Average Error: 0.6 → 0.0
Time: 1.4s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\frac{-1}{-1 - e^{b - a}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{-1}{-1 - e^{b - a}}
(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b) :precision binary64 (/ -1.0 (- -1.0 (exp (- b a)))))
double code(double a, double b) {
	return (((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b)))));
}
↓
double code(double a, double b) {
	return (-1.0 / ((double) (-1.0 - ((double) exp(((double) (b - a)))))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.6
Target0.0
Herbie0.0
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.6

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

  3. Applied clear-num_binary640.6

    \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}}\]
  4. Using strategy rm

  5. Applied frac-2neg_binary640.6

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

  6. Simplified0.6

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020210 
(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))))