Average Error: 0.7 → 0.7
Time: 17.2s
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 r14731085 = a;
        double r14731086 = exp(r14731085);
        double r14731087 = b;
        double r14731088 = exp(r14731087);
        double r14731089 = r14731086 + r14731088;
        double r14731090 = r14731086 / r14731089;
        return r14731090;
}
↓
double f(double a, double b) {
        double r14731091 = a;
        double r14731092 = exp(r14731091);
        double r14731093 = b;
        double r14731094 = exp(r14731093);
        double r14731095 = r14731092 + r14731094;
        double r14731096 = r14731092 / r14731095;
        return r14731096;
}

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 2019112 
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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