Average Error: 0.1 → 0.4
Time: 21.0s
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 r7031084 = x;
        double r7031085 = y;
        double r7031086 = cos(r7031085);
        double r7031087 = r7031084 * r7031086;
        double r7031088 = z;
        double r7031089 = sin(r7031085);
        double r7031090 = r7031088 * r7031089;
        double r7031091 = r7031087 - r7031090;
        return r7031091;
}
↓
double f(double x, double y, double z) {
        double r7031092 = z;
        double r7031093 = -r7031092;
        double r7031094 = y;
        double r7031095 = sin(r7031094);
        double r7031096 = r7031093 * r7031095;
        double r7031097 = cos(r7031094);
        double r7031098 = cbrt(r7031097);
        double r7031099 = r7031098 * r7031098;
        double r7031100 = x;
        double r7031101 = r7031099 * r7031100;
        double r7031102 = r7031098 * r7031101;
        double r7031103 = r7031096 + r7031102;
        return r7031103;
}

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))))