Average Error: 0.1 → 0.3
Time: 23.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(x \cdot {\left(\frac{1}{2} + \frac{1}{2} \cdot \cos \left(y + y\right)\right)}^{\frac{1}{3}}\right) - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(x \cdot {\left(\frac{1}{2} + \frac{1}{2} \cdot \cos \left(y + y\right)\right)}^{\frac{1}{3}}\right) - \sin y \cdot z
double f(double x, double y, double z) {
        double r11510713 = x;
        double r11510714 = y;
        double r11510715 = cos(r11510714);
        double r11510716 = r11510713 * r11510715;
        double r11510717 = z;
        double r11510718 = sin(r11510714);
        double r11510719 = r11510717 * r11510718;
        double r11510720 = r11510716 - r11510719;
        return r11510720;
}
↓
double f(double x, double y, double z) {
        double r11510721 = y;
        double r11510722 = cos(r11510721);
        double r11510723 = cbrt(r11510722);
        double r11510724 = x;
        double r11510725 = 0.5;
        double r11510726 = r11510721 + r11510721;
        double r11510727 = cos(r11510726);
        double r11510728 = r11510725 * r11510727;
        double r11510729 = r11510725 + r11510728;
        double r11510730 = 0.3333333333333333;
        double r11510731 = pow(r11510729, r11510730);
        double r11510732 = r11510724 * r11510731;
        double r11510733 = r11510723 * r11510732;
        double r11510734 = sin(r11510721);
        double r11510735 = z;
        double r11510736 = r11510734 * r11510735;
        double r11510737 = r11510733 - r11510736;
        return r11510737;
}

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 pow1/316.3

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

  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. Using strategy rm

  10. Applied sqr-cos0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))