(- 1.0 (* (/ 1 r) (fabs x)))

Average Error: 0.1 → 0.1

Time: 906.0ms

Precision: binary64

Math

\[1 - \frac{1}{r} \cdot \left|x\right|\]

↓

\[1 - \frac{1}{r} \cdot \left|x\right|\]

C

double code(double r, double x) {
	return ((double) (1.0 - ((double) (((double) (1.0 / r)) * ((double) fabs(x))))));
}

↓

double code(double r, double x) {
	return ((double) (1.0 - ((double) (((double) (1.0 / r)) * ((double) fabs(x))))));
}

Error

Bits error versus r

Bits error versus x

Derivation

1. Initial program 0.1

   \[1 - \frac{1}{r} \cdot \left|x\right|\]

2. Final simplification 0.1

   \[\leadsto 1 - \frac{1}{r} \cdot \left|x\right|\]

Reproduce

herbie shell --seed 2020152 
(FPCore (r x)
  :name "(- 1.0 (* (/ 1 r) (fabs x)))"
  :precision binary64
  (- 1.0 (* (/ 1.0 r) (fabs x))))