Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
Internal Precision: 128
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}}{2 + \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}}\]

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  2. Initial simplification0.0

    \[\leadsto \frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]

  3. Final simplification0.0

    \[\leadsto \frac{1 + \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}}{2 + \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}}\]

Runtime

Time bar (total: 16.1s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.0100%
herbie shell --seed 2018353 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))