Average Error: 0.2 → 0.2
Time: 4.9s
Precision: binary64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B} \]
↓
\[\frac{\frac{\tan B}{\sin B} - x}{\tan B} \]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{\frac{\tan B}{\sin B} - x}{\tan B}

(FPCore (B x)
 :precision binary64
 (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))
↓
(FPCore (B x) :precision binary64 (/ (- (/ (tan B) (sin B)) x) (tan B)))
double code(double B, double x) {
	return -(x * (1.0 / tan(B))) + (1.0 / sin(B));
}
↓
double code(double B, double x) {
	return ((tan(B) / sin(B)) - x) / tan(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

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

  4. Applied frac-sub_binary6411.5

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

  5. Simplified11.5

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

  7. Applied associate-/r*_binary640.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2021196 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))