Average Error: 0.7 → 0.7
Time: 2.7s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\sqrt{e^{a}} \cdot \frac{\sqrt{e^{a}}}{e^{a} + e^{b}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\sqrt{e^{a}} \cdot \frac{\sqrt{e^{a}}}{e^{a} + e^{b}}
(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))
↓
(FPCore (a b)
 :precision binary64
 (* (sqrt (exp a)) (/ (sqrt (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 sqrt(exp(a)) * (sqrt(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

Original0.7
Target0.0
Herbie0.7
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied *-un-lft-identity_binary640.7

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

  4. Applied add-sqr-sqrt_binary640.7

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

  5. Applied times-frac_binary640.7

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

  6. Final simplification0.7

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

Alternatives

Reproduce

herbie shell --seed 2021113 
(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))))