Average Error: 15.5 → 0.4
Time: 19.8s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{r}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{r}}
double f(double r, double a, double b) {
        double r26340 = r;
        double r26341 = b;
        double r26342 = sin(r26341);
        double r26343 = r26340 * r26342;
        double r26344 = a;
        double r26345 = r26344 + r26341;
        double r26346 = cos(r26345);
        double r26347 = r26343 / r26346;
        return r26347;
}
↓
double f(double r, double a, double b) {
        double r26348 = b;
        double r26349 = sin(r26348);
        double r26350 = a;
        double r26351 = cos(r26350);
        double r26352 = cos(r26348);
        double r26353 = r26351 * r26352;
        double r26354 = sin(r26350);
        double r26355 = r26354 * r26349;
        double r26356 = r26353 - r26355;
        double r26357 = r;
        double r26358 = r26356 / r26357;
        double r26359 = r26349 / r26358;
        return r26359;
}

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 15.5

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

  2. Simplified15.5

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

  4. Applied cos-sum0.3

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

  5. Simplified0.3

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

  6. Taylor expanded around inf 0.3

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))