Average Error: 0.1 → 0.6
Time: 19.6s
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 r7967552 = x;
        double r7967553 = y;
        double r7967554 = cos(r7967553);
        double r7967555 = r7967552 * r7967554;
        double r7967556 = z;
        double r7967557 = sin(r7967553);
        double r7967558 = r7967556 * r7967557;
        double r7967559 = r7967555 + r7967558;
        return r7967559;
}
↓
double f(double x, double y, double z) {
        double r7967560 = x;
        double r7967561 = y;
        double r7967562 = cos(r7967561);
        double r7967563 = r7967560 * r7967562;
        double r7967564 = z;
        double r7967565 = cbrt(r7967564);
        double r7967566 = r7967565 * r7967565;
        double r7967567 = sin(r7967561);
        double r7967568 = r7967567 * r7967565;
        double r7967569 = r7967566 * r7967568;
        double r7967570 = r7967563 + r7967569;
        return r7967570;
}

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 2019163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))