Average Error: 0.1 → 0.2
Time: 4.6s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r209309 = x;
        double r209310 = y;
        double r209311 = sin(r209310);
        double r209312 = r209309 * r209311;
        double r209313 = z;
        double r209314 = cos(r209310);
        double r209315 = r209313 * r209314;
        double r209316 = r209312 + r209315;
        return r209316;
}
↓
double f(double x, double y, double z) {
        double r209317 = x;
        double r209318 = y;
        double r209319 = sin(r209318);
        double r209320 = r209317 * r209319;
        double r209321 = z;
        double r209322 = cos(r209318);
        double r209323 = 2.0;
        double r209324 = pow(r209322, r209323);
        double r209325 = 0.3333333333333333;
        double r209326 = pow(r209324, r209325);
        double r209327 = r209321 * r209326;
        double r209328 = cbrt(r209322);
        double r209329 = r209327 * r209328;
        double r209330 = r209320 + r209329;
        return r209330;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  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 pow1/316.1

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

  7. Applied pow1/316.1

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

  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. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))