Average Error: 15.0 → 0.4
Time: 6.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r15938 = r;
        double r15939 = b;
        double r15940 = sin(r15939);
        double r15941 = a;
        double r15942 = r15941 + r15939;
        double r15943 = cos(r15942);
        double r15944 = r15940 / r15943;
        double r15945 = r15938 * r15944;
        return r15945;
}
↓
double f(double r, double a, double b) {
        double r15946 = r;
        double r15947 = b;
        double r15948 = sin(r15947);
        double r15949 = r15946 * r15948;
        double r15950 = 1.0;
        double r15951 = a;
        double r15952 = cos(r15951);
        double r15953 = cos(r15947);
        double r15954 = r15952 * r15953;
        double r15955 = sin(r15951);
        double r15956 = r15955 * r15948;
        double r15957 = r15954 - r15956;
        double r15958 = r15950 / r15957;
        double r15959 = r15949 * r15958;
        return r15959;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]

  6. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Final simplification0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))