Average Error: 0.7 → 0.7
Time: 1.8s
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 r103086 = a;
        double r103087 = exp(r103086);
        double r103088 = b;
        double r103089 = exp(r103088);
        double r103090 = r103087 + r103089;
        double r103091 = r103087 / r103090;
        return r103091;
}
↓
double f(double a, double b) {
        double r103092 = a;
        double r103093 = exp(r103092);
        double r103094 = b;
        double r103095 = exp(r103094);
        double r103096 = r103093 + r103095;
        double r103097 = r103093 / r103096;
        return r103097;
}

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 2020100 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

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

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