Average Error: 0.1 → 0.6
Time: 42.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r11555572 = x;
        double r11555573 = y;
        double r11555574 = cos(r11555573);
        double r11555575 = r11555572 * r11555574;
        double r11555576 = z;
        double r11555577 = sin(r11555573);
        double r11555578 = r11555576 * r11555577;
        double r11555579 = r11555575 + r11555578;
        return r11555579;
}
↓
double f(double x, double y, double z) {
        double r11555580 = x;
        double r11555581 = y;
        double r11555582 = cos(r11555581);
        double r11555583 = r11555580 * r11555582;
        double r11555584 = z;
        double r11555585 = cbrt(r11555584);
        double r11555586 = r11555585 * r11555585;
        double r11555587 = sin(r11555581);
        double r11555588 = r11555587 * r11555585;
        double r11555589 = r11555586 * r11555588;
        double r11555590 = r11555583 + r11555589;
        return r11555590;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

    \[\leadsto x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))