Details

Time bar (total: 19.7s)

sample58.0ms

Algorithm
intervals
Results
21.0ms291×body80valid
9.0ms23×body1280valid
8.0ms30×body640valid
3.0ms12×body320valid
2.0ms13×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.9b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.6b
(* (* x (pow sin 2.0)) x)
6.9b
(* x (pow sin 2.0))
18.2b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite105.0ms

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:
34.0ms
(/ (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))
26.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series851.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
150.0ms
(* (* x (pow sin 2.0)) x)
135.0ms
(* x (pow sin 2.0))
266.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify83.0ms

Algorithm
egg-herbie
Counts
429 → 429
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014095107
150014951

prune1.3s

Filtered
429 candidates to 317 candidates (73.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New41514429
Fresh000
Picked101
Done000
Total41614430

Merged error: 7.6b

Counts
430 → 14

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
6.8b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
12.1b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
1327×add-sqr-sqrt
1034×unswap-sqr
455×add-exp-log
371×prod-exp
351×times-frac
309×unpow-prod-down
305×associate-*l*
275×sqr-pow
255×associate-*r*
186×add-cube-cbrt *-un-lft-identity
117×associate-/r*
89×pow-to-exp pow-exp
58×add-cbrt-cube
53×div-exp
33×cbrt-unprod
29×pow1
22×*-commutative
18×pow-prod-down
7×cbrt-undiv
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
1×frac-2neg clear-num div-inv
Counts
3 → 792
Calls
3 calls:
67.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
46.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
18.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series817.0ms

Counts
3 → 9
Calls
3 calls:
317.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
279.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
221.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify185.0ms

Algorithm
egg-herbie
Counts
801 → 801
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0289215658
1500115301

prune2.8s

Filtered
801 candidates to 608 candidates (75.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New78813801
Fresh11213
Picked101
Done000
Total80015815

Merged error: 1.5b

Counts
815 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
1.1b
(/ 1 (* x (pow sin (/ 2.0 2))))
4.7b
(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
757×add-sqr-sqrt
487×associate-/r*
452×add-exp-log
365×times-frac
362×*-un-lft-identity
330×associate-*r*
312×frac-times
306×add-cube-cbrt
288×unswap-sqr
271×prod-exp
270×unpow-prod-down
179×div-exp
152×sqr-pow
138×associate-*l*
124×associate-/l*
86×pow-to-exp pow-exp
83×rec-exp 1-exp
44×add-cbrt-cube
42×clear-num
41×frac-2neg
32×*-commutative
24×associate-*r/
19×pow1
15×cbrt-unprod
13×associate-*l/
12×cbrt-undiv
9×pow-prod-down
6×pow-flip
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×un-div-inv inv-pow
Counts
4 → 1014
Calls
4 calls:
32.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
14.0ms
(/ 1 (* x (pow sin (/ 2.0 2))))
63.0ms
(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
20.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series863.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
196.0ms
(/ 1 (* x (pow sin (/ 2.0 2))))
185.0ms
(* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2)))))
221.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify192.0ms

Algorithm
egg-herbie
Counts
1026 → 1026
Iterations

Useful iterations: 1 (65.0ms)

IterNodesCost
0353212418
1500111977

prune2.7s

Filtered
1026 candidates to 543 candidates (52.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New102241026
Fresh41014
Picked101
Done000
Total1027141041

Merged error: 1.5b

Counts
1041 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
15.7b
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
15.7b
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
15.7b
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
1442×add-sqr-sqrt
1281×associate-/r*
1056×cbrt-div
936×frac-times
751×*-un-lft-identity
583×add-cube-cbrt
566×unpow-prod-down
556×associate-*r*
555×times-frac
492×unswap-sqr
453×cbrt-prod
354×associate-/l*
292×sqr-pow
238×associate-*l*
120×clear-num
117×frac-2neg
72×associate-*r/
56×*-commutative
39×associate-*l/
30×add-exp-log
21×prod-exp
9×pow1 un-div-inv add-cbrt-cube
7×pow-to-exp pow-exp
6×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down cbrt-unprod
Counts
4 → 1602
Calls
4 calls:
20.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
77.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
77.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
80.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
217.0ms
(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
367.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
364.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))
361.0ms
(cbrt (* (/ 1 (pow cos (/ 2.0 2))) (/ 1 (* x (pow sin (/ 2.0 2))))))

simplify319.0ms

Algorithm
egg-herbie
Counts
1614 → 1614
Iterations

Useful iterations: 1 (58.0ms)

IterNodesCost
0317626021
1500125081

prune4.9s

Filtered
1614 candidates to 765 candidates (47.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New161221614
Fresh21113
Picked101
Done000
Total1615131628

Merged error: 1.5b

Counts
1628 → 13

regimes336.0ms

Accuracy

0% (1.2b remaining)

Error of 2.9b against oracle of 1.7b and baseline of 2.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03845
13845

end0.0ms

sample1.8s

Algorithm
intervals
Results
682.0ms9166×body80valid
366.0ms865×body1280valid
297.0ms982×body640valid
128.0ms590×body320valid
50.0ms308×body160valid