Average Error: 0.6 → 0.6
Time: 24.1s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r4131586 = a;
        double r4131587 = exp(r4131586);
        double r4131588 = b;
        double r4131589 = exp(r4131588);
        double r4131590 = r4131587 + r4131589;
        double r4131591 = r4131587 / r4131590;
        return r4131591;
}
↓
double f(double a, double b) {
        double r4131592 = 1.0;
        double r4131593 = a;
        double r4131594 = exp(r4131593);
        double r4131595 = b;
        double r4131596 = exp(r4131595);
        double r4131597 = r4131594 + r4131596;
        double r4131598 = r4131597 / r4131594;
        double r4131599 = r4131592 / r4131598;
        return r4131599;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.6

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

  3. Applied clear-num0.6

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

  4. Final simplification0.6

    \[\leadsto \frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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