Average Error: 0.1 → 0.6
Time: 21.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r11076376 = x;
        double r11076377 = y;
        double r11076378 = cos(r11076377);
        double r11076379 = r11076376 * r11076378;
        double r11076380 = z;
        double r11076381 = sin(r11076377);
        double r11076382 = r11076380 * r11076381;
        double r11076383 = r11076379 + r11076382;
        return r11076383;
}
↓
double f(double x, double y, double z) {
        double r11076384 = x;
        double r11076385 = y;
        double r11076386 = cos(r11076385);
        double r11076387 = r11076384 * r11076386;
        double r11076388 = z;
        double r11076389 = cbrt(r11076388);
        double r11076390 = r11076389 * r11076389;
        double r11076391 = sin(r11076385);
        double r11076392 = r11076391 * r11076389;
        double r11076393 = r11076390 * r11076392;
        double r11076394 = r11076387 + r11076393;
        return r11076394;
}

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

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))