Average Error: 0.1 → 0.2
Time: 14.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{1}{3}\right)}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{1}{3}\right)}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r207334 = x;
        double r207335 = y;
        double r207336 = sin(r207335);
        double r207337 = r207334 * r207336;
        double r207338 = z;
        double r207339 = cos(r207335);
        double r207340 = r207338 * r207339;
        double r207341 = r207337 + r207340;
        return r207341;
}
↓
double f(double x, double y, double z) {
        double r207342 = x;
        double r207343 = y;
        double r207344 = sin(r207343);
        double r207345 = r207342 * r207344;
        double r207346 = z;
        double r207347 = cos(r207343);
        double r207348 = 2.0;
        double r207349 = pow(r207347, r207348);
        double r207350 = 1.0;
        double r207351 = 3.0;
        double r207352 = r207350 / r207351;
        double r207353 = pow(r207349, r207352);
        double r207354 = r207346 * r207353;
        double r207355 = cbrt(r207347);
        double r207356 = r207354 * r207355;
        double r207357 = r207345 + r207356;
        return r207357;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \sin y + z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)}\]

  4. Applied associate-*r*0.4

    \[\leadsto x \cdot \sin y + \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}}\]
  5. Using strategy rm

  6. Applied pow1/316.0

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  7. Applied pow1/316.0

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  8. Applied pow-prod-down0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

  9. Simplified0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

  10. Final simplification0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{1}{3}\right)}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))