Average Error: 0.2 → 0.2
Time: 6.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x}{\frac{\sin B}{\cos B}}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x}{\frac{\sin B}{\cos B}}\right) + \frac{1}{\sin 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 * (x / (sin(B) / cos(B)))) + (1.0 / 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. Taylor expanded around inf 0.2

    \[\leadsto \left(-\color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\right) + \frac{1}{\sin B}\]
  3. Using strategy rm

  4. Applied associate-/l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))