Average Error: 0.1 → 0.2
Time: 21.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r13339384 = x;
        double r13339385 = y;
        double r13339386 = sin(r13339385);
        double r13339387 = r13339384 * r13339386;
        double r13339388 = z;
        double r13339389 = cos(r13339385);
        double r13339390 = r13339388 * r13339389;
        double r13339391 = r13339387 + r13339390;
        return r13339391;
}
↓
double f(double x, double y, double z) {
        double r13339392 = x;
        double r13339393 = y;
        double r13339394 = sin(r13339393);
        double r13339395 = r13339392 * r13339394;
        double r13339396 = z;
        double r13339397 = cos(r13339393);
        double r13339398 = r13339397 * r13339397;
        double r13339399 = 0.3333333333333333;
        double r13339400 = pow(r13339398, r13339399);
        double r13339401 = r13339396 * r13339400;
        double r13339402 = cbrt(r13339397);
        double r13339403 = r13339401 * r13339402;
        double r13339404 = r13339395 + r13339403;
        return r13339404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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 pow1/315.8

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

  7. Applied pow1/315.8

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))