Average Error: 0.2 → 0.2
Time: 5.3s
Precision: binary64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\tan B}
(FPCore (B x)
 :precision binary64
 (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))
↓
(FPCore (B x) :precision binary64 (- (/ 1.0 (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 (1.0 / 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. Using strategy rm

  3. Applied pow1_binary640.2

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

  4. Applied pow1_binary640.2

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

  5. Applied pow-prod-down_binary640.2

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

  6. Simplified0.2

    \[\leadsto \left(-{\color{blue}{\left(\frac{x}{\tan B}\right)}}^{1}\right) + \frac{1}{\sin B}\]

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2021176 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))