Average Error: 14.7 → 0.4
Time: 1.1m
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\sqrt[3]{\sin b} \cdot \sqrt[3]{\sin b}\right) \cdot \left(\sin a \cdot \sqrt[3]{\sin b}\right)\right)}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\sqrt[3]{\sin b} \cdot \sqrt[3]{\sin b}\right) \cdot \left(\sin a \cdot \sqrt[3]{\sin b}\right)\right)}}
double f(double r, double a, double b) {
        double r2964384 = r;
        double r2964385 = b;
        double r2964386 = sin(r2964385);
        double r2964387 = a;
        double r2964388 = r2964387 + r2964385;
        double r2964389 = cos(r2964388);
        double r2964390 = r2964386 / r2964389;
        double r2964391 = r2964384 * r2964390;
        return r2964391;
}
↓
double f(double r, double a, double b) {
        double r2964392 = r;
        double r2964393 = b;
        double r2964394 = sin(r2964393);
        double r2964395 = a;
        double r2964396 = cos(r2964395);
        double r2964397 = cos(r2964393);
        double r2964398 = r2964396 * r2964397;
        double r2964399 = sin(r2964395);
        double r2964400 = r2964399 * r2964394;
        double r2964401 = r2964400 * r2964400;
        double r2964402 = cbrt(r2964394);
        double r2964403 = r2964402 * r2964402;
        double r2964404 = r2964399 * r2964402;
        double r2964405 = r2964403 * r2964404;
        double r2964406 = r2964401 * r2964405;
        double r2964407 = cbrt(r2964406);
        double r2964408 = r2964398 - r2964407;
        double r2964409 = r2964394 / r2964408;
        double r2964410 = r2964392 * r2964409;
        return r2964410;
}

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 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  6. Applied add-cbrt-cube0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right) \cdot \left(\sin b \cdot \sin a\right)}}}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right) \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sin b} \cdot \sqrt[3]{\sin b}\right) \cdot \sqrt[3]{\sin b}\right)} \cdot \sin a\right)}}\]

  9. Applied associate-*l*0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sin b} \cdot \sqrt[3]{\sin b}\right) \cdot \left(\sqrt[3]{\sin b} \cdot \sin a\right)\right)}}}\]

  10. Final simplification0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\left(\sqrt[3]{\sin b} \cdot \sqrt[3]{\sin b}\right) \cdot \left(\sin a \cdot \sqrt[3]{\sin b}\right)\right)}}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))