Average Error: 0.1 → 0.2
Time: 5.0s
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 r200033 = x;
        double r200034 = y;
        double r200035 = cos(r200034);
        double r200036 = r200033 * r200035;
        double r200037 = z;
        double r200038 = sin(r200034);
        double r200039 = r200037 * r200038;
        double r200040 = r200036 - r200039;
        return r200040;
}
↓
double f(double x, double y, double z) {
        double r200041 = x;
        double r200042 = y;
        double r200043 = cos(r200042);
        double r200044 = 2.0;
        double r200045 = pow(r200043, r200044);
        double r200046 = 0.3333333333333333;
        double r200047 = pow(r200045, r200046);
        double r200048 = cbrt(r200043);
        double r200049 = r200047 * r200048;
        double r200050 = r200041 * r200049;
        double r200051 = z;
        double r200052 = sin(r200042);
        double r200053 = r200051 * r200052;
        double r200054 = r200050 - r200053;
        return r200054;
}

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 
(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))))