Average Error: 15.5 → 0.3
Time: 18.8s
Precision: binary64
Cost: 1024
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))
↓
(FPCore (r a b)
 :precision binary64
 (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
double code(double r, double a, double b) {
	return (r * sin(b)) / cos(a + b);
}
↓
double code(double r, double a, double b) {
	return (r * sin(b)) / ((cos(a) * cos(b)) - (sin(b) * sin(a)));
}

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
Alternative 1
Accuracy0.5
Cost1216
\[\frac{r \cdot \sin b}{\sqrt[3]{{\left(\cos a \cdot \cos b - \sin b \cdot \sin a\right)}^{3}}}\]
Alternative 2
Accuracy32.6
Cost1344
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt{\sin b} \cdot \left(\sqrt{\sin b} \cdot \sin a\right)}\]
Alternative 3
Accuracy32.7
Cost1344
\[\frac{\sqrt{\sin b} \cdot \left(r \cdot \sqrt{\sin b}\right)}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]

Derivation

  1. Initial program 15.5

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

  3. Applied cos-sum_binary64_5530.3

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

  5. Applied *-commutative_binary64_3500.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020322 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))