Average Error: 0.1 → 1.4
Time: 6.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}
double f(double x, double y, double z) {
        double r230088 = x;
        double r230089 = y;
        double r230090 = cos(r230089);
        double r230091 = r230088 * r230090;
        double r230092 = z;
        double r230093 = sin(r230089);
        double r230094 = r230092 * r230093;
        double r230095 = r230091 - r230094;
        return r230095;
}
↓
double f(double x, double y, double z) {
        double r230096 = x;
        double r230097 = y;
        double r230098 = cos(r230097);
        double r230099 = r230096 * r230098;
        double r230100 = z;
        double r230101 = sin(r230097);
        double r230102 = r230100 * r230101;
        double r230103 = r230099 - r230102;
        double r230104 = cbrt(r230103);
        double r230105 = r230104 * r230104;
        double r230106 = r230105 * r230104;
        return r230106;
}

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-cbrt1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019362 +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))))