Details

Time bar (total: 7.3s)

analyze508.0ms

Algorithm
search

sample145.0ms

Algorithm
intervals
Results
65.0ms45×body2560valid
52.0ms109×body1280valid
13.0ms50×body640valid
6.0ms35×body320valid
1.0ms11×body160valid
0.0ms6×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
6.0ms
(/ (- 1.0 (cos x)) (sin x))
3.0ms
(- 1.0 (cos x))

series11.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

simplify81.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22640373
35002373

prune133.0ms

Filtered
42 candidates to 58 candidates (-38.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New421658
Fresh000
Picked101
Done000
Total431659

Merged error: 0.3b

Counts
59 → 16

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
0.0b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1 sum-log
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult associate-+r+ flip3-+ unpow3 flip-+
Counts
3 → 69
Calls
3 calls:
7.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series14.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* 1/2 x)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify44.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0301375
11301346
25002346

prune146.0ms

Filtered
49 candidates to 78 candidates (-59.2%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New77178
Fresh01515
Picked101
Done000
Total781694

Merged error: 0.3b

Counts
94 → 16

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
0.0b
(* 1/240 (pow x 5))
0.1b
(* 1/24 (pow x 3))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult flip3-+ unpow3 sum-log flip-+
Counts
3 → 67
Calls
3 calls:
4.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
5.0ms
(* 1/240 (pow x 5))
6.0ms
(* 1/24 (pow x 3))

series21.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(+ (* 1/24 (pow x 3)) (* 1/240 (pow x 5)))
4.0ms
(* 1/240 (pow x 5))
4.0ms
(* 1/24 (pow x 3))

simplify41.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0268317
11130291
25001290

prune142.0ms

Filtered
48 candidates to 76 candidates (-58.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh01515
Picked011
Done000
Total761692

Merged error: 0.3b

Counts
92 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b
(log (- 1.0 (cos x)))
0.2b
(exp (log (- 1.0 (cos x))))
1.5b
(- 1.0 (cos x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
30×log-prod
25×exp-sum
24×add-cube-cbrt times-frac
8×associate-/l*
7×distribute-lft-out-- difference-of-squares
6×pow1 add-exp-log log-div add-cbrt-cube add-log-exp
4×exp-prod flip3-- exp-diff flip--
3×associate-/r*
2×log-pow associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num div-inv rem-exp-log
Counts
4 → 98
Calls
4 calls:
7.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms
(log (- 1.0 (cos x)))
4.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

series27.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms
(log (- 1.0 (cos x)))
3.0ms
(exp (log (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))

simplify81.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0289829
1791761
22667734
35001708

prune115.0ms

Filtered
66 candidates to 110 candidates (-66.7%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1028110
Fresh6814
Picked101
Done011
Total10917126

Merged error: 0.2b

Counts
126 → 17

regimes224.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.6b

bsearch58.0ms

Steps
ItersRangePoint
9
0.013014711580346009
3913691.6246505454
0.02116198789995648
10
-0.09261228311282658
-9.714411264296746e-16
-0.020073534703092734

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03621
13621

end0.0ms

analyze507.0ms

Algorithm
search

sample4.8s

Algorithm
intervals
Results
2.3s1630×body2560valid
1.6s2826×body1280valid
480.0ms1831×body640valid
167.0ms924×body320valid
70.0ms465×body160valid
24.0ms322×body80valid
6.0ms2×body5120valid

Profiling

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