Average Error: 0.7 → 1.1
Time: 1.8s
Precision: binary64
\[\frac{e^{a}}{e^{a} + e^{b}}\]
↓
\[\sqrt{\frac{e^{a}}{e^{a} + e^{b}}} \cdot \sqrt{\frac{e^{a}}{e^{a} + e^{b}}}\]
\frac{e^{a}}{e^{a} + e^{b}}
↓
\sqrt{\frac{e^{a}}{e^{a} + e^{b}}} \cdot \sqrt{\frac{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) (+ (exp a) (exp b))))
  (sqrt (/ (exp a) (+ (exp a) (exp b))))))
double code(double a, double b) {
	return (((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b)))));
}
↓
double code(double a, double b) {
	return ((double) (((double) sqrt((((double) exp(a)) / ((double) (((double) exp(a)) + ((double) exp(b))))))) * ((double) sqrt((((double) exp(a)) / ((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

Original0.7
Target0.0
Herbie1.1
\[\frac{1}{1 + e^{b - a}}\]

Derivation

  1. Initial program 0.7

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

  3. Applied add-sqr-sqrt_binary641.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020219 
(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))))