Average Error: 0.8 → 0.8
Time: 7.8s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}} \]
↓
\[\frac{e^{a}}{e^{a} + e^{b}} \]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\frac{e^{a}}{e^{a} + e^{b}}

(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}
↓
double code(double a, double b) {
	return exp(a) / (exp(a) + 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

Original0.8
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 *-un-lft-identity_binary640.8

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

  4. Applied *-un-lft-identity_binary640.8

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

  5. Applied distribute-lft-out_binary640.8

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

  6. Simplified0.8

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

  7. Final simplification0.8

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

Reproduce

herbie shell --seed 2021202 
(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))))