Average Error: 15.1 → 0.3
Time: 9.9s
Precision: binary64
Cost: 32704
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
\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

Alternatives

Alternative 1
Error0.4
Cost45568
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin b \cdot \sin a\right)}^{3}}}\]
Alternative 2
Error0.5
Cost84672
\[\frac{r \cdot \sin b}{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}} \cdot \left(\cos a \cdot \cos b + \sin b \cdot \sin a\right)\]
Alternative 3
Error0.9
Cost104128
\[\frac{\sin b}{\sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a}} \cdot \frac{r}{\sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a}}\]
Alternative 4
Error0.9
Cost104256
\[r \cdot \left(\frac{\sin b}{\sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a}} \cdot \frac{1}{\sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sqrt[3]{\cos a \cdot \cos b - \sin b \cdot \sin a}}\right)\]

Error

Derivation

  1. Initial program 15.1

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2021043 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))