Average Error: 14.5 → 0.3
Time: 24.1s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r957005 = r;
        double r957006 = b;
        double r957007 = sin(r957006);
        double r957008 = r957005 * r957007;
        double r957009 = a;
        double r957010 = r957009 + r957006;
        double r957011 = cos(r957010);
        double r957012 = r957008 / r957011;
        return r957012;
}
↓
double f(double r, double a, double b) {
        double r957013 = r;
        double r957014 = b;
        double r957015 = sin(r957014);
        double r957016 = a;
        double r957017 = cos(r957016);
        double r957018 = cos(r957014);
        double r957019 = r957017 * r957018;
        double r957020 = sin(r957016);
        double r957021 = r957020 * r957015;
        double r957022 = r957019 - r957021;
        double r957023 = r957015 / r957022;
        double r957024 = r957013 * r957023;
        return r957024;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  7. Applied associate-*l*0.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))