Average Error: 15.1 → 0.4
Time: 6.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}
double f(double r, double a, double b) {
        double r16930 = r;
        double r16931 = b;
        double r16932 = sin(r16931);
        double r16933 = a;
        double r16934 = r16933 + r16931;
        double r16935 = cos(r16934);
        double r16936 = r16932 / r16935;
        double r16937 = r16930 * r16936;
        return r16937;
}
↓
double f(double r, double a, double b) {
        double r16938 = r;
        double r16939 = b;
        double r16940 = sin(r16939);
        double r16941 = r16938 * r16940;
        double r16942 = a;
        double r16943 = cos(r16942);
        double r16944 = cos(r16939);
        double r16945 = r16943 * r16944;
        double r16946 = sin(r16942);
        double r16947 = r16946 * r16940;
        double r16948 = 3.0;
        double r16949 = pow(r16947, r16948);
        double r16950 = cbrt(r16949);
        double r16951 = r16945 - r16950;
        double r16952 = r16941 / r16951;
        return r16952;
}

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 add-log-exp0.4

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

  7. Applied associate-*r/0.4

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

  9. Applied add-cbrt-cube0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))