Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\log \left({e}^{\left(\frac{x + y}{x - y}\right)}\right)\]
\frac{x + y}{x - y}
↓
\log \left({e}^{\left(\frac{x + y}{x - y}\right)}\right)
double code(double x, double y) {
	return ((double) (((double) (x + y)) / ((double) (x - y))));
}
↓
double code(double x, double y) {
	return ((double) log(((double) pow(((double) M_E), ((double) (((double) (x + y)) / ((double) (x - y))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{x - y}\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x + y}{x - y}}\right)}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(e^{\frac{x + y}{\color{blue}{1 \cdot \left(x - y\right)}}}\right)\]

  6. Applied *-un-lft-identity0.0

    \[\leadsto \log \left(e^{\frac{\color{blue}{1 \cdot \left(x + y\right)}}{1 \cdot \left(x - y\right)}}\right)\]

  7. Applied times-frac0.0

    \[\leadsto \log \left(e^{\color{blue}{\frac{1}{1} \cdot \frac{x + y}{x - y}}}\right)\]

  8. Applied exp-prod0.0

    \[\leadsto \log \color{blue}{\left({\left(e^{\frac{1}{1}}\right)}^{\left(\frac{x + y}{x - y}\right)}\right)}\]

  9. Simplified0.0

    \[\leadsto \log \left({\color{blue}{e}}^{\left(\frac{x + y}{x - y}\right)}\right)\]

  10. Final simplification0.0

    \[\leadsto \log \left({e}^{\left(\frac{x + y}{x - y}\right)}\right)\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))