Average Error: 0.1 → 0.3
Time: 17.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r201285 = x;
        double r201286 = y;
        double r201287 = cos(r201286);
        double r201288 = r201285 * r201287;
        double r201289 = z;
        double r201290 = sin(r201286);
        double r201291 = r201289 * r201290;
        double r201292 = r201288 + r201291;
        return r201292;
}
↓
double f(double x, double y, double z) {
        double r201293 = x;
        double r201294 = y;
        double r201295 = cos(r201294);
        double r201296 = 4.0;
        double r201297 = pow(r201295, r201296);
        double r201298 = 0.1111111111111111;
        double r201299 = pow(r201297, r201298);
        double r201300 = 2.0;
        double r201301 = pow(r201295, r201300);
        double r201302 = cbrt(r201301);
        double r201303 = cbrt(r201302);
        double r201304 = r201299 * r201303;
        double r201305 = r201293 * r201304;
        double r201306 = cbrt(r201295);
        double r201307 = r201305 * r201306;
        double r201308 = z;
        double r201309 = sin(r201294);
        double r201310 = r201308 * r201309;
        double r201311 = r201307 + r201310;
        return r201311;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Using strategy rm

  9. Applied add-cube-cbrt0.3

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

  10. Applied cbrt-prod0.4

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

  11. Simplified0.3

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

  12. Taylor expanded around inf 0.3

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  13. Final simplification0.3

    \[\leadsto \left(x \cdot \left({\left({\left(\cos y\right)}^{4}\right)}^{\frac{1}{9}} \cdot \sqrt[3]{\sqrt[3]{{\left(\cos y\right)}^{2}}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))