Average Error: 0.6 → 0.6
Time: 2.2s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[e^{a} \cdot \frac{1}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
e^{a} \cdot \frac{1}{e^{a} + e^{b}}
double code(double a, double b) {
	return ((double) (((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b))))));
}
↓
double code(double a, double b) {
	return ((double) (((double) exp(a)) * ((double) (1.0 / ((double) (((double) exp(a)) + ((double) 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

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

Derivation

  1. Initial program 0.6

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

  3. Applied div-inv0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2020163 
(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))))