Average Error: 0.0 → 0.0
Time: 9.0s
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 r366581 = x;
        double r366582 = y;
        double r366583 = r366581 + r366582;
        double r366584 = r366581 - r366582;
        double r366585 = r366583 / r366584;
        return r366585;
}
↓
double f(double x, double y) {
        double r366586 = x;
        double r366587 = y;
        double r366588 = r366586 + r366587;
        double r366589 = r366586 - r366587;
        double r366590 = r366588 / r366589;
        return r366590;
}

Error

Bits error versus x

Bits error versus y

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Results

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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-cbrt-cube42.0

    \[\leadsto \frac{x + y}{\color{blue}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}}\]

  4. Applied add-cbrt-cube42.9

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}\]

  5. Applied cbrt-undiv42.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}}\]

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x + y}{x - y}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied add-log-exp0.0

    \[\leadsto \sqrt[3]{\color{blue}{\log \left(e^{{\left(\frac{x + y}{x - y}\right)}^{3}}\right)}}\]

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(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)))