Average Error: 0.4 → 0.5
Time: 4.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)\right) \cdot \left(-1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)\right) \cdot \left(-1\right)
double f(double x, double y) {
        double r416160 = 3.0;
        double r416161 = x;
        double r416162 = sqrt(r416161);
        double r416163 = r416160 * r416162;
        double r416164 = y;
        double r416165 = 1.0;
        double r416166 = 9.0;
        double r416167 = r416161 * r416166;
        double r416168 = r416165 / r416167;
        double r416169 = r416164 + r416168;
        double r416170 = r416169 - r416165;
        double r416171 = r416163 * r416170;
        return r416171;
}
↓
double f(double x, double y) {
        double r416172 = 3.0;
        double r416173 = x;
        double r416174 = sqrt(r416173);
        double r416175 = r416172 * r416174;
        double r416176 = y;
        double r416177 = 1.0;
        double r416178 = r416177 / r416173;
        double r416179 = 9.0;
        double r416180 = r416178 / r416179;
        double r416181 = r416176 + r416180;
        double r416182 = r416175 * r416181;
        double r416183 = cbrt(r416172);
        double r416184 = r416183 * r416183;
        double r416185 = cbrt(r416183);
        double r416186 = r416185 * r416185;
        double r416187 = r416185 * r416174;
        double r416188 = r416186 * r416187;
        double r416189 = r416184 * r416188;
        double r416190 = -r416177;
        double r416191 = r416189 * r416190;
        double r416192 = r416182 + r416191;
        return r416192;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-/r*0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{\frac{1}{x}}{9}}\right) - 1\right)\]
  4. Using strategy rm

  5. Applied sub-neg0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\left(y + \frac{\frac{1}{x}}{9}\right) + \left(-1\right)\right)}\]

  6. Applied distribute-lft-in0.4

    \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(3 \cdot \sqrt{x}\right) \cdot \left(-1\right)}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot \sqrt{x}\right) \cdot \left(-1\right)\]

  9. Applied associate-*l*0.5

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt{x}\right)\right)} \cdot \left(-1\right)\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.5

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \sqrt[3]{\sqrt[3]{3}}\right)} \cdot \sqrt{x}\right)\right) \cdot \left(-1\right)\]

  12. Applied associate-*l*0.5

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)}\right) \cdot \left(-1\right)\]

  13. Final simplification0.5

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{1}{x}}{9}\right) + \left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt[3]{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{3}} \cdot \sqrt{x}\right)\right)\right) \cdot \left(-1\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))