Average Error: 0.1 → 0.9
Time: 5.4s
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 r194578 = x;
        double r194579 = y;
        double r194580 = cos(r194579);
        double r194581 = r194578 * r194580;
        double r194582 = z;
        double r194583 = sin(r194579);
        double r194584 = r194582 * r194583;
        double r194585 = r194581 - r194584;
        return r194585;
}
↓
double f(double x, double y, double z) {
        double r194586 = x;
        double r194587 = y;
        double r194588 = cos(r194587);
        double r194589 = r194586 * r194588;
        double r194590 = cbrt(r194589);
        double r194591 = cbrt(r194586);
        double r194592 = r194590 * r194591;
        double r194593 = cbrt(r194588);
        double r194594 = r194592 * r194593;
        double r194595 = r194594 * r194590;
        double r194596 = z;
        double r194597 = sin(r194587);
        double r194598 = r194596 * r194597;
        double r194599 = r194595 - r194598;
        return r194599;
}

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 +o rules:numerics
(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))))