Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A

Average Error: 0.02% → 0.02%

Time: 4.8s

Precision: binary64

Cost: 704

Math

\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]

↓

\[\left(x \cdot \left(y + -1\right) + y \cdot -0.5\right) + 0.918938533204673 \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))

↓

(FPCore (x y)
 :precision binary64
 (+ (+ (* x (+ y -1.0)) (* y -0.5)) 0.918938533204673))

C

double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

↓

double code(double x, double y) {
	return ((x * (y + -1.0)) + (y * -0.5)) + 0.918938533204673;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y - 1.0d0)) - (y * 0.5d0)) + 0.918938533204673d0
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * (y + (-1.0d0))) + (y * (-0.5d0))) + 0.918938533204673d0
end function

Java

public static double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}

↓

public static double code(double x, double y) {
	return ((x * (y + -1.0)) + (y * -0.5)) + 0.918938533204673;
}

Python

def code(x, y):
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673

↓

def code(x, y):
	return ((x * (y + -1.0)) + (y * -0.5)) + 0.918938533204673

Julia

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y - 1.0)) - Float64(y * 0.5)) + 0.918938533204673)
end

↓

function code(x, y)
	return Float64(Float64(Float64(x * Float64(y + -1.0)) + Float64(y * -0.5)) + 0.918938533204673)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
end

↓

function tmp = code(x, y)
	tmp = ((x * (y + -1.0)) + (y * -0.5)) + 0.918938533204673;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - N[(y * 0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y * -0.5), $MachinePrecision]), $MachinePrecision] + 0.918938533204673), $MachinePrecision]

Derivation

1. Initial program 0.02

   \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]

2. Final simplification 0.02

   \[\leadsto \left(x \cdot \left(y + -1\right) + y \cdot -0.5\right) + 0.918938533204673 \]

Alternatives

Alternative 1
Error	44.45%
Cost	1248

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+62}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1550:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-280}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-271}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-68}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-54}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 2
Error	43.22%
Cost	1116

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-148}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-298}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-133}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-88}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{-38}:\\ \;\;\;\;0.918938533204673\\ \mathbf{elif}\;y \leq 1.1:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]

Alternative 3
Error	1.56%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -430000 \lor \neg \left(x \leq 110000\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + \left(x \cdot y + y \cdot -0.5\right)\\ \end{array} \]

Alternative 4
Error	1.54%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -320000 \lor \neg \left(x \leq 470000\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 + y \cdot \left(x + -0.5\right)\\ \end{array} \]

Alternative 5
Error	2.37%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.36:\\ \;\;\;\;y \cdot \left(x + -0.5\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + y \cdot -0.5\\ \end{array} \]

Alternative 6
Error	2.36%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.42 \lor \neg \left(y \leq 1.6\right):\\ \;\;\;\;y \cdot \left(x + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.918938533204673 - x\\ \end{array} \]

Alternative 7
Error	0.02%
Cost	576

\[\left(0.918938533204673 + y \cdot \left(x + -0.5\right)\right) - x \]

Alternative 8
Error	16.63%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -78000000:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.85:\\ \;\;\;\;0.918938533204673 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.5\\ \end{array} \]

Alternative 9
Error	46.24%
Cost	392

\[\begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-11}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-36}:\\ \;\;\;\;0.918938533204673\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 10
Error	70.43%
Cost	64

\[0.918938533204673 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))