Average Error: 0.0 → 0.0
Time: 13.1s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left({e}^{\left(\frac{x + y}{x - y}\right)}\right)\]
\frac{x + y}{x - y}
↓
\log \left({e}^{\left(\frac{x + y}{x - y}\right)}\right)
double f(double x, double y) {
        double r398975 = x;
        double r398976 = y;
        double r398977 = r398975 + r398976;
        double r398978 = r398975 - r398976;
        double r398979 = r398977 / r398978;
        return r398979;
}
↓
double f(double x, double y) {
        double r398980 = exp(1.0);
        double r398981 = x;
        double r398982 = y;
        double r398983 = r398981 + r398982;
        double r398984 = r398981 - r398982;
        double r398985 = r398983 / r398984;
        double r398986 = pow(r398980, r398985);
        double r398987 = log(r398986);
        return r398987;
}

Error

Bits error versus x

Bits error versus y

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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 2019209 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

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