Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 1.8min

Precision: binary64

Cost: 20032

Math

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

↓

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

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) (* (- a 0.5) (log t))))

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) + ((a - 0.5) * log(t));
}

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) + ((a - 0.5d0) * log(t))
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) + ((a - 0.5) * Math.log(t));
}

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) + ((a - 0.5) * math.log(t))

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(Float64(a - 0.5) * log(t)))
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) + ((a - 0.5) * log(t));
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[(a - 0.5), $MachinePrecision] * N[Log[t], $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

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

Alternatives

Alternative 1
Error	12.6
Cost	20436

\[\begin{array}{l} t_1 := -0.5 \cdot \log t\\ t_2 := \left(\log z + \left(\log y + t_1\right)\right) - t\\ t_3 := a \cdot \log t - \left(t - \log z\right)\\ t_4 := \left(\log z + \left(t_1 + \log x\right)\right) - t\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-209}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-104}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	12.6
Cost	20436

\[\begin{array}{l} t_1 := -0.5 \cdot \log t\\ t_2 := a \cdot \log t - \left(t - \log z\right)\\ t_3 := \left(\log z + \left(t_1 + \log x\right)\right) - t\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-156}:\\ \;\;\;\;\left(\frac{\log t}{-2} + \left(\log z + \log y\right)\right) - t\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-215}:\\ \;\;\;\;\left(\log z + \left(\log y + t_1\right)\right) - t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	12.6
Cost	20436

\[\begin{array}{l} t_1 := a \cdot \log t - \left(t - \log z\right)\\ t_2 := \left(\log z + \left(-0.5 \cdot \log t + \log x\right)\right) - t\\ \mathbf{if}\;a \leq -8 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{\log t}{-2} + \left(\log z + \log y\right)\right) - t\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-214}:\\ \;\;\;\;\left(\left(\log z - \frac{\log t}{2}\right) - \left(-\log y\right)\right) - t\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	12.4
Cost	20040

\[\begin{array}{l} t_1 := a \cdot \log t - \left(t - \log z\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-6}:\\ \;\;\;\;\left(\log z + \left(\log y + -0.5 \cdot \log t\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	0.9
Cost	20036

\[\begin{array}{l} \mathbf{if}\;t \leq 210:\\ \;\;\;\;\left(a - 0.5\right) \cdot \log t + \left(\log z + \log \left(y + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \log t - \left(t - \log z\right)\\ \end{array} \]

Alternative 6
Error	14.4
Cost	13504

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

Alternative 7
Error	14.8
Cost	13248

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

Alternative 8
Error	25.2
Cost	7120

\[\begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;a \leq -2.36 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+38}:\\ \;\;\;\;-t\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+83}:\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	39.9
Cost	128

\[-t \]

Reproduce

herbie shell --seed 2023033 
(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))))