Average Error: 39.1 → 39.1
Time: 14.0s
Precision: 64
Internal Precision: 1408
\[\log \left(1 + x\right)\]
↓
\[\log \left(1 + x\right)\]

Error

Bits error versus x

Target

Original39.1
Target0.3
Herbie39.1
\[\begin{array}{l} \mathbf{if}\;1 + x = 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \log \left(1 + x\right)}{\left(1 + x\right) - 1}\\ \end{array}\]

Derivation

  1. Initial program 39.1

    \[\log \left(1 + x\right)\]
  2. Removed slow pow expressions.

Runtime

Time bar (total: 14.0s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x)
  :name "ln(1 + x)"

  :herbie-target
  (if (== (+ 1 x) 1) x (/ (* x (log (+ 1 x))) (- (+ 1 x) 1)))

  (log (+ 1 x)))