Average Error: 0.7 → 0.7
Time: 2.5s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{1 \cdot \left(e^{a} + e^{b}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{1 \cdot \left(e^{a} + e^{b}\right)}
double f(double a, double b) {
        double r128774 = a;
        double r128775 = exp(r128774);
        double r128776 = b;
        double r128777 = exp(r128776);
        double r128778 = r128775 + r128777;
        double r128779 = r128775 / r128778;
        return r128779;
}
↓
double f(double a, double b) {
        double r128780 = a;
        double r128781 = exp(r128780);
        double r128782 = 1.0;
        double r128783 = b;
        double r128784 = exp(r128783);
        double r128785 = r128781 + r128784;
        double r128786 = r128782 * r128785;
        double r128787 = r128781 / r128786;
        return r128787;
}

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

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

  4. Final simplification0.7

    \[\leadsto \frac{e^{a}}{1 \cdot \left(e^{a} + e^{b}\right)}\]

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))))