Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - z \cdot \sin y
double f(double x, double y, double z) {
        double r161944 = x;
        double r161945 = y;
        double r161946 = cos(r161945);
        double r161947 = r161944 * r161946;
        double r161948 = z;
        double r161949 = sin(r161945);
        double r161950 = r161948 * r161949;
        double r161951 = r161947 - r161950;
        return r161951;
}
↓
double f(double x, double y, double z) {
        double r161952 = x;
        double r161953 = y;
        double r161954 = cos(r161953);
        double r161955 = r161952 * r161954;
        double r161956 = z;
        double r161957 = sin(r161953);
        double r161958 = r161956 * r161957;
        double r161959 = r161955 - r161958;
        return r161959;
}

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. Final simplification0.1

    \[\leadsto x \cdot \cos y - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020034 +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))))