Average Error: 0.6 → 0.6
Time: 14.6s
Precision: 64
Internal Precision: 320
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[(e^{\log_* (1 + \frac{e^{a}}{e^{a} + e^{b}})} - 1)^*\]

Error

Bits error versus a

Bits error versus b

Target

Original0.6
Target0.0
Herbie0.6
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied expm1-log1p-u0.6

    \[\leadsto \color{blue}{(e^{\log_* (1 + \frac{e^{a}}{e^{a} + e^{b}})} - 1)^*}\]

Runtime

Time bar (total: 14.6s)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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