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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Precision: binary64

Cost: 704

• Unsound rule application detected in e-graph. Results may not be sound.

• 43.3% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (+ (+ (* x x) (* x 2.0)) (* 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 * x) + (x * 2.0)) + (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 * x) + (x * 2.0d0)) + (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 * x) + (x * 2.0)) + (y * y);
}

Python

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

↓

def code(x, y):
	return ((x * x) + (x * 2.0)) + (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 * x) + Float64(x * 2.0)) + 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 * x) + (x * 2.0)) + (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 * x), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	704

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

Alternative 2
Accuracy	83.4%
Cost	972

\[\begin{array}{l} \mathbf{if}\;y \cdot y \leq 7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{elif}\;y \cdot y \leq 3.1 \cdot 10^{+220}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \cdot y \leq 1.22 \cdot 10^{+256}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 3
Accuracy	69.4%
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-177}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-76}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+58}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 4
Accuracy	89.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;y \cdot y + \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \end{array} \]

Alternative 5
Accuracy	100.0%
Cost	576

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

Alternative 6
Accuracy	59.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 7
Accuracy	20.6%
Cost	192

\[x \cdot 2 \]

Reproduce

herbie shell --seed 2023271 
(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)))