Average Error: 0.1 → 0.2
Time: 16.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r224535 = x;
        double r224536 = y;
        double r224537 = sin(r224536);
        double r224538 = r224535 * r224537;
        double r224539 = z;
        double r224540 = cos(r224536);
        double r224541 = r224539 * r224540;
        double r224542 = r224538 + r224541;
        return r224542;
}
↓
double f(double x, double y, double z) {
        double r224543 = x;
        double r224544 = y;
        double r224545 = sin(r224544);
        double r224546 = r224543 * r224545;
        double r224547 = z;
        double r224548 = cos(r224544);
        double r224549 = 2.0;
        double r224550 = pow(r224548, r224549);
        double r224551 = 3.0;
        double r224552 = pow(r224550, r224551);
        double r224553 = cbrt(r224552);
        double r224554 = 0.3333333333333333;
        double r224555 = pow(r224553, r224554);
        double r224556 = r224547 * r224555;
        double r224557 = cbrt(r224548);
        double r224558 = r224556 * r224557;
        double r224559 = r224546 + r224558;
        return r224559;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

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 pow1/316.2

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

  7. Applied pow1/316.2

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

  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. Using strategy rm

  11. Applied add-cbrt-cube0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))