Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.41% → 0.41%

Time: 25.3s

Precision: binary64

Cost: 20032

Math

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

↓

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

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 z) (log (+ x y))) 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(z) + log((x + y))) - 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(z) + log((x + y))) - 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(z) + Math.log((x + y))) - 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(z) + math.log((x + y))) - 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(z) + log(Float64(x + y))) - 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(z) + log((x + y))) - 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[z], $MachinePrecision] + N[Log[N[(x + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.41%
Target	0.41%
Herbie	0.41%

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

Derivation

1. Initial program 0.41

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

2. Final simplification 0.41

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

Alternatives

Alternative 1
Error	1.64%
Cost	20425

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -20 \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \left(\log \left(x + y\right) + \log t \cdot -0.5\right)\right) - t\\ \end{array} \]

Alternative 2
Error	1.62%
Cost	20425

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -20 \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(x + y\right) + \left(\log z + \log t \cdot -0.5\right)\right) - t\\ \end{array} \]

Alternative 3
Error	19.35%
Cost	20297

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -20 \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \left(\log y + \log t \cdot -0.5\right)\right) - t\\ \end{array} \]

Alternative 4
Error	19.34%
Cost	20297

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -20 \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\log z + \log y\right) + \log t \cdot -0.5\right) - t\\ \end{array} \]

Alternative 5
Error	23.71%
Cost	20233

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -20 \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log z + \log \left(y \cdot {t}^{-0.5}\right)\right) - t\\ \end{array} \]

Alternative 6
Error	30.79%
Cost	19904

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

Alternative 7
Error	13.26%
Cost	14537

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -1 \cdot 10^{+29} \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log \left(\left(x + y\right) \cdot z\right) + \frac{\log t}{-0.5 - a} \cdot \left(0.25 - a \cdot a\right)\right) - t\\ \end{array} \]

Alternative 8
Error	13.26%
Cost	14153

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -1 \cdot 10^{+29} \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(\left(x + y\right) \cdot z\right)\right) - t\\ \end{array} \]

Alternative 9
Error	27.65%
Cost	14025

\[\begin{array}{l} \mathbf{if}\;a + -0.5 \leq -1 \cdot 10^{+29} \lor \neg \left(a + -0.5 \leq -0.4\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot \log t + \log \left(y \cdot z\right)\right) - t\\ \end{array} \]

Alternative 10
Error	22.1%
Cost	13768

\[\begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{-87}:\\ \;\;\;\;\left(\log y + t_1\right) - t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-8}:\\ \;\;\;\;\left(\log t \cdot -0.5 + \log \left(\left(x + y\right) \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1 - t\\ \end{array} \]

Alternative 11
Error	33.71%
Cost	13640

\[\begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;a \leq -4 \cdot 10^{-87}:\\ \;\;\;\;\left(\log y + t_1\right) - t\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-7}:\\ \;\;\;\;\left(\log t \cdot -0.5 + \log \left(y \cdot z\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1 - t\\ \end{array} \]

Alternative 12
Error	35.7%
Cost	13576

\[\begin{array}{l} t_1 := a \cdot \log t\\ \mathbf{if}\;a \leq -4 \cdot 10^{-87}:\\ \;\;\;\;\left(\log y + t_1\right) - t\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-16}:\\ \;\;\;\;\log \left(y \cdot \left(z \cdot {t}^{-0.5}\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\log z - t\right)\\ \end{array} \]

Alternative 13
Error	23.23%
Cost	13248

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

Alternative 14
Error	42.47%
Cost	13248

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

Alternative 15
Error	36.05%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;a \leq -2600 \lor \neg \left(a \leq 1.65 \cdot 10^{+77}\right):\\ \;\;\;\;a \cdot \log t + -1\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) - t\\ \end{array} \]

Alternative 16
Error	22.87%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;a \leq -0.34 \lor \neg \left(a \leq 1.85 \cdot 10^{-16}\right):\\ \;\;\;\;a \cdot \log t - t\\ \mathbf{else}:\\ \;\;\;\;\log \left(x + y\right) - t\\ \end{array} \]

Alternative 17
Error	58.98%
Cost	6720

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

Alternative 18
Error	61.79%
Cost	192

\[-1 - t \]

Alternative 19
Error	62.3%
Cost	128

\[-t \]

Reproduce

herbie shell --seed 2023090 
(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))))