Average Error: 0.7 → 0.7
Time: 12.2s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{b} + e^{a}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{b} + e^{a}}{e^{a}}}
double f(double a, double b) {
        double r103702 = a;
        double r103703 = exp(r103702);
        double r103704 = b;
        double r103705 = exp(r103704);
        double r103706 = r103703 + r103705;
        double r103707 = r103703 / r103706;
        return r103707;
}
↓
double f(double a, double b) {
        double r103708 = 1.0;
        double r103709 = b;
        double r103710 = exp(r103709);
        double r103711 = a;
        double r103712 = exp(r103711);
        double r103713 = r103710 + r103712;
        double r103714 = r103713 / r103712;
        double r103715 = r103708 / r103714;
        return r103715;
}

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 clear-num0.7

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

  4. Simplified0.7

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

  5. Final simplification0.7

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

Reproduce

herbie shell --seed 2019347 +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))))