Average Error: 0.7 → 0.7
Time: 37.5s
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 r28045452 = a;
        double r28045453 = exp(r28045452);
        double r28045454 = b;
        double r28045455 = exp(r28045454);
        double r28045456 = r28045453 + r28045455;
        double r28045457 = r28045453 / r28045456;
        return r28045457;
}
↓
double f(double a, double b) {
        double r28045458 = a;
        double r28045459 = exp(r28045458);
        double r28045460 = b;
        double r28045461 = exp(r28045460);
        double r28045462 = r28045459 + r28045461;
        double r28045463 = r28045459 / r28045462;
        return r28045463;
}

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. Taylor expanded around inf 0.7

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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