Average Error: 0.1 → 0.2
Time: 22.5s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r138408 = x;
        double r138409 = y;
        double r138410 = cos(r138409);
        double r138411 = r138408 * r138410;
        double r138412 = z;
        double r138413 = sin(r138409);
        double r138414 = r138412 * r138413;
        double r138415 = r138411 - r138414;
        return r138415;
}
↓
double f(double x, double y, double z) {
        double r138416 = x;
        double r138417 = y;
        double r138418 = cos(r138417);
        double r138419 = 2.0;
        double r138420 = pow(r138418, r138419);
        double r138421 = 0.3333333333333333;
        double r138422 = pow(r138420, r138421);
        double r138423 = r138416 * r138422;
        double r138424 = cbrt(r138418);
        double r138425 = r138423 * r138424;
        double r138426 = z;
        double r138427 = sin(r138417);
        double r138428 = r138426 * r138427;
        double r138429 = r138425 - r138428;
        return r138429;
}

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

    \[x \cdot \cos y - z \cdot \sin y\]
  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. Simplified0.3

    \[\leadsto \left(x \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  8. Using strategy rm

  9. Applied pow1/30.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))