(/ (- 1 (pow (+ 1 x) (- n))) x)

Average Error: 44.1 → 44.1

Time: 6.8s

Precision: binary64

Math

\[\frac{1 - {\left(1 + x\right)}^{\left(-n\right)}}{x}\]

↓

\[\frac{1 - {\left(1 + x\right)}^{\left(-n\right)}}{x}\]

Error

Bits error versus x

Bits error versus n

Derivation

1. Initial program 44.1

   \[\frac{1 - {\left(1 + x\right)}^{\left(-n\right)}}{x}\]

2. Final simplification 44.1

   \[\leadsto \frac{1 - {\left(1 + x\right)}^{\left(-n\right)}}{x}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x n)
  :name "(/ (- 1 (pow (+ 1 x) (- n))) x)"
  :precision binary64
  (/ (- 1.0 (pow (+ 1.0 x) (neg n))) x))