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

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: 64

Math

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

↓

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

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));
}

Error

Bits error versus x

Bits error versus y

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

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

2. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

  :herbie-target
  (+ (* y y) (+ (* 2 x) (* x x)))

  (+ (+ (* x 2) (* x x)) (* y y)))