Details

Time bar (total: 47.4s)

sample61.0ms

Algorithm
intervals
Results
21.0ms292×body80valid
12.0ms29×body640valid
9.0ms22×body1280valid
3.0ms16×body320valid
1.0ms7×body160valid

simplify43.0ms

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

localize14.0ms

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))

rewrite106.0ms

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 add-log-exp
3×associate-/l*
1×frac-2neg clear-num div-inv
Counts
4 → 409
Calls
4 calls:
40.0ms
(/ (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))

series903.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
159.0ms
(* (* x (pow sin 2.0)) x)
140.0ms
(* x (pow sin 2.0))
285.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify80.0ms

Algorithm
egg-herbie
Counts
421 → 421
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013965063
150014907

prune1.0s

Filtered
421 candidates to 309 candidates (26.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New40417421
Fresh000
Picked101
Done000
Total40517422

Merged error: 6.1b

Counts
422 → 17

localize21.0ms

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))))

rewrite483.0ms

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×frac-2neg pow-prod-down clear-num add-log-exp
Counts
3 → 2868
Calls
3 calls:
30.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
122.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
20.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series806.0ms

Counts
3 → 9
Calls
3 calls:
243.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
324.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
239.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify919.0ms

Algorithm
egg-herbie
Counts
2877 → 2877
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0500169780

prune8.7s

Filtered
2877 candidates to 2082 candidates (27.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New2864132877
Fresh13316
Picked101
Done000
Total2878162894

Merged error: 1.7b

Counts
2894 → 16

localize22.0ms

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))))

rewrite542.0ms

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×add-log-exp
3×pow-prod-down
Counts
4 → 3100
Calls
4 calls:
32.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
76.0ms
(/ (/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (cbrt x))
86.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
22.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
262.0ms
(/ (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))
295.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
216.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify669.0ms

Algorithm
egg-herbie
Counts
3112 → 3112
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0500166194

prune11.3s

Filtered
3112 candidates to 2058 candidates (33.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New310843112
Fresh51015
Picked101
Done000
Total3114143128

Merged error: 0.7b

Counts
3128 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))))
1.3b
(/ (* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x)) (cbrt x))
2.6b
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
4.1b
(* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x))

rewrite785.0ms

Algorithm
rewrite-expression-head
Rules
5655×add-sqr-sqrt
5283×times-frac
2467×*-un-lft-identity
2293×add-cube-cbrt
2174×unswap-sqr
1686×unpow-prod-down
1378×associate-*l*
1331×cbrt-prod
1298×associate-*r*
1038×sqr-pow
877×associate-/r*
713×add-exp-log
612×frac-times
451×associate-/l*
364×associate-/l/
349×prod-exp
337×div-exp
312×swap-sqr
186×*-commutative
131×pow-to-exp pow-exp
121×add-cbrt-cube
96×clear-num
94×frac-2neg
88×div-inv
71×rec-exp 1-exp
68×associate-*l/
55×cbrt-undiv
43×cbrt-unprod
34×pow-unpow
23×pow-flip pow-prod-down
18×associate-*r/
11×pow1
4×un-div-inv add-log-exp
2×pow-pow
1×inv-pow
Counts
4 → 4078
Calls
4 calls:
34.0ms
(/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))))
150.0ms
(/ (* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x)) (cbrt x))
84.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
81.0ms
(* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x))

series1.4s

Counts
4 → 12
Calls
4 calls:
354.0ms
(/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2))))
350.0ms
(/ (* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x)) (cbrt x))
300.0ms
(/ (/ 1 (pow cos (/ 2.0 2))) (* (pow sin (/ 2.0 2)) (* (cbrt x) (cbrt x))))
362.0ms
(* (/ 1 (* (pow cos (/ 2.0 2)) (pow sin (/ 2.0 2)))) (/ (cos (* 2.0 x)) x))

simplify855.0ms

Algorithm
egg-herbie
Counts
4090 → 4090
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0500181915

prune15.4s

Filtered
4090 candidates to 2906 candidates (28.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New408554090
Fresh31013
Picked101
Done000
Total4089154104

Merged error: 0.0b

Counts
4104 → 15

regimes400.0ms

Accuracy

7.2% (2.6b remaining)

Error of 2.9b against oracle of 0.2b and baseline of 3.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05348
15348

end0.0ms

sample1.7s

Algorithm
intervals
Results
642.0ms9067×body80valid
318.0ms774×body1280valid
277.0ms972×body640valid
114.0ms554×body320valid
49.0ms315×body160valid