Average Error: 0.1 → 0.5
Time: 14.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r167247 = x;
        double r167248 = y;
        double r167249 = cos(r167248);
        double r167250 = r167247 * r167249;
        double r167251 = z;
        double r167252 = sin(r167248);
        double r167253 = r167251 * r167252;
        double r167254 = r167250 - r167253;
        return r167254;
}
↓
double f(double x, double y, double z) {
        double r167255 = x;
        double r167256 = y;
        double r167257 = cos(r167256);
        double r167258 = r167255 * r167257;
        double r167259 = z;
        double r167260 = cbrt(r167259);
        double r167261 = sin(r167256);
        double r167262 = cbrt(r167261);
        double r167263 = r167259 * r167261;
        double r167264 = cbrt(r167263);
        double r167265 = r167262 * r167264;
        double r167266 = r167260 * r167265;
        double r167267 = r167266 * r167264;
        double r167268 = r167258 - r167267;
        return r167268;
}

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-cbrt0.6

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

  5. Applied cbrt-prod0.5

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 
(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))))