Details

Time bar (total: 10.6s)

sample137.0ms

Algorithm
intervals
Results
54.0ms73×body1280valid
27.0ms51×body640valid
26.0ms187×body80valid
5.0ms14×body320valid
5.0ms20×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.5b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.6b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.8b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.5b
(/ (pow t 3.0) (* l l))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
8.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
10.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
24.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms
(/ (pow t 3.0) (* l l))

series330.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
76.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
161.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
39.0ms
(/ (pow t 3.0) (* l l))

simplify119.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
08571728
147841448
250011444

prune317.0ms

Filtered
96 candidates to 156 candidates (-62.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New14610156
Fresh000
Picked101
Done000
Total14710157

Merged error: 23.0b

Counts
157 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.6b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.8b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
29.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series356.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
81.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
42.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
179.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014303890
150023397

prune609.0ms

Filtered
152 candidates to 241 candidates (-58.6%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New23110241
Fresh099
Picked101
Done000
Total23219251

Merged error: 15.7b

Counts
251 → 19

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.6b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
13.8b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
1884×add-exp-log
1025×prod-exp
732×div-exp
334×pow-exp
204×times-frac
199×pow-to-exp
151×add-cbrt-cube
136×associate-*l*
105×add-sqr-sqrt
97×*-un-lft-identity
92×add-cube-cbrt
78×cbrt-unprod
54×unpow-prod-down
47×associate-*l/
38×sqr-pow
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+
7×div-inv
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 585
Calls
4 calls:
27.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
15.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
26.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
43.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series383.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
82.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
184.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
597 → 597
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0256013410
1500112284

prune1.2s

Filtered
235 candidates to 597 candidates (-154.0%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New5889597
Fresh81018
Picked101
Done000
Total59719616

Merged error: 12.6b

Counts
616 → 19

localize36.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.5b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.1b
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
10.0b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
1214×add-exp-log
792×prod-exp
329×div-exp
159×pow-exp
142×add-cbrt-cube
96×pow-to-exp
79×cbrt-unprod
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×frac-times flip3-+ flip-+ add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 322
Calls
4 calls:
14.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
33.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
28.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series425.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
175.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
136.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify90.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
016868270
150017412

prune573.0ms

Filtered
129 candidates to 334 candidates (-158.9%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New32212334
Fresh51318
Picked101
Done000
Total32825353

Merged error: 10.9b

Counts
353 → 25

regimes896.0ms

Accuracy

48.2% (1.7b remaining)

Error of 13.0b against oracle of 11.2b and baseline of 14.6b

bsearch239.0ms

Steps
ItersRangePoint
9
3.646966899770778e-171
7.349802595259254e-163
7.200238959681474e-163
9
-1.6285460939773177e-128
-1.38073140355896e-137
-3.815008251180652e-129

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
071106
171106

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.6s2074×body1280valid
879.0ms1659×body640valid
749.0ms6140×body80valid
307.0ms791×body320valid
111.0ms426×body160valid

Profiling

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