Average Error: 0.1 → 0.6
Time: 15.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r163977 = x;
        double r163978 = y;
        double r163979 = cos(r163978);
        double r163980 = r163977 * r163979;
        double r163981 = z;
        double r163982 = sin(r163978);
        double r163983 = r163981 * r163982;
        double r163984 = r163980 + r163983;
        return r163984;
}
↓
double f(double x, double y, double z) {
        double r163985 = x;
        double r163986 = y;
        double r163987 = cos(r163986);
        double r163988 = r163985 * r163987;
        double r163989 = z;
        double r163990 = cbrt(r163989);
        double r163991 = r163990 * r163990;
        double r163992 = cbrt(r163991);
        double r163993 = r163990 * r163992;
        double r163994 = cbrt(r163990);
        double r163995 = r163993 * r163994;
        double r163996 = sin(r163986);
        double r163997 = r163990 * r163996;
        double r163998 = r163995 * r163997;
        double r163999 = r163988 + r163998;
        return r163999;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.6

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

  8. Applied associate-*r*0.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))