Average Error: 0.1 → 0.3
Time: 23.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(z \cdot \sqrt[3]{\cos y \cdot \cos y}\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
\sqrt[3]{\cos y} \cdot \left(z \cdot \sqrt[3]{\cos y \cdot \cos y}\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r9104217 = x;
        double r9104218 = y;
        double r9104219 = sin(r9104218);
        double r9104220 = r9104217 * r9104219;
        double r9104221 = z;
        double r9104222 = cos(r9104218);
        double r9104223 = r9104221 * r9104222;
        double r9104224 = r9104220 + r9104223;
        return r9104224;
}
↓
double f(double x, double y, double z) {
        double r9104225 = y;
        double r9104226 = cos(r9104225);
        double r9104227 = cbrt(r9104226);
        double r9104228 = z;
        double r9104229 = r9104226 * r9104226;
        double r9104230 = cbrt(r9104229);
        double r9104231 = r9104228 * r9104230;
        double r9104232 = r9104227 * r9104231;
        double r9104233 = x;
        double r9104234 = sin(r9104225);
        double r9104235 = r9104233 * r9104234;
        double r9104236 = r9104232 + r9104235;
        return r9104236;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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 pow1/316.3

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

  7. Applied pow1/316.3

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

  8. Applied pow-prod-down0.2

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

  10. Applied *-un-lft-identity0.2

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

  11. Applied cbrt-prod0.2

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

  12. Applied associate-*r*0.2

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

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))))