Average Error: 0.7 → 0.7
Time: 56.4s
Precision: 64
Internal Precision: 320
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{\sqrt{e^{a}}}{e^{a} + e^{b}} \cdot \sqrt{e^{a}}\]

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

    \[\frac{e^{a}}{e^{a} + e^{b}}\]

  2. Initial simplification0.7

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

  4. Applied *-un-lft-identity0.7

    \[\leadsto \frac{e^{a}}{\color{blue}{1 \cdot \left(e^{a} + e^{b}\right)}}\]

  5. Applied add-sqr-sqrt0.7

    \[\leadsto \frac{\color{blue}{\sqrt{e^{a}} \cdot \sqrt{e^{a}}}}{1 \cdot \left(e^{a} + e^{b}\right)}\]

  6. Applied times-frac0.7

    \[\leadsto \color{blue}{\frac{\sqrt{e^{a}}}{1} \cdot \frac{\sqrt{e^{a}}}{e^{a} + e^{b}}}\]

  7. Simplified0.7

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

  8. Final simplification0.7

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

Runtime

Time bar (total: 56.4s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.70.70.60.10%
herbie shell --seed 2018263 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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