(- (/ (- 1) b) (+ (/ 1 (* (* a b) a)) (/ 1 a)))

Average Error: 0.1 → 0.1

Time: 971.0ms

Precision: binary64

Math

\[\frac{-1}{b} - \left(\frac{1}{\left(a \cdot b\right) \cdot a} + \frac{1}{a}\right)\]

↓

\[\frac{-1}{b} - \left(\frac{1}{\left(a \cdot b\right) \cdot a} + \frac{1}{a}\right)\]

Error

Bits error versus b

Bits error versus a

Derivation

1. Initial program 0.1

   \[\frac{-1}{b} - \left(\frac{1}{\left(a \cdot b\right) \cdot a} + \frac{1}{a}\right)\]

2. Final simplification 0.1

   \[\leadsto \frac{-1}{b} - \left(\frac{1}{\left(a \cdot b\right) \cdot a} + \frac{1}{a}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b a)
  :name "(- (/ (- 1) b) (+ (/ 1 (* (* a b) a)) (/ 1 a)))"
  :precision binary64
  (- (/ (neg 1.0) b) (+ (/ 1.0 (* (* a b) a)) (/ 1.0 a))))