Average Error: 0.2 → 0.2
Time: 30.4s
Precision: binary64
Cost: 1024
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{\sqrt[3]{1}}{\sin B} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) - \frac{x}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{\sqrt[3]{1}}{\sin B} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) - \frac{x}{\tan B}
(FPCore (B x)
 :precision binary64
 (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))
↓
(FPCore (B x)
 :precision binary64
 (- (* (/ (cbrt 1.0) (sin B)) (* (cbrt 1.0) (cbrt 1.0))) (/ 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 ((cbrt(1.0) / sin(B)) * (cbrt(1.0) * cbrt(1.0))) - (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. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt_binary640.2

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\sin B} - \frac{x}{\tan B}\]

  5. Applied associate-/l*_binary640.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sin B}{\sqrt[3]{1}}}} - \frac{x}{\tan B}\]
  6. Using strategy rm

  7. Applied sub-neg_binary640.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sin B}{\sqrt[3]{1}}} + \left(-\frac{x}{\tan B}\right)}\]

  8. Simplified0.2

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sin B}{\sqrt[3]{1}}} + \color{blue}{\frac{-x}{\tan B}}\]
  9. Using strategy rm

  10. Applied div-inv_binary640.2

    \[\leadsto \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\color{blue}{\sin B \cdot \frac{1}{\sqrt[3]{1}}}} + \frac{-x}{\tan B}\]

  11. Applied times-frac_binary640.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1}}{\sin B} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\sqrt[3]{1}}}} + \frac{-x}{\tan B}\]

  12. Simplified0.2

    \[\leadsto \frac{\sqrt[3]{1}}{\sin B} \cdot \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right)} + \frac{-x}{\tan B}\]

  13. Final simplification0.2

    \[\leadsto \frac{\sqrt[3]{1}}{\sin B} \cdot \left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) - \frac{x}{\tan B}\]

Reproduce

herbie shell --seed 2020322 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))