Average Error: 14.8 → 0.3
Time: 17.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r25342 = r;
        double r25343 = b;
        double r25344 = sin(r25343);
        double r25345 = a;
        double r25346 = r25345 + r25343;
        double r25347 = cos(r25346);
        double r25348 = r25344 / r25347;
        double r25349 = r25342 * r25348;
        return r25349;
}
↓
double f(double r, double a, double b) {
        double r25350 = r;
        double r25351 = b;
        double r25352 = sin(r25351);
        double r25353 = cos(r25351);
        double r25354 = a;
        double r25355 = cos(r25354);
        double r25356 = r25353 * r25355;
        double r25357 = sin(r25354);
        double r25358 = r25357 * r25352;
        double r25359 = r25356 - r25358;
        double r25360 = r25352 / r25359;
        double r25361 = r25350 * r25360;
        return r25361;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 add-cbrt-cube0.4

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

  6. Applied add-cbrt-cube0.4

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

  7. Applied cbrt-unprod0.4

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

  8. Simplified0.4

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

  9. Taylor expanded around inf 0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019298 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))