Average Error: 0.0 → 0.0
Time: 14.6s
Precision: 64
Internal Precision: 128
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]

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. Final simplification0.0

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

Runtime

Time bar (total: 14.6s)Debug log

start99.0ms

Algorithm
intervals

setup671.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))
0.0b
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))
0.0b
(+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))
0.0b
(+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Counts
4 → 102
Calls

4 calls. Slowest were:

11.0ms
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))
7.0ms
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))
2.0ms
(+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))

series65.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

21.0ms
(+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))
19.0ms
(+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))
13.0ms
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))

simplify9.1s

Counts
78 → 114
Calls

78 calls. Slowest were:

815.0ms
(* (* (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))) (/ (* 2 t) (+ 1 t))) (* (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))) (/ (* 2 t) (+ 1 t))))
772.0ms
(* (* (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))) (/ (* 2 t) (+ 1 t))) (* (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))) (/ (* 2 t) (+ 1 t))))
531.0ms
(* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))

prune1.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018359 
(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))))))