Average Error: 0.7 → 0.6
Time: 3.4s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}} \]
↓
\[e^{a - \sqrt{{\log \left(e^{a} + e^{b}\right)}^{2}}} \]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a - \sqrt{{\log \left(e^{a} + e^{b}\right)}^{2}}}

(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b)
 :precision binary64
 (exp (- a (sqrt (pow (log (+ (exp a) (exp b))) 2.0)))))
double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}
↓
double code(double a, double b) {
	return exp((a - sqrt(pow(log((exp(a) + exp(b))), 2.0))));
}

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
Herbie0.6
\[\frac{1}{1 + e^{b - a}} \]

Derivation

  1. Initial program 0.7

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

  2. Applied egg-rr0.5

    \[\leadsto \color{blue}{e^{a - \log \left(e^{a} + e^{b}\right)}} \]

  3. Applied egg-rr0.6

    \[\leadsto e^{a - \color{blue}{\sqrt{{\log \left(e^{a} + e^{b}\right)}^{2}}}} \]

  4. Final simplification0.6

    \[\leadsto e^{a - \sqrt{{\log \left(e^{a} + e^{b}\right)}^{2}}} \]

Reproduce

herbie shell --seed 2022130 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

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