Average Error: 0.1 → 0.3
Time: 14.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r2927707 = x;
        double r2927708 = y;
        double r2927709 = cos(r2927708);
        double r2927710 = r2927707 * r2927709;
        double r2927711 = z;
        double r2927712 = sin(r2927708);
        double r2927713 = r2927711 * r2927712;
        double r2927714 = r2927710 - r2927713;
        return r2927714;
}
↓
double f(double x, double y, double z) {
        double r2927715 = y;
        double r2927716 = cos(r2927715);
        double r2927717 = cbrt(r2927716);
        double r2927718 = x;
        double r2927719 = r2927716 * r2927716;
        double r2927720 = 0.3333333333333333;
        double r2927721 = pow(r2927719, r2927720);
        double r2927722 = sqrt(r2927721);
        double r2927723 = r2927718 * r2927722;
        double r2927724 = r2927723 * r2927722;
        double r2927725 = r2927717 * r2927724;
        double r2927726 = z;
        double r2927727 = sin(r2927715);
        double r2927728 = r2927726 * r2927727;
        double r2927729 = r2927725 - r2927728;
        return r2927729;
}

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 pow1/316.0

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

  7. Applied pow1/316.0

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

  8. Applied pow-prod-down0.2

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

  10. Applied add-sqr-sqrt0.3

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

  11. Applied associate-*r*0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 +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))))