Average Error: 0.7 → 0.7
Time: 14.2s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r7233109 = a;
        double r7233110 = exp(r7233109);
        double r7233111 = b;
        double r7233112 = exp(r7233111);
        double r7233113 = r7233110 + r7233112;
        double r7233114 = r7233110 / r7233113;
        return r7233114;
}
↓
double f(double a, double b) {
        double r7233115 = a;
        double r7233116 = exp(r7233115);
        double r7233117 = b;
        double r7233118 = exp(r7233117);
        double r7233119 = r7233116 + r7233118;
        double r7233120 = r7233116 / r7233119;
        return r7233120;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  2. Final simplification0.7

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

Reproduce

herbie shell --seed 2019163 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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