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

Average Accuracy: 99.9% → 99.9%

Time: 14.3s

Precision: binary64

Cost: 7104

Math

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

↓

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

FPCore

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

↓

(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)));
}

↓

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

↓

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)));
}

↓

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)))

↓

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

↓

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

↓

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]

↓

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]

Target

Original	99.9%
Target	99.8%
Herbie	99.9%

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

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%

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

Alternatives

Alternative 1
Accuracy	81.7%
Cost	7377

\[\begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+82} \lor \neg \left(y \leq 1.45 \cdot 10^{+116}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 2
Accuracy	81.7%
Cost	7376

\[\begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+31}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+82}:\\ \;\;\;\;y + y \cdot \left(\log z - z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+116}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	98.5%
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.035:\\ \;\;\;\;y \cdot \log z + \left(y + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 4
Accuracy	77.9%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+142} \lor \neg \left(y \leq 3.8 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 5
Accuracy	55.4%
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 90000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 6
Accuracy	71.8%
Cost	448

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

Alternative 7
Accuracy	46.1%
Cost	192

\[x \cdot 0.5 \]

Alternative 8
Accuracy	2.1%
Cost	64

\[y \]

Reproduce

herbie shell --seed 2023137 
(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)))))