Average Error: 15.1 → 0.4
Time: 24.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\sin b \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)\right)}}
double f(double r, double a, double b) {
        double r482038 = r;
        double r482039 = b;
        double r482040 = sin(r482039);
        double r482041 = a;
        double r482042 = r482041 + r482039;
        double r482043 = cos(r482042);
        double r482044 = r482040 / r482043;
        double r482045 = r482038 * r482044;
        return r482045;
}
↓
double f(double r, double a, double b) {
        double r482046 = r;
        double r482047 = b;
        double r482048 = sin(r482047);
        double r482049 = r482046 * r482048;
        double r482050 = a;
        double r482051 = cos(r482050);
        double r482052 = cos(r482047);
        double r482053 = r482051 * r482052;
        double r482054 = sin(r482050);
        double r482055 = r482048 * r482054;
        double r482056 = r482055 * r482055;
        double r482057 = r482055 * r482056;
        double r482058 = cbrt(r482057);
        double r482059 = r482053 - r482058;
        double r482060 = r482049 / r482059;
        return r482060;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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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 associate-*r/0.3

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

  7. Applied add-cbrt-cube0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019153 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))