Average Error: 0.2 → 0.2
Time: 5.0s
Precision: binary64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}
(FPCore (B x)
 :precision binary64
 (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))
↓
(FPCore (B x) :precision binary64 (/ (- 1.0 (* 1.0 (* x (cos B)))) (sin B)))
double code(double B, double x) {
	return ((double) (((double) -(((double) (x * (1.0 / ((double) tan(B))))))) + (1.0 / ((double) sin(B)))));
}
↓
double code(double B, double x) {
	return (((double) (1.0 - ((double) (1.0 * ((double) (x * ((double) cos(B)))))))) / ((double) sin(B)));
}

Error

Bits error versus B

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]

  3. Taylor expanded around inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied associate-*r/_binary640.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{1 \cdot \left(x \cdot \cos B\right)}{\sin B}}\]

  6. Applied sub-div_binary640.2

    \[\leadsto \color{blue}{\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}}\]

  7. Simplified0.2

    \[\leadsto \frac{\color{blue}{1 - \left(x \cdot \cos B\right) \cdot 1}}{\sin B}\]

  8. Final simplification0.2

    \[\leadsto \frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}\]

Reproduce

herbie shell --seed 2020210 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))