Average Error: 24.9 → 18.0
Time: 1.3m
Precision: 64
Internal Precision: 576
\[\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]
\[\frac{t}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}} \cdot \frac{\sqrt{x - 1}}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}\]

Error

Bits error versus t

Bits error versus x

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 24.9

    \[\frac{t \cdot \sqrt{x - 1}}{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt25.0

    \[\leadsto \frac{t \cdot \sqrt{x - 1}}{\color{blue}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t} \cdot \sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}}\]
  4. Applied times-frac18.0

    \[\leadsto \color{blue}{\frac{t}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}} \cdot \frac{\sqrt{x - 1}}{\sqrt{\ell \cdot \ell + \left(\left(x + 1\right) \cdot t\right) \cdot t}}}\]

Runtime

Time bar (total: 1.3m)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (t x l)
  :name "t*sqrt(x-1)/(l*l+(x+1)*t*t)"
  (/ (* t (sqrt (- x 1))) (+ (* l l) (* (* (+ x 1) t) t))))