Details

Time bar (total: 3.4s)

sample12.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05122
16122
done6122

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize7.0ms

Local error

Found 1 expressions with local error:

16.8b
(/ x (+ (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
10.0ms
(/ x (+ (* x x) 1.0))

series61.0ms

Counts
1 → 3
Calls
1 calls:
61.0ms
(/ x (+ (* x x) 1.0))

simplify2.9s

Counts
32 → 32
Iterations

Useful iterations: 2 (231.0ms)

IterNodesCost
0749614
11838647
26978407
334198407
done51038407

prune142.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (+ (* x x) 1.0))
16.5b
(* x (/ 1 (+ (* x x) 1.0)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×associate-*r* add-exp-log
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp associate-/r/
3×associate-/r* associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
2 → 71
Calls
2 calls:
12.0ms
(/ 1 (+ (* x x) 1.0))
41.0ms
(* x (/ 1 (+ (* x x) 1.0)))

series135.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(/ 1 (+ (* x x) 1.0))
77.0ms
(* x (/ 1 (+ (* x x) 1.0)))

simplify149.0ms

Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
012822024