Average Error: 0.1 → 0.6
Time: 5.9s
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 r205327 = x;
        double r205328 = y;
        double r205329 = sin(r205328);
        double r205330 = r205327 * r205329;
        double r205331 = z;
        double r205332 = cos(r205328);
        double r205333 = r205331 * r205332;
        double r205334 = r205330 + r205333;
        return r205334;
}
↓
double f(double x, double y, double z) {
        double r205335 = x;
        double r205336 = cbrt(r205335);
        double r205337 = r205336 * r205336;
        double r205338 = y;
        double r205339 = sin(r205338);
        double r205340 = r205336 * r205339;
        double r205341 = r205337 * r205340;
        double r205342 = z;
        double r205343 = cos(r205338);
        double r205344 = r205342 * r205343;
        double r205345 = r205341 + r205344;
        return r205345;
}

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 2019356 
(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))))