Average Error: 0.1 → 0.3
Time: 5.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r238507 = x;
        double r238508 = y;
        double r238509 = cos(r238508);
        double r238510 = r238507 * r238509;
        double r238511 = z;
        double r238512 = sin(r238508);
        double r238513 = r238511 * r238512;
        double r238514 = r238510 + r238513;
        return r238514;
}
↓
double f(double x, double y, double z) {
        double r238515 = x;
        double r238516 = y;
        double r238517 = cos(r238516);
        double r238518 = 2.0;
        double r238519 = pow(r238517, r238518);
        double r238520 = cbrt(r238519);
        double r238521 = r238515 * r238520;
        double r238522 = cbrt(r238517);
        double r238523 = r238521 * r238522;
        double r238524 = z;
        double r238525 = sin(r238516);
        double r238526 = r238524 * r238525;
        double r238527 = r238523 + r238526;
        return r238527;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied cbrt-unprod0.3

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

  7. Simplified0.3

    \[\leadsto \left(x \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  8. Final simplification0.3

    \[\leadsto \left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))