Average Error: 0.7 → 0.7
Time: 13.3s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{b} + e^{a}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{b} + e^{a}}
double f(double a, double b) {
        double r114940 = a;
        double r114941 = exp(r114940);
        double r114942 = b;
        double r114943 = exp(r114942);
        double r114944 = r114941 + r114943;
        double r114945 = r114941 / r114944;
        return r114945;
}
↓
double f(double a, double b) {
        double r114946 = a;
        double r114947 = exp(r114946);
        double r114948 = b;
        double r114949 = exp(r114948);
        double r114950 = r114949 + r114947;
        double r114951 = r114947 / r114950;
        return r114951;
}

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 +-commutative0.7

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

  4. Final simplification0.7

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

Reproduce

herbie shell --seed 2019305 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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