Average Error: 0.1 → 0.2
Time: 5.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r224106 = x;
        double r224107 = y;
        double r224108 = cos(r224107);
        double r224109 = r224106 * r224108;
        double r224110 = z;
        double r224111 = sin(r224107);
        double r224112 = r224110 * r224111;
        double r224113 = r224109 - r224112;
        return r224113;
}
↓
double f(double x, double y, double z) {
        double r224114 = x;
        double r224115 = y;
        double r224116 = cos(r224115);
        double r224117 = 2.0;
        double r224118 = pow(r224116, r224117);
        double r224119 = 0.3333333333333333;
        double r224120 = pow(r224118, r224119);
        double r224121 = cbrt(r224116);
        double r224122 = r224120 * r224121;
        double r224123 = r224114 * r224122;
        double r224124 = z;
        double r224125 = sin(r224115);
        double r224126 = r224124 * r224125;
        double r224127 = r224123 - r224126;
        return r224127;
}

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 pow1/316.4

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

  7. Applied pow1/316.4

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

  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. Simplified0.2

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

  11. Applied associate-*l*0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))