Average Error: 15.1 → 0.3
Time: 7.6s
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 r16594 = r;
        double r16595 = b;
        double r16596 = sin(r16595);
        double r16597 = r16594 * r16596;
        double r16598 = a;
        double r16599 = r16598 + r16595;
        double r16600 = cos(r16599);
        double r16601 = r16597 / r16600;
        return r16601;
}
↓
double f(double r, double a, double b) {
        double r16602 = r;
        double r16603 = b;
        double r16604 = sin(r16603);
        double r16605 = a;
        double r16606 = cos(r16605);
        double r16607 = cos(r16603);
        double r16608 = r16606 * r16607;
        double r16609 = sin(r16605);
        double r16610 = r16609 * r16604;
        double r16611 = r16608 - r16610;
        double r16612 = r16604 / r16611;
        double r16613 = r16602 * r16612;
        return r16613;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))