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

# Try it out

Results

 In Out
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

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