Details

Time bar (total: 4.5s)

sample49.0ms

Algorithm
intervals
Results
15.0ms277×body160nan
11.0ms520×body80nan
7.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1119
2129
done129

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
32.3b
(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×add-cube-cbrt sqrt-prod add-log-exp
3×pow1 fma-def
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(sqrt (- (* x x) 1.0))

series128.0ms

Counts
2 → 6
Calls
2 calls:
71.0ms
(+ x (sqrt (- (* x x) 1.0)))
56.0ms
(sqrt (- (* x x) 1.0))

simplify1.2s

Counts
41 → 41
Iterations

Useful iterations: 3 (364.0ms)

IterNodesCost
095483
1233428
2586392
31757355
done5001355

prune109.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.125 (pow x 3)) (/ 0.5 x))
0.0b
(+ x (- x (+ (/ 0.125 (pow x 3)) (/ 0.5 x))))
0.4b
(/ 0.125 (pow x 3))

rewrite420.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
80×times-frac
59×add-sqr-sqrt add-cube-cbrt
43×fma-def
21×unpow-prod-down cube-prod
17×associate-+r+
15×prod-diff
14×add-log-exp
12×associate-/r* distribute-lft-out
8×add-exp-log
7×cube-mult unpow3 sqr-pow
5×sum-log add-cbrt-cube
3×pow1 expm1-log1p-u div-exp log1p-expm1-u associate-/l*
2×+-commutative flip3-+ diff-log flip-+ div-inv distribute-lft-out--
1×cbrt-undiv pow-to-exp associate-+r- sub-neg frac-2neg frac-add pow-exp clear-num
Counts
3 → 162
Calls
3 calls:
48.0ms
(+ (/ 0.125 (pow x 3)) (/ 0.5 x))
360.0ms
(+ x (- x (+ (/ 0.125 (pow x 3)) (/ 0.5 x))))
5.0ms
(/ 0.125 (pow x 3))

series169.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(+ (/ 0.125 (pow x 3)) (/ 0.5 x))
49.0ms
(+ x (- x (+ (/ 0.125 (pow x 3)) (/ 0.5 x))))
36.0ms
(/ 0.125 (pow x 3))

simplify765.0ms

Counts
171 → 171
Iterations

Useful iterations: done (761.0ms)

IterNodesCost
01901814
14401472
212121352
done50001351

prune352.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11314
done1314

end0.0ms

sample1.3s

Algorithm
intervals
Results
340.0ms7725×body160nan
322.0ms16077×body80nan
228.0ms8000×body80valid