Average Error: 0.1 → 0.3
Time: 46.6s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\sqrt[3]{\cos y \cdot \cos y} \cdot z\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left(\sqrt[3]{\cos y \cdot \cos y} \cdot z\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r7664418 = x;
        double r7664419 = y;
        double r7664420 = sin(r7664419);
        double r7664421 = r7664418 * r7664420;
        double r7664422 = z;
        double r7664423 = cos(r7664419);
        double r7664424 = r7664422 * r7664423;
        double r7664425 = r7664421 + r7664424;
        return r7664425;
}
↓
double f(double x, double y, double z) {
        double r7664426 = y;
        double r7664427 = cos(r7664426);
        double r7664428 = cbrt(r7664427);
        double r7664429 = r7664427 * r7664427;
        double r7664430 = cbrt(r7664429);
        double r7664431 = z;
        double r7664432 = r7664430 * r7664431;
        double r7664433 = r7664428 * r7664432;
        double r7664434 = x;
        double r7664435 = sin(r7664426);
        double r7664436 = r7664434 * r7664435;
        double r7664437 = r7664433 + r7664436;
        return r7664437;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied cbrt-unprod0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))