Average Error: 0.1 → 0.6
Time: 54.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + x \cdot \cos y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + x \cdot \cos y
double f(double x, double y, double z) {
        double r10241974 = x;
        double r10241975 = y;
        double r10241976 = cos(r10241975);
        double r10241977 = r10241974 * r10241976;
        double r10241978 = z;
        double r10241979 = sin(r10241975);
        double r10241980 = r10241978 * r10241979;
        double r10241981 = r10241977 + r10241980;
        return r10241981;
}
↓
double f(double x, double y, double z) {
        double r10241982 = z;
        double r10241983 = cbrt(r10241982);
        double r10241984 = cbrt(r10241983);
        double r10241985 = r10241983 * r10241983;
        double r10241986 = cbrt(r10241985);
        double r10241987 = r10241984 * r10241986;
        double r10241988 = y;
        double r10241989 = sin(r10241988);
        double r10241990 = r10241987 * r10241989;
        double r10241991 = r10241990 * r10241985;
        double r10241992 = x;
        double r10241993 = cos(r10241988);
        double r10241994 = r10241992 * r10241993;
        double r10241995 = r10241991 + r10241994;
        return r10241995;
}

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

    \[x \cdot \cos y + z \cdot \sin y\]
  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

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

  7. Applied cbrt-prod0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))