Average Error: 0.2 → 0.2
Time: 7.0s
Precision: binary64
Cost: 19776
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin 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 (cos B)) (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 / sin(B)) - ((x * cos(B)) / 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

Alternatives

Alternative 1
Error0.2
Cost19776
\[\frac{1}{\sin B} - \cos B \cdot \frac{x}{\sin B}\]
Alternative 2
Error0.2
Cost13248
\[\frac{1}{\sin B} - \frac{x}{\tan B}\]
Alternative 3
Error0.9
Cost7176
\[\begin{array}{l} \mathbf{if}\;x \leq -1.1034874914804986 \lor \neg \left(x \leq 1.3878256789184826\right):\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array}\]
Alternative 4
Error1.6
Cost7176
\[\begin{array}{l} \mathbf{if}\;x \leq -1.802072515051807 \cdot 10^{-10} \lor \neg \left(x \leq 1.0781172739611247 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B}\\ \end{array}\]
Alternative 5
Error17.8
Cost6920
\[\begin{array}{l} \mathbf{if}\;B \leq -0.0003805296447401917 \lor \neg \left(B \leq 1.5765190973992149 \cdot 10^{-09}\right):\\ \;\;\;\;\frac{1}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array}\]
Alternative 6
Error35.2
Cost320
\[\frac{1 - x}{B}\]
Alternative 7
Error60.4
Cost64
\[1\]

Error

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 tan-quot_binary640.2

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

  5. Applied associate-/r/_binary640.2

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

  7. Applied associate-*l/_binary640.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2021044 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))