Average Error: 0.6 → 0.5
Time: 16.7s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r7726467 = a;
        double r7726468 = exp(r7726467);
        double r7726469 = b;
        double r7726470 = exp(r7726469);
        double r7726471 = r7726468 + r7726470;
        double r7726472 = r7726468 / r7726471;
        return r7726472;
}
↓
double f(double a, double b) {
        double r7726473 = a;
        double r7726474 = exp(r7726473);
        double r7726475 = b;
        double r7726476 = exp(r7726475);
        double r7726477 = r7726474 + r7726476;
        double r7726478 = log(r7726477);
        double r7726479 = r7726473 - r7726478;
        double r7726480 = exp(r7726479);
        return r7726480;
}

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

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Target

Original0.6
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied add-exp-log0.6

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

  4. Applied div-exp0.5

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]

  5. Final simplification0.5

    \[\leadsto e^{a - \log \left(e^{a} + e^{b}\right)}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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