Average Error: 0.1 → 0.4
Time: 5.5s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r152930 = x;
        double r152931 = y;
        double r152932 = cos(r152931);
        double r152933 = r152930 * r152932;
        double r152934 = z;
        double r152935 = sin(r152931);
        double r152936 = r152934 * r152935;
        double r152937 = r152933 - r152936;
        return r152937;
}
↓
double f(double x, double y, double z) {
        double r152938 = x;
        double r152939 = y;
        double r152940 = cos(r152939);
        double r152941 = cbrt(r152940);
        double r152942 = r152941 * r152941;
        double r152943 = cbrt(r152942);
        double r152944 = r152941 * r152943;
        double r152945 = cbrt(r152941);
        double r152946 = r152944 * r152945;
        double r152947 = r152938 * r152946;
        double r152948 = r152947 * r152941;
        double r152949 = z;
        double r152950 = sin(r152939);
        double r152951 = r152949 * r152950;
        double r152952 = r152948 - r152951;
        return r152952;
}

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 add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Applied associate-*r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(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))))