Details

Time bar (total: 58.0s)

sample55.0ms

Algorithm
intervals
Results
20.0ms292×body80valid
9.0ms22×body1280valid
8.0ms29×body640valid
3.0ms16×body320valid
1.0ms7×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0278
1688
22438
312668
450018

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.3b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.3b
(* (* x (pow sin 2.0)) x)
7.2b
(* x (pow sin 2.0))
21.1b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
424×add-sqr-sqrt
243×unswap-sqr
217×associate-*r*
171×times-frac
164×associate-*l*
122×add-exp-log
114×add-cube-cbrt *-un-lft-identity
89×unpow-prod-down
82×prod-exp
65×sqr-pow
57×associate-/r*
34×add-cbrt-cube
20×pow1
18×pow-to-exp pow-exp *-commutative
16×div-exp cbrt-unprod
10×pow-prod-down
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
1×frac-2neg clear-num div-inv
Counts
4 → 417
Calls
4 calls:
39.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
11.0ms
(* (* x (pow sin 2.0)) x)
6.0ms
(* x (pow sin 2.0))
24.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series869.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
150.0ms
(* (* x (pow sin 2.0)) x)
141.0ms
(* x (pow sin 2.0))
272.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify86.0ms

Algorithm
egg-herbie
Counts
429 → 429
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014095107
150014951

prune1.1s

Filtered
429 candidates to 317 candidates (26.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New41217429
Fresh000
Picked101
Done000
Total41317430

Merged error: 6.1b

Counts
430 → 17

localize15.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
8.0b
(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
11.8b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
4860×times-frac
4436×add-sqr-sqrt
1968×associate-*r*
1905×unswap-sqr
1828×add-cube-cbrt *-un-lft-identity
1547×associate-*l*
1406×unpow-prod-down
892×sqr-pow
317×add-exp-log
257×*-commutative
168×prod-exp
136×associate-/l*
121×div-exp
102×associate-/r*
56×pow-to-exp pow-exp
49×add-cbrt-cube
48×associate-/l/
21×div-inv
17×cbrt-undiv
16×cbrt-unprod
8×pow1
3×expm1-log1p-u frac-2neg pow-prod-down clear-num log1p-expm1-u add-log-exp
Counts
3 → 2874
Calls
3 calls:
28.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
118.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
19.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series779.0ms

Counts
3 → 9
Calls
3 calls:
229.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
316.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
233.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify674.0ms

Algorithm
egg-herbie
Counts
2883 → 2883
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0500169776

prune9.1s

Filtered
2883 candidates to 2088 candidates (27.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New2869142883
Fresh13316
Picked101
Done000
Total2883172900

Merged error: 1.7b

Counts
2900 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
1.3b
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
2.6b
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
4.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite553.0ms

Algorithm
rewrite-expression-head
Rules
4845×times-frac
4579×add-sqr-sqrt
2052×add-cube-cbrt *-un-lft-identity
1766×unswap-sqr
1533×associate-*r*
1296×unpow-prod-down
1277×cbrt-prod
732×sqr-pow
608×associate-*l*
335×add-exp-log
312×swap-sqr
184×*-commutative
164×associate-/l*
163×associate-/r*
153×prod-exp
152×div-exp
82×add-cbrt-cube
77×div-inv
62×pow-to-exp pow-exp
61×associate-/l/
35×cbrt-undiv
30×cbrt-unprod
21×rec-exp 1-exp
9×pow1
5×frac-2neg clear-num
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
Counts
4 → 3108
Calls
4 calls:
31.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
72.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
81.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
24.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
364.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
299.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
214.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify647.0ms

Algorithm
egg-herbie
Counts
3120 → 3120
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0500266262

prune11.1s

Filtered
3120 candidates to 2066 candidates (33.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New311643120
Fresh51116
Picked101
Done000
Total3122153137

Merged error: 0.7b

Counts
3137 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
1.3b
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
1.9b
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt (* (cbrt x) (cbrt x))))))
4.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
10343×add-sqr-sqrt
8065×times-frac
5749×cbrt-prod
5302×unswap-sqr
3197×associate-*r*
3136×add-cube-cbrt *-un-lft-identity
2238×unpow-prod-down
1254×sqr-pow
764×associate-*l*
572×swap-sqr
340×*-commutative
335×add-exp-log
233×associate-/r*
164×associate-/l*
153×prod-exp
152×div-exp
147×div-inv
82×add-cbrt-cube
62×pow-to-exp pow-exp
61×associate-/l/
35×cbrt-undiv
30×cbrt-unprod
21×rec-exp 1-exp
9×pow1
5×frac-2neg clear-num
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
Counts
4 → 4928
Calls
4 calls:
31.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
72.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
145.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt (* (cbrt x) (cbrt x))))))
22.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
370.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
406.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt (* (cbrt x) (cbrt x))))))
213.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify1.2s

Algorithm
egg-herbie
Counts
4940 → 4940
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
06151135684

prune25.4s

Filtered
4940 candidates to 3797 candidates (23.1%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New493824940
Fresh01414
Picked011
Done000
Total4938174955

Merged error: 0.5b

Counts
4955 → 17

regimes484.0ms

Accuracy

10.6% (2.3b remaining)

Error of 2.8b against oracle of 0.6b and baseline of 3.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06490
16490

end0.0ms

sample1.7s

Algorithm
intervals
Results
656.0ms9067×body80valid
314.0ms774×body1280valid
283.0ms972×body640valid
119.0ms554×body320valid
49.0ms315×body160valid