Details

Time bar (total: 5.9s)

sample76.0ms

Algorithm
intervals
Results
30.0ms299×body80valid
11.0ms33×body640valid
11.0ms22×body1280valid
3.0ms11×body320valid
3.0ms15×body160valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0484516
1484516

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.4b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
4.7b
(* (* x (pow s 2.0)) x)
8.1b
(* x (pow s 2.0))
17.1b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite37.0ms

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:
10.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
9.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series219.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms
(* (* x (pow s 2.0)) x)
32.0ms
(* x (pow s 2.0))
80.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify69.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049651594
149651594

prune370.0ms

Filtered
72 candidates to 127 candidates (-76.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1189127
Fresh011
Picked101
Done000
Total11910129

Merged error: 10.4b

Counts
129 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

3.6b
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
4.9b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
8.1b
(* x (pow s 2.0))
8.1b
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
17×add-sqr-sqrt
16×associate-*r*
14×associate-*l*
12×add-cube-cbrt *-un-lft-identity
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
11.0ms
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
12.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
5.0ms
(* x (pow s 2.0))
7.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
78.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
29.0ms
(* x (pow s 2.0))
51.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

simplify60.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049921911
149921911

prune263.0ms

Filtered
71 candidates to 158 candidates (-122.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1517158
Fresh459
Picked101
Done000
Total15612168

Merged error: 9.6b

Counts
168 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
3.6b
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
4.9b
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
8.1b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
1442×add-exp-log
1342×prod-exp
354×pow-to-exp pow-exp
124×div-exp
74×add-cbrt-cube
46×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l*
9×associate-*r*
6×pow1 cbrt-undiv unpow-prod-down
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 → 406
Calls
4 calls:
26.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
13.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
18.0ms
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
11.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
58.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
78.0ms
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
60.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

simplify140.0ms

Algorithm
egg-herbie
Counts
418 → 418
Iterations

Useful iterations: 0 (88.0ms)

IterNodesCost
049638463
149638463

prune278.0ms

Filtered
69 candidates to 418 candidates (-505.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New4126418
Fresh3811
Picked101
Done000
Total41614430

Merged error: 4.9b

Counts
430 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
3.6b
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
4.2b
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
4.9b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
1496×add-exp-log
1387×prod-exp
356×pow-to-exp pow-exp
127×div-exp
92×add-cbrt-cube
59×cbrt-unprod
11×pow1 associate-*l*
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-undiv
4×pow-prod-down add-log-exp
3×unpow-prod-down times-frac associate-*r* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv sqr-pow
Counts
4 → 414
Calls
4 calls:
23.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
13.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
10.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
19.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
60.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
52.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
83.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
054938937

prune195.0ms

Filtered
66 candidates to 426 candidates (-545.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New4224426
Fresh21113
Picked101
Done000
Total42515440

Merged error: 3.7b

Counts
440 → 15

regimes665.0ms

Accuracy

24.4% (4.7b remaining)

Error of 7.8b against oracle of 3.1b and baseline of 9.3b

bsearch109.0ms

Steps
ItersRangePoint
8
9.475315765848704e-276
2.9049089413808126e-272
1.0954292840385535e-275

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03576
13576

end0.0ms

sample2.1s

Algorithm
intervals
Results
764.0ms9092×body80valid
390.0ms810×body1280valid
319.0ms943×body640valid
148.0ms590×body320valid
49.0ms299×body160valid

Profiling

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