Average Error: 0.1 → 0.2
Time: 17.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r9383989 = x;
        double r9383990 = y;
        double r9383991 = cos(r9383990);
        double r9383992 = r9383989 * r9383991;
        double r9383993 = z;
        double r9383994 = sin(r9383990);
        double r9383995 = r9383993 * r9383994;
        double r9383996 = r9383992 - r9383995;
        return r9383996;
}
↓
double f(double x, double y, double z) {
        double r9383997 = y;
        double r9383998 = cos(r9383997);
        double r9383999 = cbrt(r9383998);
        double r9384000 = r9383998 * r9383998;
        double r9384001 = 0.3333333333333333;
        double r9384002 = pow(r9384000, r9384001);
        double r9384003 = x;
        double r9384004 = r9384002 * r9384003;
        double r9384005 = r9383999 * r9384004;
        double r9384006 = z;
        double r9384007 = sin(r9383997);
        double r9384008 = r9384006 * r9384007;
        double r9384009 = r9384005 - r9384008;
        return r9384009;
}

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 pow1/316.2

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

  7. Applied pow1/316.2

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))