Details

Time bar (total: 6.9s)

sample61.0ms

Algorithm
intervals
Results
23.0ms279×body80valid
9.0ms22×body1280valid
9.0ms30×body640valid
3.0ms13×body320valid
2.0ms11×body160valid

simplify42.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.5b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.4b
(* (* x (pow sin 2.0)) x)
7.0b
(* x (pow sin 2.0))
17.3b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 115
Calls
4 calls:
11.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms
(* (* x (pow sin 2.0)) x)
5.0ms
(* x (pow sin 2.0))
14.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series859.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
147.0ms
(* (* x (pow sin 2.0)) x)
162.0ms
(* x (pow sin 2.0))
261.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0435927
12042771
25002771

prune260.0ms

Filtered
127 candidates to 65 candidates (51.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh000
Picked101
Done000
Total1199128

Merged error: 15.7b

Counts
128 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.4b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.3b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 186
Calls
4 calls:
7.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
14.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
9.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
12.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series884.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
294.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
157.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
291.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05862140
127921433
250021421

prune273.0ms

Filtered
198 candidates to 62 candidates (31.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1917198
Fresh448
Picked101
Done000
Total19611207

Merged error: 2.7b

Counts
207 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.7b
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
44×prod-exp
21×add-cbrt-cube
17×associate-*l*
16×add-sqr-sqrt
14×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
11×pow1
8×cbrt-unprod
6×unpow-prod-down
5×associate-*r*
4×add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sqr-pow
1×pow2 frac-2neg pow-plus pow-prod-down clear-num associate-/r* pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 106
Calls
4 calls:
3.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
100.0ms
(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
220.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
206.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03161464
112291191
250021118

prune319.0ms

Filtered
118 candidates to 67 candidates (56.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh6410
Picked101
Done000
Total11514129

Merged error: 0.0b

Counts
129 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.7b
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
42×prod-exp
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac add-cbrt-cube
14×pow-to-exp associate-*l* pow-exp
6×unpow-prod-down associate-/r* cbrt-unprod associate-/l*
5×pow1
4×add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg associate-*r* clear-num *-commutative div-inv sqr-pow
1×rec-exp pow-flip 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
6.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
7.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
13.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
9.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1 (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
69.0ms
(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
209.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
229.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03191407
111421257
250011243

prune293.0ms

Filtered
130 candidates to 72 candidates (55.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1273130
Fresh5813
Picked101
Done000
Total13311144

Merged error: 0.0b

Counts
144 → 11

regimes309.0ms

Accuracy

11.5% (2.3b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.8b

bsearch56.0ms

Steps
ItersRangePoint
7
1.575817464578155e+223
2.8294313938164436e+224
2.5325376410005843e+223

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03830
13830

end0.0ms

sample1.9s

Algorithm
intervals
Results
759.0ms9063×body80valid
364.0ms810×body1280valid
328.0ms1007×body640valid
136.0ms567×body320valid
50.0ms306×body160valid

Profiling

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