Average Error: 0.7 → 0.7
Time: 3.2s
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 r139606 = a;
        double r139607 = exp(r139606);
        double r139608 = b;
        double r139609 = exp(r139608);
        double r139610 = r139607 + r139609;
        double r139611 = r139607 / r139610;
        return r139611;
}
↓
double f(double a, double b) {
        double r139612 = a;
        double r139613 = exp(r139612);
        double r139614 = b;
        double r139615 = exp(r139614);
        double r139616 = r139613 + r139615;
        double r139617 = r139613 / r139616;
        return r139617;
}

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 2020002 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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