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

Average Error: 0.1 → 0.1

Time: 20.6s

Precision: binary64

Cost: 7232

Math

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

↓

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

FPCore

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

↓

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

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 (y * ((1.0 - z) - log((1.0 / z)))) + (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) + (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 = (y * ((1.0d0 - z) - log((1.0d0 / z)))) + (x * 0.5d0)
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 (y * ((1.0 - z) - Math.log((1.0 / z)))) + (x * 0.5);
}

Python

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

↓

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

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(y * Float64(Float64(1.0 - z) - log(Float64(1.0 / z)))) + Float64(x * 0.5))
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 = (y * ((1.0 - z) - log((1.0 / z)))) + (x * 0.5);
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[(y * N[(N[(1.0 - z), $MachinePrecision] - N[Log[N[(1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $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. Taylor expanded in z around inf 0.1

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

3. Applied egg-rr 0.1

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

Alternatives

Alternative 1
Error	10.4
Cost	7376

\[\begin{array}{l} t_0 := y + y \cdot \left(\log z - z\right)\\ t_1 := x \cdot 0.5 - z \cdot y\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.9
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.0026:\\ \;\;\;\;x \cdot 0.5 + \left(1 + \log z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + \left(y + \left(-z\right) \cdot y\right)\\ \end{array} \]

Alternative 3
Error	0.1
Cost	7104

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

Alternative 4
Error	14.1
Cost	6984

\[\begin{array}{l} t_0 := \left(1 + \log z\right) \cdot y\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+127}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	28.8
Cost	652

\[\begin{array}{l} t_0 := -y \cdot z\\ \mathbf{if}\;z \leq 6 \cdot 10^{+18}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+70}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	17.8
Cost	448

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

Alternative 7
Error	34.2
Cost	192

\[0.5 \cdot x \]

Reproduce

herbie shell --seed 2023010 
(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)))))