Average Error: 0.7 → 0.7
Time: 14.4s
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 r3277116 = a;
        double r3277117 = exp(r3277116);
        double r3277118 = b;
        double r3277119 = exp(r3277118);
        double r3277120 = r3277117 + r3277119;
        double r3277121 = r3277117 / r3277120;
        return r3277121;
}
↓
double f(double a, double b) {
        double r3277122 = a;
        double r3277123 = exp(r3277122);
        double r3277124 = b;
        double r3277125 = exp(r3277124);
        double r3277126 = r3277123 + r3277125;
        double r3277127 = r3277123 / r3277126;
        return r3277127;
}

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. Taylor expanded around -inf 0.7

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2019149 +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))))