Average Error: 0.1 → 0.9
Time: 5.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r218527 = x;
        double r218528 = y;
        double r218529 = cos(r218528);
        double r218530 = r218527 * r218529;
        double r218531 = z;
        double r218532 = sin(r218528);
        double r218533 = r218531 * r218532;
        double r218534 = r218530 - r218533;
        return r218534;
}
↓
double f(double x, double y, double z) {
        double r218535 = x;
        double r218536 = y;
        double r218537 = cos(r218536);
        double r218538 = r218535 * r218537;
        double r218539 = cbrt(r218538);
        double r218540 = cbrt(r218535);
        double r218541 = r218539 * r218540;
        double r218542 = cbrt(r218537);
        double r218543 = r218541 * r218542;
        double r218544 = r218543 * r218539;
        double r218545 = z;
        double r218546 = sin(r218536);
        double r218547 = r218545 * r218546;
        double r218548 = r218544 - r218547;
        return r218548;
}

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-cbrt0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x \cdot \cos y}\right) \cdot \sqrt[3]{x \cdot \cos y}} - z \cdot \sin y\]
  4. Using strategy rm

  5. Applied cbrt-prod0.9

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

  6. Applied associate-*r*0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2020018 
(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))))