Average Error: 15.1 → 0.4
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]
\frac{r \cdot \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 r15960 = r;
        double r15961 = b;
        double r15962 = sin(r15961);
        double r15963 = r15960 * r15962;
        double r15964 = a;
        double r15965 = r15964 + r15961;
        double r15966 = cos(r15965);
        double r15967 = r15963 / r15966;
        return r15967;
}
↓
double f(double r, double a, double b) {
        double r15968 = r;
        double r15969 = b;
        double r15970 = sin(r15969);
        double r15971 = r15968 * r15970;
        double r15972 = a;
        double r15973 = cos(r15972);
        double r15974 = cos(r15969);
        double r15975 = r15973 * r15974;
        double r15976 = sin(r15972);
        double r15977 = r15976 * r15970;
        double r15978 = 3.0;
        double r15979 = pow(r15977, r15978);
        double r15980 = cbrt(r15979);
        double r15981 = r15975 - r15980;
        double r15982 = r15971 / r15981;
        return r15982;
}

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 add-cbrt-cube0.4

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

  6. Applied add-cbrt-cube0.4

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

  7. Applied cbrt-unprod0.4

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

  8. Simplified0.4

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

  9. 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 2020036 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))