Average Error: 14.6 → 0.3
Time: 6.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r15091 = r;
        double r15092 = b;
        double r15093 = sin(r15092);
        double r15094 = a;
        double r15095 = r15094 + r15092;
        double r15096 = cos(r15095);
        double r15097 = r15093 / r15096;
        double r15098 = r15091 * r15097;
        return r15098;
}
↓
double f(double r, double a, double b) {
        double r15099 = r;
        double r15100 = b;
        double r15101 = sin(r15100);
        double r15102 = r15099 * r15101;
        double r15103 = a;
        double r15104 = cos(r15103);
        double r15105 = cos(r15100);
        double r15106 = r15104 * r15105;
        double r15107 = sin(r15103);
        double r15108 = r15107 * r15101;
        double r15109 = r15106 - r15108;
        double r15110 = r15102 / r15109;
        return r15110;
}

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 14.6

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  6. Final simplification0.3

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))