Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\sqrt[3]{{\left(\sqrt[3]{\frac{x + y}{x - y} \cdot \frac{x + y}{x - y}} \cdot \sqrt[3]{\frac{x + y}{x - y}}\right)}^{3}}\]
\frac{x + y}{x - y}
↓
\sqrt[3]{{\left(\sqrt[3]{\frac{x + y}{x - y} \cdot \frac{x + y}{x - y}} \cdot \sqrt[3]{\frac{x + y}{x - y}}\right)}^{3}}
double f(double x, double y) {
        double r507196 = x;
        double r507197 = y;
        double r507198 = r507196 + r507197;
        double r507199 = r507196 - r507197;
        double r507200 = r507198 / r507199;
        return r507200;
}
↓
double f(double x, double y) {
        double r507201 = x;
        double r507202 = y;
        double r507203 = r507201 + r507202;
        double r507204 = r507201 - r507202;
        double r507205 = r507203 / r507204;
        double r507206 = r507205 * r507205;
        double r507207 = cbrt(r507206);
        double r507208 = cbrt(r507205);
        double r507209 = r507207 * r507208;
        double r507210 = 3.0;
        double r507211 = pow(r507209, r507210);
        double r507212 = cbrt(r507211);
        return r507212;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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-cube41.2

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

  4. Applied add-cbrt-cube42.0

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

  5. Applied cbrt-undiv42.0

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

  6. Simplified0.0

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

  8. Applied add-cube-cbrt0.1

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +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)))