Average Error: 0.7 → 1.1
Time: 31.9s
Precision: 64
Internal Precision: 320
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{\frac{e^{a}}{\sqrt{e^{a} + e^{b}}}}{\sqrt{e^{a} + e^{b}}}\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.7

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

  3. Applied add-sqr-sqrt1.3

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

  4. Applied associate-/r*1.1

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

Runtime

Time bar (total: 31.9s)Debug logProfile

herbie shell --seed 2018195 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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