Details

Time bar (total: 13.5s)

sample126.0ms

Algorithm
intervals
Results
45.0ms52×body2560valid
32.0ms37×body640valid
22.0ms46×body1280valid
9.0ms39×body320valid
4.0ms64×body80valid
3.0ms18×body160valid

simplify32.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize15.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
15.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
35.0ms
(- 1.0 (cos x))
44.0ms
(/ (- 1.0 (cos x)) (* x x))

series110.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(- 1.0 (cos x))
90.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify2.4s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0116808
1269678
2747566
32669526
done5001517

prune567.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 1/720 (pow x 4) 1/2)
11.2b
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 1/720 (pow x 4) 1/2)
1.0ms
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

series208.0ms

Counts
2 → 6
Calls
2 calls:
143.0ms
(fma 1/720 (pow x 4) 1/2)
65.0ms
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify2.5s

Counts
26 → 26
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
035298
155292
2140255
3556255
43220255
done5000255

prune85.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
2.0b
(- 1.0 (cos x))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×add-sqr-sqrt *-un-lft-identity
76×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
9×prod-diff
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u fma-neg div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 165
Calls
3 calls:
43.0ms
(/ (/ (- 1.0 (cos x)) x) x)
43.0ms
(/ (- 1.0 (cos x)) x)
16.0ms
(- 1.0 (cos x))

series161.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(/ (/ (- 1.0 (cos x)) x) x)
55.0ms
(/ (- 1.0 (cos x)) x)
31.0ms
(- 1.0 (cos x))

simplify3.1s

Counts
174 → 174
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
02592577
15832358
214622183
347652121
done50002121

prune448.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ x (sqrt (- 1.0 (cos x))))
0.2b
(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
360×add-sqr-sqrt *-un-lft-identity
310×sqrt-prod
232×add-cube-cbrt
64×distribute-lft-out-- difference-of-squares
38×associate-/r*
22×sqrt-div
21×associate-/r/
18×prod-diff
13×flip3-- flip--
11×add-exp-log add-cbrt-cube div-inv associate-/l*
8×add-log-exp
6×fma-neg
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×sub-neg frac-2neg diff-log clear-num associate-/l/
Counts
4 → 404
Calls
4 calls:
14.0ms
(/ x (sqrt (- 1.0 (cos x))))
44.0ms
(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
21.0ms
(- 1.0 (cos x))
15.0ms
(- 1.0 (cos x))

series276.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ x (sqrt (- 1.0 (cos x))))
70.0ms
(/ (sqrt (- 1.0 (cos x))) (/ x (sqrt (- 1.0 (cos x)))))
29.0ms
(- 1.0 (cos x))
26.0ms
(- 1.0 (cos x))

simplify2.0s

Counts
416 → 416
Iterations

Useful iterations: done (2.0s)

IterNodesCost
046210179
19438950
230248128
done50007825

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes47.0ms

bsearch1.0ms