Average Error: 0.1 → 0.2
Time: 22.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r6204509 = x;
        double r6204510 = y;
        double r6204511 = sin(r6204510);
        double r6204512 = r6204509 * r6204511;
        double r6204513 = z;
        double r6204514 = cos(r6204510);
        double r6204515 = r6204513 * r6204514;
        double r6204516 = r6204512 + r6204515;
        return r6204516;
}
↓
double f(double x, double y, double z) {
        double r6204517 = y;
        double r6204518 = cos(r6204517);
        double r6204519 = cbrt(r6204518);
        double r6204520 = r6204518 * r6204518;
        double r6204521 = 0.16666666666666666;
        double r6204522 = pow(r6204520, r6204521);
        double r6204523 = z;
        double r6204524 = r6204523 * r6204522;
        double r6204525 = r6204522 * r6204524;
        double r6204526 = r6204519 * r6204525;
        double r6204527 = x;
        double r6204528 = sin(r6204517);
        double r6204529 = r6204527 * r6204528;
        double r6204530 = r6204526 + r6204529;
        return r6204530;
}

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 pow1/315.4

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

  7. Applied pow1/315.4

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

  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. Using strategy rm

  10. Applied sqr-pow0.2

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

  11. Applied associate-*r*0.2

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

  12. Final simplification0.2

    \[\leadsto \sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}} \cdot \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{6}}\right)\right) + x \cdot \sin y\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))