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

Average Error: 0.1 → 0.1

Time: 15.3s

Precision: binary64

Cost: 7232

Math

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

↓

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

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)) (* x 0.5)) (* 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 ((y * (1.0 - z)) + (x * 0.5)) + (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 = ((y * (1.0d0 - z)) + (x * 0.5d0)) + (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 ((y * (1.0 - z)) + (x * 0.5)) + (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 ((y * (1.0 - z)) + (x * 0.5)) + (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(Float64(y * Float64(1.0 - z)) + Float64(x * 0.5)) + 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 = ((y * (1.0 - z)) + (x * 0.5)) + (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[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * N[Log[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. Applied egg-rr 32.1

   \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, 0.5, \left(-y\right) \cdot \left(\left(1 - z\right) + \log z\right)\right)}{\left(x \cdot x\right) \cdot 0.25 - {\left(y \cdot \left(\left(1 - z\right) + \log z\right)\right)}^{2}}}} \]

3. Applied egg-rr 0.1

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

4. Final simplification 0.1

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

Alternatives

Alternative 1
Error	18.2
Cost	7908

\[\begin{array}{l} t_0 := y + y \cdot \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;z \leq 9.750121678722319 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.601651853852565 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.264198730403987 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6973478007336074 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7072352691899534 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.443128411842131 \cdot 10^{-108}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 1.2702279249719782 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.777676946523487 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.976740139952437 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	18.2
Cost	7908

\[\begin{array}{l} t_0 := y + y \cdot \log z\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;z \leq 9.750121678722319 \cdot 10^{-243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.601651853852565 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.264198730403987 \cdot 10^{-185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6973478007336074 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7072352691899534 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.443128411842131 \cdot 10^{-108}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;z \leq 1.2702279249719782 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;z \leq 4.777676946523487 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.976740139952437 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	10.2
Cost	7888

\[\begin{array}{l} t_0 := y \cdot \left(\left(1 - z\right) + \log z\right)\\ t_1 := x \cdot 0.5 - y \cdot z\\ \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq -1 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot 0.5 \leq -2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 0.5 \leq 4 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	1.0
Cost	7108

\[\begin{array}{l} \mathbf{if}\;z \leq 0.007715337657317832:\\ \;\;\;\;y \cdot \log z + \left(y + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 5
Error	0.1
Cost	7104

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

Alternative 6
Error	29.2
Cost	784

\[\begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -44076373566.74853:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -2.3341987457342914 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.2891885953503045 \cdot 10^{-130}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.7315744430565743 \cdot 10^{-150}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5\\ \end{array} \]

Alternative 7
Error	18.4
Cost	448

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

Alternative 8
Error	34.6
Cost	192

\[x \cdot 0.5 \]

Reproduce

herbie shell --seed 2022316 
(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)))))