Average Error: 0.0 → 0.0
Time: 12.5s
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 r441789 = x;
        double r441790 = y;
        double r441791 = r441789 + r441790;
        double r441792 = r441789 - r441790;
        double r441793 = r441791 / r441792;
        return r441793;
}
↓
double f(double x, double y) {
        double r441794 = exp(1.0);
        double r441795 = x;
        double r441796 = y;
        double r441797 = r441795 + r441796;
        double r441798 = r441795 - r441796;
        double r441799 = r441797 / r441798;
        double r441800 = pow(r441794, r441799);
        double r441801 = log(r441800);
        return r441801;
}

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 +o rules:numerics
(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)))