Average Error: 0.8 → 0.8
Time: 27.7s
Precision: 64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}
double f(double a, double b) {
        double r11943567 = a;
        double r11943568 = exp(r11943567);
        double r11943569 = b;
        double r11943570 = exp(r11943569);
        double r11943571 = r11943568 + r11943570;
        double r11943572 = r11943568 / r11943571;
        return r11943572;
}
↓
double f(double a, double b) {
        double r11943573 = 1.0;
        double r11943574 = a;
        double r11943575 = exp(r11943574);
        double r11943576 = b;
        double r11943577 = exp(r11943576);
        double r11943578 = r11943575 + r11943577;
        double r11943579 = r11943578 / r11943575;
        double r11943580 = r11943573 / r11943579;
        return r11943580;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.8
Target0.0
Herbie0.8
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.8

    \[\frac{e^{a}}{e^{a} + e^{b}}\]
  2. Using strategy rm

  3. Applied clear-num0.8

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}}\]

  4. Final simplification0.8

    \[\leadsto \frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}\]

Reproduce

herbie shell --seed 2019120 +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))))