Details

Time bar (total: 11.8s)

sample111.0ms

Algorithm
intervals
Results
66.0ms821×body80nan
15.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
done1613

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
27×times-frac
24×add-sqr-sqrt
20×add-cube-cbrt
16×sqrt-prod
7×associate-/l*
4×add-exp-log add-cbrt-cube distribute-lft-out add-log-exp difference-of-squares
3×associate-/r* div-inv
2×pow1 sqrt-div associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-out flip3-- frac-2neg flip3-+ div-exp frac-add clear-num sum-log flip-- flip-+
Counts
2 → 62
Calls
2 calls:
75.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
15.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series335.0ms

Counts
2 → 6
Calls
2 calls:
143.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
192.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify2.1s

Counts
68 → 68
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01521133
13271052
2820994
32399983
done5001975

prune273.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (- 1.0 (* x x)))
0.3b
(/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x))
0.3b
(/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x))
0.5b
(* (/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
203×add-sqr-sqrt sqrt-prod
188×times-frac
115×add-cube-cbrt *-un-lft-identity
64×associate-*r*
62×cbrt-prod
22×associate-*l*
21×unswap-sqr
20×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
12×associate-/r*
6×pow1 cbrt-undiv div-exp
4×cbrt-div prod-exp cbrt-unprod div-inv add-log-exp
2×flip3-- frac-2neg sqrt-div clear-num flip-- associate-/l/
1×frac-times sqrt-undiv pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 271
Calls
4 calls:
6.0ms
(cbrt (- 1.0 (* x x)))
16.0ms
(/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x))
36.0ms
(/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x))
153.0ms
(* (/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x)))

series815.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(cbrt (- 1.0 (* x x)))
52.0ms
(/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x))
177.0ms
(/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x))
271.0ms
(* (/ (fabs (cbrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (cbrt (- 1.0 (* x x)))) (sqrt x)))

simplify2.6s

Counts
283 → 283
Iterations

Useful iterations: done (2.6s)

IterNodesCost
04437069
111336575
235346165
done50006147

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
11626
done1626

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.2s23838×body80nan
808.0ms8000×body80valid