Average Error: 0.6 → 0.5
Time: 17.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a - \log \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \log \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r4140201 = a;
        double r4140202 = exp(r4140201);
        double r4140203 = b;
        double r4140204 = exp(r4140203);
        double r4140205 = r4140202 + r4140204;
        double r4140206 = r4140202 / r4140205;
        return r4140206;
}
↓
double f(double a, double b) {
        double r4140207 = a;
        double r4140208 = exp(r4140207);
        double r4140209 = b;
        double r4140210 = exp(r4140209);
        double r4140211 = r4140208 + r4140210;
        double r4140212 = log(r4140211);
        double r4140213 = r4140207 - r4140212;
        double r4140214 = exp(r4140213);
        return r4140214;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.5
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied add-exp-log0.6

    \[\leadsto \frac{e^{a}}{\color{blue}{e^{\log \left(e^{a} + e^{b}\right)}}}\]

  4. Applied div-exp0.5

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}}\]

  5. Final simplification0.5

    \[\leadsto e^{a - \log \left(e^{a} + e^{b}\right)}\]

Reproduce

herbie shell --seed 2019168 +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))))