Details

Time bar (total: 5.0s)

sample79.0ms

Algorithm
intervals
Results
45.0ms61×body2560valid
9.0ms46×body640valid
8.0ms30×body1280valid
4.0ms79×body80valid
4.0ms27×body320valid
1.0ms13×body160valid

simplify4.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
17.0b
(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
7.0ms
(- 1.0 (cos x))
21.0ms
(/ (- 1.0 (cos x)) (* x x))

series77.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(- 1.0 (cos x))
56.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify57.0ms

Counts
48 → 48

prune124.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(/ (sqrt (- 1.0 (cos x))) x)
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
20.0ms
(/ (sqrt (- 1.0 (cos x))) x)
17.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))

series242.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (sqrt (- 1.0 (cos x))) x)
103.0ms
(/ (sqrt (- 1.0 (cos x))) x)
22.0ms
(- 1.0 (cos x))
22.0ms
(- 1.0 (cos x))

simplify95.0ms

Counts
138 → 138

prune342.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 (cos x)))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
5×cbrt-prod add-cube-cbrt
4×pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
3×sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 57
Calls
4 calls:
4.0ms
(cbrt (- 1.0 (cos x)))
6.0ms
(- 1.0 (cos x))
6.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))

series206.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (- 1.0 (cos x)))
21.0ms
(- 1.0 (cos x))
27.0ms
(- 1.0 (cos x))
22.0ms
(- 1.0 (cos x))

simplify48.0ms

Counts
69 → 69

prune265.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))
1.9b
(log (exp (- 1.0 (cos x))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
6×add-cube-cbrt log-pow
5×pow1 log-prod exp-prod
4×add-exp-log sub-neg add-cbrt-cube distribute-lft-out-- difference-of-squares
3×flip3-- diff-log flip--
2×exp-sum
1×log-div exp-diff rem-log-exp
Counts
4 → 62
Calls
4 calls:
7.0ms
(- 1.0 (cos x))
6.0ms
(- 1.0 (cos x))
7.0ms
(- 1.0 (cos x))
21.0ms
(log (exp (- 1.0 (cos x))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(- 1.0 (cos x))
27.0ms
(- 1.0 (cos x))
23.0ms
(- 1.0 (cos x))
22.0ms
(log (exp (- 1.0 (cos x))))

simplify124.0ms

Counts
74 → 74

prune259.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes68.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.9b

bsearch63.0ms

Steps
ItersRangePoint
8
0.00035048323440066366
1.494961173861339
0.028415194585869028
3
-0.031006959526126927
-0.023229637516429813
-0.030520876900520858

simplify1.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.2s1607×body2560valid
640.0ms1461×body640valid
353.0ms1254×body1280valid
122.0ms904×body320valid
100.0ms2256×body80valid
87.0ms518×body160valid