Average Error: 0.1 → 0.4
Time: 21.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)
double f(double x, double y, double z) {
        double r9788571 = x;
        double r9788572 = y;
        double r9788573 = cos(r9788572);
        double r9788574 = r9788571 * r9788573;
        double r9788575 = z;
        double r9788576 = sin(r9788572);
        double r9788577 = r9788575 * r9788576;
        double r9788578 = r9788574 - r9788577;
        return r9788578;
}
↓
double f(double x, double y, double z) {
        double r9788579 = z;
        double r9788580 = -r9788579;
        double r9788581 = y;
        double r9788582 = sin(r9788581);
        double r9788583 = r9788580 * r9788582;
        double r9788584 = cos(r9788581);
        double r9788585 = cbrt(r9788584);
        double r9788586 = r9788585 * r9788585;
        double r9788587 = x;
        double r9788588 = r9788586 * r9788587;
        double r9788589 = r9788585 * r9788588;
        double r9788590 = r9788583 + r9788589;
        return r9788590;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 sub-neg0.1

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))