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

Average Error: 0.1 → 0.1

Time: 1.1s

Precision: binary64

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);
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2022068 
(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)))