Average Error: 0.2 → 0.1
Time: 5.1s
Precision: binary64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{1 \cdot x}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{1 \cdot 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)) (/ (* 1.0 x) (tan 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) sin(B))) - (((double) (1.0 * x)) / ((double) 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 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: 0.1 bits

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

  5. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))