Details

Time bar (total: 12.4s)

analyze2.1s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14

sample133.0ms

Algorithm
intervals
Results
53.0ms69×body1280valid
33.0ms63×body640valid
12.0ms97×body80valid
9.0ms24×body320valid
4.0ms36×body80invalid
2.0ms4×body640invalid
1.0ms3×body160valid
1.0ms2×body320invalid
0.0ms2×body160invalid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0508625

prune14.0ms

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: 31.8b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
15.4b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.4b
(/ (pow t 3.0) (* l l))

rewrite57.0ms

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:
13.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
23.0ms
(* (* (* (/ (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))

series353.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
168.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
53.0ms
(/ (pow t 3.0) (* l l))

simplify60.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049972562
149972562

prune297.0ms

Filtered
98 candidates to 156 candidates (-59.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New14610156
Fresh011
Picked101
Done000
Total14711158

Merged error: 24.6b

Counts
158 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.6b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.4b
(* (* (* (/ (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))

rewrite82.0ms

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:
16.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
13.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
32.0ms
(* (* (* (/ (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))

series365.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
184.0ms
(* (* (* (/ (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))

simplify94.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049665639
149665639

prune735.0ms

Filtered
138 candidates to 241 candidates (-74.6%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New22912241
Fresh3710
Picked101
Done000
Total23319252

Merged error: 18.9b

Counts
252 → 19

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ (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)))
3.0b
(* (* (/ (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))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.4b
(* (* (* (/ (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))

rewrite188.0ms

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:
28.0ms
(* (/ (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)))
33.0ms
(* (* (/ (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))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
46.0ms
(* (* (* (/ (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))

series384.0ms

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)))
80.0ms
(* (* (/ (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))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin 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))

simplify216.0ms

Algorithm
egg-herbie
Counts
597 → 597
Iterations

Useful iterations: 0 (125.0ms)

IterNodesCost
0496716982
1496716982

prune1.1s

Filtered
231 candidates to 597 candidates (-158.4%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New58512597
Fresh51318
Picked101
Done000
Total59125616

Merged error: 15.9b

Counts
616 → 25

localize35.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k)))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.2b
(/ (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k)))) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
13.0b
(* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
1328×add-exp-log
863×prod-exp
359×div-exp
181×pow-exp
142×add-cbrt-cube
107×pow-to-exp
79×cbrt-unprod
44×associate-*l*
40×add-sqr-sqrt
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
21×unpow-prod-down
20×associate-*l/
10×cbrt-prod
9×associate-*r/
8×pow1
5×associate-*r* associate-/l/ unswap-sqr sqr-pow
4×frac-times flip3-+ flip-+ add-log-exp
3×*-commutative distribute-lft-out
2×pow-prod-down div-inv
1×frac-2neg clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 344
Calls
4 calls:
14.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k)))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
35.0ms
(/ (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k)))) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
29.0ms
(* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (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))
133.0ms
(/ (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k)))) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
76.0ms
(* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (* (/ (pow (cbrt t) 3.0) l) (sin k)) (sin k))))

simplify118.0ms

Algorithm
egg-herbie
Counts
356 → 356
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0501511216

prune434.0ms

Filtered
112 candidates to 356 candidates (-217.9%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New34115356
Fresh101424
Picked101
Done000
Total35229381

Merged error: 8.9b

Counts
381 → 29

regimes1.1s

Accuracy

28.4% (6.6b remaining)

Error of 14.1b against oracle of 7.5b and baseline of 16.7b

bsearch148.0ms

Steps
ItersRangePoint
9
6.106666891408135e-55
4.986858432388585e-46
6.6296042558633e-55
5
-1.0859655280831384e-153
-4.195404074005216e-154
-4.261306571800381e-154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
069147
169147

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.6s2015×body1280valid
880.0ms1618×body640valid
414.0ms3250×body80valid
292.0ms767×body320valid
167.0ms1342×body80invalid
93.0ms350×body160valid
69.0ms131×body640invalid
55.0ms136×body320invalid
22.0ms86×body160invalid
17.0ms22×body1280invalid

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