Average Error: 0.7 → 0.7
Time: 1.6s
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 r122320 = a;
        double r122321 = exp(r122320);
        double r122322 = b;
        double r122323 = exp(r122322);
        double r122324 = r122321 + r122323;
        double r122325 = r122321 / r122324;
        return r122325;
}
↓
double f(double a, double b) {
        double r122326 = a;
        double r122327 = exp(r122326);
        double r122328 = b;
        double r122329 = exp(r122328);
        double r122330 = r122327 + r122329;
        double r122331 = r122327 / r122330;
        return r122331;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2020036 +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))))