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

Average Error: 0.1 → 0.1

Time: 9.1s

Precision: binary64

Cost: 7232

Math

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

↓

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

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)) (* y (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)) + (y * 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)) + (y * 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)) + (y * 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)) + (y * 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(Float64(y * Float64(1.0 - z)) + Float64(y * 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)) + (y * 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[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(y * N[Log[z], $MachinePrecision]), $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

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	18.7
Cost	7180

\[\begin{array}{l} \mathbf{if}\;z \leq 7.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;z \leq 2.52 \cdot 10^{-51}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-7}:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x \cdot 0.5\right)\\ \end{array} \]

Alternative 2
Error	18.7
Cost	7116

\[\begin{array}{l} t_0 := y \cdot \left(1 + \log z\right)\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;z \leq 9 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	18.7
Cost	7116

\[\begin{array}{l} t_0 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-7}:\\ \;\;\;\;y + y \cdot \log z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	10.8
Cost	7112

\[\begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	10.8
Cost	7112

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \]

Alternative 6
Error	0.9
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 3:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, x \cdot 0.5\right)\\ \end{array} \]

Alternative 7
Error	0.1
Cost	7104

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

Alternative 8
Error	27.7
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 9
Error	18.3
Cost	448

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

Alternative 10
Error	34.8
Cost	192

\[x \cdot 0.5 \]

Reproduce

herbie shell --seed 2022329 
(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)))))