Average Error: 13.0 → 10.0
Time: 58.2s
Precision: 64
Internal Precision: 384
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
↓
\[\frac{{\left(\left(x \cdot 2 + 2\right) + F \cdot F\right)}^{\left(-\frac{1}{2}\right)} \cdot F}{\sin B} - \frac{x}{\tan B}\]

Error

Bits error versus F

Bits error versus B

Bits error versus x

Derivation

  1. Initial program 13.0

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

  2. Applied simplify12.9

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

  4. Applied associate-*r/10.0

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

Runtime

Time bar (total: 58.2s)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2))))))