Average Error: 15.1 → 0.3
Time: 35.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin a \cdot \sin b + \cos b \cdot \cos a} \cdot \left(\sin a \cdot \sin b + \cos b \cdot \cos a\right)} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin a \cdot \sin b + \cos b \cdot \cos a} \cdot \left(\sin a \cdot \sin b + \cos b \cdot \cos a\right)} \cdot r
double f(double r, double a, double b) {
        double r950723 = r;
        double r950724 = b;
        double r950725 = sin(r950724);
        double r950726 = a;
        double r950727 = r950726 + r950724;
        double r950728 = cos(r950727);
        double r950729 = r950725 / r950728;
        double r950730 = r950723 * r950729;
        return r950730;
}
↓
double f(double r, double a, double b) {
        double r950731 = b;
        double r950732 = sin(r950731);
        double r950733 = cos(r950731);
        double r950734 = a;
        double r950735 = cos(r950734);
        double r950736 = r950733 * r950735;
        double r950737 = sin(r950734);
        double r950738 = r950737 * r950732;
        double r950739 = r950736 - r950738;
        double r950740 = r950738 + r950736;
        double r950741 = r950739 / r950740;
        double r950742 = r950741 * r950740;
        double r950743 = r950732 / r950742;
        double r950744 = r;
        double r950745 = r950743 * r950744;
        return r950745;
}

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 15.1

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 flip--0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied difference-of-squares0.3

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

  9. Applied times-frac0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\frac{\cos a \cdot \cos b + \sin a \cdot \sin b}{1} \cdot \frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\cos a \cdot \cos b + \sin a \cdot \sin b}}}\]

  10. Simplified0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019146 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))