Average Error: 0.1 → 0.6
Time: 18.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y
double f(double x, double y, double z) {
        double r133322 = x;
        double r133323 = y;
        double r133324 = sin(r133323);
        double r133325 = r133322 * r133324;
        double r133326 = z;
        double r133327 = cos(r133323);
        double r133328 = r133326 * r133327;
        double r133329 = r133325 + r133328;
        return r133329;
}
↓
double f(double x, double y, double z) {
        double r133330 = x;
        double r133331 = cbrt(r133330);
        double r133332 = r133331 * r133331;
        double r133333 = y;
        double r133334 = sin(r133333);
        double r133335 = r133331 * r133334;
        double r133336 = r133332 * r133335;
        double r133337 = z;
        double r133338 = cos(r133333);
        double r133339 = r133337 * r133338;
        double r133340 = r133336 + r133339;
        return r133340;
}

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

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019305 
(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))))