Average Error: 0.6 → 0.7
Time: 19.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{\sqrt[3]{\left(e^{a} + e^{b}\right) \cdot \left(\left(e^{a} + e^{b}\right) \cdot \left(e^{a} + e^{b}\right)\right)}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{\sqrt[3]{\left(e^{a} + e^{b}\right) \cdot \left(\left(e^{a} + e^{b}\right) \cdot \left(e^{a} + e^{b}\right)\right)}}
double f(double a, double b) {
        double r4769749 = a;
        double r4769750 = exp(r4769749);
        double r4769751 = b;
        double r4769752 = exp(r4769751);
        double r4769753 = r4769750 + r4769752;
        double r4769754 = r4769750 / r4769753;
        return r4769754;
}
↓
double f(double a, double b) {
        double r4769755 = a;
        double r4769756 = exp(r4769755);
        double r4769757 = b;
        double r4769758 = exp(r4769757);
        double r4769759 = r4769756 + r4769758;
        double r4769760 = r4769759 * r4769759;
        double r4769761 = r4769759 * r4769760;
        double r4769762 = cbrt(r4769761);
        double r4769763 = r4769756 / r4769762;
        return r4769763;
}

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
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied add-cbrt-cube0.7

    \[\leadsto \frac{e^{a}}{\color{blue}{\sqrt[3]{\left(\left(e^{a} + e^{b}\right) \cdot \left(e^{a} + e^{b}\right)\right) \cdot \left(e^{a} + e^{b}\right)}}}\]

  4. Final simplification0.7

    \[\leadsto \frac{e^{a}}{\sqrt[3]{\left(e^{a} + e^{b}\right) \cdot \left(\left(e^{a} + e^{b}\right) \cdot \left(e^{a} + e^{b}\right)\right)}}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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