Average Error: 0.7 → 0.7
Time: 3.4s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}
double f(double a, double b) {
        double r146502 = a;
        double r146503 = exp(r146502);
        double r146504 = b;
        double r146505 = exp(r146504);
        double r146506 = r146503 + r146505;
        double r146507 = r146503 / r146506;
        return r146507;
}
↓
double f(double a, double b) {
        double r146508 = a;
        double r146509 = exp(r146508);
        double r146510 = b;
        double r146511 = exp(r146510);
        double r146512 = r146509 + r146511;
        double r146513 = r146509 / r146512;
        return r146513;
}

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. Final simplification0.7

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

Reproduce

herbie shell --seed 2020002 +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))))