Average Error: 0.2 → 0.2
Time: 5.9s
Precision: binary64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \frac{-1}{\frac{\tan B}{1 \cdot x}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} + \frac{-1}{\frac{\tan B}{1 \cdot x}}
(FPCore (B x)
 :precision binary64
 (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))
↓
(FPCore (B x)
 :precision binary64
 (+ (/ 1.0 (sin B)) (/ -1.0 (/ (tan B) (* 1.0 x)))))
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) sin(B))) + (-1.0 / (((double) tan(B)) / ((double) (1.0 * x))))));
}

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 Error: 0.2 bits

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

  2. SimplifiedError: 0.2 bits

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

  4. Applied associate-*r/Error: 0.2 bits

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

  6. Applied clear-numError: 0.2 bits

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

  7. SimplifiedError: 0.2 bits

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

  8. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))