Average Error: 0.1 → 0.6
Time: 11.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r270283 = x;
        double r270284 = y;
        double r270285 = sin(r270284);
        double r270286 = r270283 * r270285;
        double r270287 = z;
        double r270288 = cos(r270284);
        double r270289 = r270287 * r270288;
        double r270290 = r270286 + r270289;
        return r270290;
}
↓
double f(double x, double y, double z) {
        double r270291 = x;
        double r270292 = y;
        double r270293 = sin(r270292);
        double r270294 = r270291 * r270293;
        double r270295 = cbrt(r270294);
        double r270296 = r270295 * r270295;
        double r270297 = r270296 * r270295;
        double r270298 = z;
        double r270299 = cos(r270292);
        double r270300 = r270298 * r270299;
        double r270301 = r270297 + r270300;
        return r270301;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))