Average Error: 13.6 → 10.8
Time: 1.3m
Precision: 64
Internal Precision: 576
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
↓
\[\left({\left(\left(2 + x \cdot 2\right) + F \cdot F\right)}^{\left(-\frac{1}{2}\right)} \cdot F\right) \cdot \frac{1}{\sin B} - \frac{x}{\tan B}\]

Error

Bits error versus F

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 13.6

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

  2. Applied simplify13.5

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

  4. Applied div-inv13.5

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

  5. Applied associate-*r*10.8

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed 2018195 
(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))))))