Average Error: 0.1 → 0.3
Time: 18.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(x \cdot {\left(\frac{1}{2} + \frac{1}{2} \cdot \cos \left(y + y\right)\right)}^{\frac{1}{3}}\right) - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(x \cdot {\left(\frac{1}{2} + \frac{1}{2} \cdot \cos \left(y + y\right)\right)}^{\frac{1}{3}}\right) - \sin y \cdot z
double f(double x, double y, double z) {
        double r7304513 = x;
        double r7304514 = y;
        double r7304515 = cos(r7304514);
        double r7304516 = r7304513 * r7304515;
        double r7304517 = z;
        double r7304518 = sin(r7304514);
        double r7304519 = r7304517 * r7304518;
        double r7304520 = r7304516 - r7304519;
        return r7304520;
}
↓
double f(double x, double y, double z) {
        double r7304521 = y;
        double r7304522 = cos(r7304521);
        double r7304523 = cbrt(r7304522);
        double r7304524 = x;
        double r7304525 = 0.5;
        double r7304526 = r7304521 + r7304521;
        double r7304527 = cos(r7304526);
        double r7304528 = r7304525 * r7304527;
        double r7304529 = r7304525 + r7304528;
        double r7304530 = 0.3333333333333333;
        double r7304531 = pow(r7304529, r7304530);
        double r7304532 = r7304524 * r7304531;
        double r7304533 = r7304523 * r7304532;
        double r7304534 = sin(r7304521);
        double r7304535 = z;
        double r7304536 = r7304534 * r7304535;
        double r7304537 = r7304533 - r7304536;
        return r7304537;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied cbrt-unprod0.3

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

  8. Applied pow1/30.2

    \[\leadsto \left(x \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  9. Using strategy rm

  10. Applied sqr-cos0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))