;
	tmp = 0.0;
	if (t_0 <= -1e+85)
		tmp = t_1;
	elseif (t_0 <= 5e+142)
		tmp = 0.5 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Log[z], $MachinePrecision] + N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+85], t$95$1, If[LessEqual[t$95$0, 5e+142], N[(0.5 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < -1e85 or 5.0000000000000001e142 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 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

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 58.5

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

   5. Applied rewrites 58.5%

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

   if -1e85 < (*.f64 y (+.f64 (-.f64 #s(literal 1 binary64) z) (log.f64 z))) < 5.0000000000000001e142

   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

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{1}{2}} \]

      2. lower-*.f64 61.6

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

   5. Applied rewrites 61.6%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\log z + \left(1 - z\right)\right) \cdot y \leq -1 \cdot 10^{+85}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;\left(\log z + \left(1 - z\right)\right) \cdot y \leq 5 \cdot 10^{+142}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \]
5. 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 2024230 
(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)))))