Average Error: 0.7 → 1.0
Time: 22.4s
Precision: 64
Internal Precision: 576
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\sqrt{\frac{e^{a}}{e^{a} + e^{b}}} \cdot \sqrt{\frac{e^{a}}{e^{a} + e^{b}}}\]

Error

Bits error versus a

Bits error versus b

Target

Original0.7
Target0.0
Herbie1.0
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied add-sqr-sqrt1.0

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

Runtime

Time bar (total: 22.4s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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