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

Average Error: 0.1 → 0.1

Time: 10.5s

Precision: binary64

Cost: 7104

Math

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

↓

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

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 (+ (- z (log z)) -1.0))))

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 * ((z - log(z)) + -1.0));
}

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 * ((z - log(z)) + (-1.0d0)))
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 * ((z - Math.log(z)) + -1.0));
}

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 * ((z - math.log(z)) + -1.0))

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(z - log(z)) + -1.0)))
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 * ((z - log(z)) + -1.0));
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[(z - N[Log[z], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Applied egg-rr 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	18.2
Cost	7248

\[\begin{array}{l} t_0 := y + y \cdot \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;z \leq 3.447372656530312 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.512840654730543 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.8325739678698683 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7911040484514093 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	10.9
Cost	7112

\[\begin{array}{l} t_0 := y \cdot \left(1 - \left(z - \log z\right)\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.0222823367011279 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.8
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.018346947734456505:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 4
Error	14.8
Cost	6984

\[\begin{array}{l} t_0 := y \cdot \left(1 + \log z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+224}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	29.6
Cost	652

\[\begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq 802521.5941995165:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+194}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	29.6
Cost	652

\[\begin{array}{l} \mathbf{if}\;z \leq 802521.5941995165:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;y - y \cdot z\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+194}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 7
Error	18.3
Cost	448

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

Alternative 8
Error	34.6
Cost	192

\[x \cdot 0.5 \]

Alternative 9
Error	62.7
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022217 
(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)))))