Numeric.Log:$clog1p from log-domain-0.10.2.1, A

Average Error: 0.0 → 0.0

Time: 3.4s

Precision: binary64

Cost: 704

Math

\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

↓

\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

FPCore

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

↓

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

C

double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

↓

double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) + (x * x)) + (y * y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) + (x * x)) + (y * y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

↓

public static double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

Python

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

↓

def code(x, y):
	return ((x * 2.0) + (x * x)) + (y * y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) + Float64(x * x)) + Float64(y * y))
end

↓

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) + Float64(x * x)) + Float64(y * y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) + (x * x)) + (y * y);
end

↓

function tmp = code(x, y)
	tmp = ((x * 2.0) + (x * x)) + (y * y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] + N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[y \cdot y + \left(2 \cdot x + x \cdot x\right) \]

Derivation

1. Initial program 0.0

   \[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]

Alternatives

Alternative 1
Error	23.2
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -25572862.72717592:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -9.938356869604385 \cdot 10^{-164}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 9.282300542943664 \cdot 10^{-56}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 4.778144478351412 \cdot 10^{-29}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 44922926616.97669:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	3.5
Cost	712

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;y \leq -1.0840736581174195 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6371166991061447 \cdot 10^{-64}:\\ \;\;\;\;\left(2 + x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.5
Cost	712

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -25572862.72717592:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.223511457728723 \cdot 10^{-9}:\\ \;\;\;\;\left(x + x\right) + y \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	9.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -9.758240634193972 \cdot 10^{-54}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 8.510344111833907 \cdot 10^{-35}:\\ \;\;\;\;\left(2 + x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 5
Error	24.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -25572862.72717592:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 7.602111201258022 \cdot 10^{-5}:\\ \;\;\;\;x + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 6
Error	41.1
Cost	192

\[x + x \]

Reproduce

herbie shell --seed 2022320 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2.0 x) (* x x)))

  (+ (+ (* x 2.0) (* x x)) (* y y)))