Details

Time bar (total: 4.1s)

sample44.0ms

Algorithm
intervals
Results
20.0ms739×body80nan
9.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0913
11213
21613
done1613

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
28×add-sqr-sqrt
27×times-frac
22×add-cube-cbrt
20×sqrt-prod
7×associate-/l*
5×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
4×pow1 sqrt-div distribute-lft-out
3×associate-/r* div-inv
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square distribute-rgt-out frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp frac-add clear-num sum-log flip-+
Counts
3 → 78
Calls
3 calls:
3.0ms
(sqrt (- 1.0 (* x x)))
7.0ms
(/ (sqrt (- 1.0 (* x x))) x)
29.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series294.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(sqrt (- 1.0 (* x x)))
133.0ms
(/ (sqrt (- 1.0 (* x x))) x)
104.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify487.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
01751379
13921272
211901200
done50011200

prune213.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x))))
0.0b
(cbrt (- 1.0 (* x x)))
0.0b
(cbrt (- 1.0 (* x x)))
0.0b
(cbrt (- 1.0 (* x x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
30×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-- pow1/3 flip--
7×swap-sqr associate-*r* associate-*l* difference-of-squares
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 93
Calls
4 calls:
15.0ms
(* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x))))
2.0ms
(cbrt (- 1.0 (* x x)))
2.0ms
(cbrt (- 1.0 (* x x)))
2.0ms
(cbrt (- 1.0 (* x x)))

series813.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(* (cbrt (- 1.0 (* x x))) (cbrt (- 1.0 (* x x))))
203.0ms
(cbrt (- 1.0 (* x x)))
195.0ms
(cbrt (- 1.0 (* x x)))
199.0ms
(cbrt (- 1.0 (* x x)))

simplify484.0ms

Counts
105 → 105
Iterations

Useful iterations: done (480.0ms)

IterNodesCost
01521994
13331814
210861706
done50011594

prune368.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01329
11429
done1429

end0.0ms

sample1.3s

Algorithm
intervals
Results
668.0ms24242×body80nan
283.0ms8000×body80valid