Average Error: 15.1 → 0.4
Time: 17.4s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sqrt[3]{{\left(\sin a\right)}^{3} \cdot {\left(\sin b\right)}^{3}}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sqrt[3]{{\left(\sin a\right)}^{3} \cdot {\left(\sin b\right)}^{3}}}
double f(double r, double a, double b) {
        double r25289 = r;
        double r25290 = b;
        double r25291 = sin(r25290);
        double r25292 = r25289 * r25291;
        double r25293 = a;
        double r25294 = r25293 + r25290;
        double r25295 = cos(r25294);
        double r25296 = r25292 / r25295;
        return r25296;
}
↓
double f(double r, double a, double b) {
        double r25297 = r;
        double r25298 = b;
        double r25299 = sin(r25298);
        double r25300 = cos(r25298);
        double r25301 = a;
        double r25302 = cos(r25301);
        double r25303 = r25300 * r25302;
        double r25304 = sin(r25301);
        double r25305 = 3.0;
        double r25306 = pow(r25304, r25305);
        double r25307 = pow(r25299, r25305);
        double r25308 = r25306 * r25307;
        double r25309 = cbrt(r25308);
        double r25310 = r25303 - r25309;
        double r25311 = r25299 / r25310;
        double r25312 = r25297 * r25311;
        return r25312;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied add-log-exp0.4

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

  12. Applied add-cbrt-cube0.4

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

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019294 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))