Average Error: 0.6 → 0.9
Time: 49.6s
Precision: 64
Internal Precision: 320
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\sqrt{\frac{e^{a}}{e^{a} + e^{b}}} \cdot \sqrt{\frac{e^{a}}{e^{a} + e^{b}}}\]

Error

Bits error versus a

Bits error versus b

Target

Original0.6
Target0.0
Herbie0.9
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied add-sqr-sqrt0.9

    \[\leadsto \color{blue}{\sqrt{\frac{e^{a}}{e^{a} + e^{b}}} \cdot \sqrt{\frac{e^{a}}{e^{a} + e^{b}}}}\]

Runtime

Time bar (total: 49.6s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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