Average Error: 16.2 → 0.4
Time: 13.0s
Precision: 64
Internal precision: 128
\[\frac{e^{a}}{e^{a} + e^{b}}\]
⬇
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]

Error

Bits error versus a

Bits error versus b

Target

Original16.2
Comparison13.8
Herbie0.4
\[ \frac{1}{1 + e^{b - a}} \]

Derivation

  1. Initial program 16.2

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log 16.3

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{\log \left(e^{a} + e^{b}\right)}}}\]

  4. Applied div-exp 0.4

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 13.0s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(423096448 1014512670 484312817 1860575417 3187364312 1647742334)'
(FPCore (a b)
  :name "Quotient of sum of exps"

  :target
  (/ 1 (+ 1 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))