Average Error: 0.6 → 0.6
Time: 28.0s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r3479009 = a;
        double r3479010 = exp(r3479009);
        double r3479011 = b;
        double r3479012 = exp(r3479011);
        double r3479013 = r3479010 + r3479012;
        double r3479014 = r3479010 / r3479013;
        return r3479014;
}
↓
double f(double a, double b) {
        double r3479015 = 1.0;
        double r3479016 = a;
        double r3479017 = exp(r3479016);
        double r3479018 = b;
        double r3479019 = exp(r3479018);
        double r3479020 = r3479017 + r3479019;
        double r3479021 = r3479020 / r3479017;
        double r3479022 = r3479015 / r3479021;
        return r3479022;
}

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

Derivation

  1. Initial program 0.6

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

  3. Applied clear-num0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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