Average Error: 0.2 → 0.2
Time: 22.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{\left(-\frac{x \cdot \cos B}{\sin B}\right) \cdot \frac{\sin B}{\sqrt{1}} + \frac{1}{1} \cdot \sqrt{1}}{\frac{\frac{\sin B}{1}}{\sqrt{1}}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{\left(-\frac{x \cdot \cos B}{\sin B}\right) \cdot \frac{\sin B}{\sqrt{1}} + \frac{1}{1} \cdot \sqrt{1}}{\frac{\frac{\sin B}{1}}{\sqrt{1}}}
double code(double B, double x) {
	return ((double) (((double) -(((double) (x * ((double) (1.0 / ((double) tan(B)))))))) + ((double) (1.0 / ((double) sin(B))))));
}
↓
double code(double B, double x) {
	return ((double) (((double) (((double) (((double) -(((double) (((double) (x * ((double) cos(B)))) / ((double) sin(B)))))) * ((double) (((double) sin(B)) / ((double) sqrt(1.0)))))) + ((double) (((double) (1.0 / 1.0)) * ((double) sqrt(1.0)))))) / ((double) (((double) (((double) sin(B)) / 1.0)) / ((double) sqrt(1.0))))));
}

Error

Bits error versus B

Bits error versus x

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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 clear-num0.2

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

  4. Applied un-div-inv0.2

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

  6. Applied add-sqr-sqrt0.2

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

  7. Applied associate-/l*0.2

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

  8. Applied div-inv0.2

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

  9. Applied associate-/r*0.2

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

  10. Applied distribute-neg-frac0.2

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

  11. Applied frac-add0.2

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

  12. Simplified0.2

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

  13. Taylor expanded around inf 0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020114 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))