Average Error: 0.1 → 0.6
Time: 17.9s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)
double f(double x, double y, double z) {
        double r11488258 = x;
        double r11488259 = y;
        double r11488260 = cos(r11488259);
        double r11488261 = r11488258 * r11488260;
        double r11488262 = z;
        double r11488263 = sin(r11488259);
        double r11488264 = r11488262 * r11488263;
        double r11488265 = r11488261 + r11488264;
        return r11488265;
}
↓
double f(double x, double y, double z) {
        double r11488266 = x;
        double r11488267 = y;
        double r11488268 = cos(r11488267);
        double r11488269 = r11488266 * r11488268;
        double r11488270 = sin(r11488267);
        double r11488271 = cbrt(r11488270);
        double r11488272 = r11488271 * r11488271;
        double r11488273 = z;
        double r11488274 = r11488272 * r11488273;
        double r11488275 = r11488271 * r11488274;
        double r11488276 = r11488269 + r11488275;
        return r11488276;
}

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

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

  4. Applied associate-*r*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))