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 r16371 = r;
        double r16372 = b;
        double r16373 = sin(r16372);
        double r16374 = a;
        double r16375 = r16374 + r16372;
        double r16376 = cos(r16375);
        double r16377 = r16373 / r16376;
        double r16378 = r16371 * r16377;
        return r16378;
}
↓
double f(double r, double a, double b) {
        double r16379 = r;
        double r16380 = b;
        double r16381 = sin(r16380);
        double r16382 = r16379 * r16381;
        double r16383 = 1.0;
        double r16384 = a;
        double r16385 = cos(r16384);
        double r16386 = cos(r16380);
        double r16387 = r16385 * r16386;
        double r16388 = sin(r16384);
        double r16389 = r16388 * r16381;
        double r16390 = r16387 - r16389;
        double r16391 = r16383 / r16390;
        double r16392 = r16382 * r16391;
        return r16392;
}

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 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))