Average Error: 0.7 → 1.0
Time: 6.6s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{e^{a}}{\log \left(e^{e^{a}} \cdot e^{e^{b}}\right)}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{\log \left(e^{e^{a}} \cdot e^{e^{b}}\right)}
(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b)
 :precision binary64
 (/ (exp a) (log (* (exp (exp a)) (exp (exp b))))))
double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}
↓
double code(double a, double b) {
	return exp(a) / log(exp(exp(a)) * exp(exp(b)));
}

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
Herbie1.0
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied add-log-exp_binary64_21630.8

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

  4. Applied add-log-exp_binary64_21631.0

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

  5. Applied sum-log_binary64_22151.0

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

  6. Final simplification1.0

    \[\leadsto \frac{e^{a}}{\log \left(e^{e^{a}} \cdot e^{e^{b}}\right)}\]

Reproduce

herbie shell --seed 2021098 
(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))))