Average Error: 0.7 → 0.7
Time: 2.4s
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 r138065 = a;
        double r138066 = exp(r138065);
        double r138067 = b;
        double r138068 = exp(r138067);
        double r138069 = r138066 + r138068;
        double r138070 = r138066 / r138069;
        return r138070;
}
↓
double f(double a, double b) {
        double r138071 = a;
        double r138072 = exp(r138071);
        double r138073 = b;
        double r138074 = exp(r138073);
        double r138075 = r138072 + r138074;
        double r138076 = r138072 / r138075;
        return r138076;
}

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 2020057 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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