Average Error: 0.4 → 0.5
Time: 20.6s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\left(\sqrt{\sqrt[3]{3.0}} \cdot \left(\left(\left(\frac{1.0}{x \cdot 9.0} + y\right) - 1.0\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3.0}}\right) \cdot \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\left(\sqrt{\sqrt[3]{3.0}} \cdot \left(\left(\left(\frac{1.0}{x \cdot 9.0} + y\right) - 1.0\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3.0}}\right) \cdot \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right)
double f(double x, double y) {
        double r17299341 = 3.0;
        double r17299342 = x;
        double r17299343 = sqrt(r17299342);
        double r17299344 = r17299341 * r17299343;
        double r17299345 = y;
        double r17299346 = 1.0;
        double r17299347 = 9.0;
        double r17299348 = r17299342 * r17299347;
        double r17299349 = r17299346 / r17299348;
        double r17299350 = r17299345 + r17299349;
        double r17299351 = r17299350 - r17299346;
        double r17299352 = r17299344 * r17299351;
        return r17299352;
}
↓
double f(double x, double y) {
        double r17299353 = 3.0;
        double r17299354 = cbrt(r17299353);
        double r17299355 = sqrt(r17299354);
        double r17299356 = 1.0;
        double r17299357 = x;
        double r17299358 = 9.0;
        double r17299359 = r17299357 * r17299358;
        double r17299360 = r17299356 / r17299359;
        double r17299361 = y;
        double r17299362 = r17299360 + r17299361;
        double r17299363 = r17299362 - r17299356;
        double r17299364 = sqrt(r17299357);
        double r17299365 = r17299363 * r17299364;
        double r17299366 = r17299355 * r17299365;
        double r17299367 = r17299366 * r17299355;
        double r17299368 = r17299354 * r17299354;
        double r17299369 = r17299367 * r17299368;
        return r17299369;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.4
Herbie0.5
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\]

  6. Applied associate-*l*0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\color{blue}{\left(\sqrt{\sqrt[3]{3.0}} \cdot \sqrt{\sqrt[3]{3.0}}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\right)\]

  9. Applied associate-*l*0.5

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{3.0}} \cdot \left(\sqrt{\sqrt[3]{3.0}} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\right)\right)}\]

  10. Final simplification0.5

    \[\leadsto \left(\left(\sqrt{\sqrt[3]{3.0}} \cdot \left(\left(\left(\frac{1.0}{x \cdot 9.0} + y\right) - 1.0\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3.0}}\right) \cdot \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))