Average Error: 0.7 → 0.7
Time: 15.8s
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 r5383678 = a;
        double r5383679 = exp(r5383678);
        double r5383680 = b;
        double r5383681 = exp(r5383680);
        double r5383682 = r5383679 + r5383681;
        double r5383683 = r5383679 / r5383682;
        return r5383683;
}
↓
double f(double a, double b) {
        double r5383684 = a;
        double r5383685 = exp(r5383684);
        double r5383686 = b;
        double r5383687 = exp(r5383686);
        double r5383688 = r5383685 + r5383687;
        double r5383689 = r5383685 / r5383688;
        return r5383689;
}

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 2019163 +o rules:numerics
(FPCore (a b)
  :name "Quotient of sum of exps"

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

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