Average Error: 0.1 → 0.3
Time: 5.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r245929 = x;
        double r245930 = y;
        double r245931 = cos(r245930);
        double r245932 = r245929 * r245931;
        double r245933 = z;
        double r245934 = sin(r245930);
        double r245935 = r245933 * r245934;
        double r245936 = r245932 - r245935;
        return r245936;
}
↓
double f(double x, double y, double z) {
        double r245937 = x;
        double r245938 = y;
        double r245939 = cos(r245938);
        double r245940 = 2.0;
        double r245941 = pow(r245939, r245940);
        double r245942 = cbrt(r245941);
        double r245943 = r245937 * r245942;
        double r245944 = cbrt(r245939);
        double r245945 = r245943 * r245944;
        double r245946 = z;
        double r245947 = sin(r245938);
        double r245948 = r245946 * r245947;
        double r245949 = r245945 - r245948;
        return r245949;
}

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-cbrt0.4

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

  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))