Average Error: 13.5 → 10.5
Time: 51.9s
Precision: 64
Ground Truth: 128
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left({F}^2 + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
⬇
\[\frac{-x}{\tan B} + F \cdot \frac{{\left({F}^2 + \left(x + \left(2 + x\right)\right)\right)}^{\left(-\frac{1}{2}\right)}}{\sin B}\]

Error

Bits error versus F

Bits error versus B

Bits error versus x

Derivation

  1. Initial program 13.5

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left({F}^2 + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]

  2. Applied simplify 13.4

    \[\leadsto \color{blue}{\frac{-x}{\tan B} + \frac{F}{\sin B} \cdot {\left(\left(x + x\right) + \left({F}^2 + 2\right)\right)}^{\left(-\frac{1}{2}\right)}}\]
  3. Using strategy rm

  4. Applied div-inv 13.4

    \[\leadsto \frac{-x}{\tan B} + \color{blue}{\left(F \cdot \frac{1}{\sin B}\right)} \cdot {\left(\left(x + x\right) + \left({F}^2 + 2\right)\right)}^{\left(-\frac{1}{2}\right)}\]

  5. Applied associate-*l* 10.5

    \[\leadsto \frac{-x}{\tan B} + \color{blue}{F \cdot \left(\frac{1}{\sin B} \cdot {\left(\left(x + x\right) + \left({F}^2 + 2\right)\right)}^{\left(-\frac{1}{2}\right)}\right)}\]

  6. Applied simplify 10.5

    \[\leadsto \frac{-x}{\tan B} + F \cdot \color{blue}{\frac{{\left({F}^2 + \left(x + \left(2 + x\right)\right)\right)}^{\left(-\frac{1}{2}\right)}}{\sin B}}\]
  7. Removed slow pow expressions

Runtime

Total time: 51.9s Debug log

Please include this information when filing a bug report:

herbie --seed '#(1970926902 2838004698 1520827932 3596742335 1902902264 903431426)'
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (sqr F) 2) (* 2 x)) (- (/ 1 2))))))