Average Error: 0.1 → 0.5
Time: 5.6s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r213361 = x;
        double r213362 = y;
        double r213363 = cos(r213362);
        double r213364 = r213361 * r213363;
        double r213365 = z;
        double r213366 = sin(r213362);
        double r213367 = r213365 * r213366;
        double r213368 = r213364 - r213367;
        return r213368;
}
↓
double f(double x, double y, double z) {
        double r213369 = x;
        double r213370 = y;
        double r213371 = cos(r213370);
        double r213372 = cbrt(r213371);
        double r213373 = r213372 * r213372;
        double r213374 = cbrt(r213373);
        double r213375 = cbrt(r213372);
        double r213376 = 4.0;
        double r213377 = pow(r213375, r213376);
        double r213378 = r213374 * r213377;
        double r213379 = r213369 * r213378;
        double r213380 = r213379 * r213372;
        double r213381 = z;
        double r213382 = sin(r213370);
        double r213383 = r213381 * r213382;
        double r213384 = r213380 - r213383;
        return r213384;
}

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

    \[x \cdot \cos y - z \cdot \sin y\]
  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 add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Applied associate-*l*0.4

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

  9. Simplified0.5

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \color{blue}{{\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  10. Final simplification0.5

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))