Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\frac{x + y}{x - y}\]
\frac{x + y}{x - y}
↓
\frac{x + y}{x - y}
double f(double x, double y) {
        double r477730 = x;
        double r477731 = y;
        double r477732 = r477730 + r477731;
        double r477733 = r477730 - r477731;
        double r477734 = r477732 / r477733;
        return r477734;
}
↓
double f(double x, double y) {
        double r477735 = x;
        double r477736 = y;
        double r477737 = r477735 + r477736;
        double r477738 = r477735 - r477736;
        double r477739 = r477737 / r477738;
        return r477739;
}

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. Applied log-pow0.0

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

  10. Simplified0.0

    \[\leadsto \frac{x + y}{x - y} \cdot \color{blue}{1}\]

  11. Final simplification0.0

    \[\leadsto \frac{x + y}{x - y}\]

Reproduce

herbie shell --seed 2020020 +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)))