Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 29.2s

Precision: binary64

Cost: 20032

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
}

↓

double code(double x, double y, double z, double t, double a) {
	return ((log((x + y)) + log(z)) - t) + (log(t) * (a + -0.5));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + ((a - 0.5d0) * log(t))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((log((x + y)) + log(z)) - t) + (log(t) * (a + (-0.5d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + ((a - 0.5) * Math.log(t));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	return ((Math.log((x + y)) + Math.log(z)) - t) + (Math.log(t) * (a + -0.5));
}

Python

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

↓

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

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(Float64(a - 0.5) * log(t)))
end

↓

function code(x, y, z, t, a)
	return Float64(Float64(Float64(log(Float64(x + y)) + log(z)) - t) + Float64(log(t) * Float64(a + -0.5)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t));
end

↓

function tmp = code(x, y, z, t, a)
	tmp = ((log((x + y)) + log(z)) - t) + (log(t) * (a + -0.5));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := N[(N[(N[(N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[Log[t], $MachinePrecision] * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.3
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 0.3

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

2. Final simplification 0.3

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

Alternatives

Alternative 1
Error	5.7
Cost	40008

\[\begin{array}{l} t_1 := \log \left(x + y\right) + \log z\\ \mathbf{if}\;t_1 \leq -700:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;t_1 \leq 695:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 2
Error	5.9
Cost	40008

\[\begin{array}{l} t_1 := \log \left(x + y\right)\\ t_2 := t_1 + \log z\\ \mathbf{if}\;t_2 \leq -700:\\ \;\;\;\;t_1 + \left(\log z + \log t \cdot -0.5\right)\\ \mathbf{elif}\;t_2 \leq 695:\\ \;\;\;\;\log \left(\left(x + y\right) \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 3
Error	21.9
Cost	39880

\[\begin{array}{l} t_1 := \log \left(x + y\right) + \log z\\ \mathbf{if}\;t_1 \leq -700:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;t_1 \leq 695:\\ \;\;\;\;\log \left(y \cdot z\right) + \left(\log t \cdot \left(a + -0.5\right) - t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 4
Error	12.2
Cost	19908

\[\begin{array}{l} \mathbf{if}\;t \leq 0.014806331649260294:\\ \;\;\;\;\left(\log z + \log y\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - t\\ \end{array} \]

Alternative 5
Error	19.8
Cost	19904

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

Alternative 6
Error	18.1
Cost	14100

\[\begin{array}{l} t_1 := \log \left(y \cdot z\right) + \left(\log t \cdot -0.5 - t\right)\\ t_2 := a \cdot \log t - t\\ \mathbf{if}\;a \leq -99.88163096015792:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.584158705320927 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.0185636329672993 \cdot 10^{-254}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{elif}\;a \leq 6.149937276568139 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7937510369420377 \cdot 10^{-6}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{\left(a + -0.5\right)}\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	9.5
Cost	13900

\[\begin{array}{l} t_1 := \log \left(\left(x + y\right) \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ t_2 := a \cdot \log t\\ \mathbf{if}\;t \leq 8.016587478948475 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.0532974712372327 \cdot 10^{-174}:\\ \;\;\;\;\log y + t_2\\ \mathbf{elif}\;t \leq 0.014806331649260294:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - t\\ \end{array} \]

Alternative 8
Error	17.2
Cost	13772

\[\begin{array}{l} t_1 := a \cdot \log t\\ t_2 := \log \left(y \cdot z\right) + \log t \cdot \left(a + -0.5\right)\\ \mathbf{if}\;t \leq 8.016587478948475 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.0532974712372327 \cdot 10^{-174}:\\ \;\;\;\;\log y + t_1\\ \mathbf{elif}\;t \leq 0.014806331649260294:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - t\\ \end{array} \]

Alternative 9
Error	21.3
Cost	13384

\[\begin{array}{l} t_1 := a \cdot \log t - t\\ \mathbf{if}\;a \leq -3.888191074739008 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.7937510369420377 \cdot 10^{-6}:\\ \;\;\;\;\left(\log z + \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	16.5
Cost	6984

\[\begin{array}{l} t_1 := a \cdot \log t - t\\ \mathbf{if}\;a \leq -3.888191074739008 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.051902984353921 \cdot 10^{-27}:\\ \;\;\;\;\log \left(x + y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	24.8
Cost	6856

\[\begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;a \leq -3.888191074739008 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 895812636793.6407:\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	37.7
Cost	6724

\[\begin{array}{l} \mathbf{if}\;t \leq 0.014806331649260294:\\ \;\;\;\;\log \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 13
Error	16.6
Cost	6720

\[a \cdot \log t - t \]

Alternative 14
Error	38.7
Cost	6596

\[\begin{array}{l} \mathbf{if}\;t \leq 0.014806331649260294:\\ \;\;\;\;\log y\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 15
Error	39.8
Cost	128

\[-t \]

Reproduce

herbie shell --seed 2022308 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))