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

Average Error: 0.1 → 0.1

Time: 12.4s

Precision: binary64

Cost: 7232

Math

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

↓

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

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 (log z))) (* y 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 + log(z))) - (y * 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 + log(z))) - (y * 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 + Math.log(z))) - (y * 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 + math.log(z))) - (y * 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 + log(z))) - Float64(y * 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 + log(z))) - (y * 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 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $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. Taylor expanded in z around 0 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	18.7
Cost	8280

\[\begin{array}{l} t_0 := y + y \cdot \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;x \cdot 0.5 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-289}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	18.7
Cost	8280

\[\begin{array}{l} t_0 := x \cdot 0.5 - y \cdot z\\ t_1 := y + y \cdot \log z\\ \mathbf{if}\;x \cdot 0.5 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;x \cdot 0.5 \leq -5 \cdot 10^{-202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 2 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	11.4
Cost	7888

\[\begin{array}{l} t_0 := y + y \cdot \left(\log z - z\right)\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;x \cdot 0.5 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 1000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	11.4
Cost	7888

\[\begin{array}{l} t_0 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;x \cdot 0.5 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq -2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \mathbf{elif}\;x \cdot 0.5 \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq 1000000:\\ \;\;\;\;y + y \cdot \left(\log z - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.1
Cost	7232

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

Alternative 6
Error	1.0
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.0006746617405501257:\\ \;\;\;\;y \cdot \log z + \left(x \cdot 0.5 + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7
Error	1.0
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.0006746617405501257:\\ \;\;\;\;x \cdot 0.5 + \left(y + y \cdot \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8
Error	0.1
Cost	7104

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

Alternative 9
Error	28.3
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -2.762612724927467 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5.35809792399716 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 10
Error	18.5
Cost	448

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

Alternative 11
Error	34.6
Cost	192

\[x \cdot 0.5 \]

Reproduce

herbie shell --seed 2022318 
(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)))))