Details

Time bar (total: 15.0s)

analyze2.3s (15.1%)

Algorithm
1×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

sample142.0ms (0.9%)

Algorithm
1×intervals
Results
58.0ms64×body1280valid
30.0ms51×body640valid
14.0ms99×body80valid
12.0ms30×body320valid
6.0ms41×body80invalid
3.0ms12×body160valid
2.0ms4×body640invalid
1.0ms3×body320invalid
1.0ms2×body160invalid

simplify28.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0508625

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 31.4b

Counts
2 → 1

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.5b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
10.5b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.7b
(/ (pow t 3.0) (* l l))

rewrite55.0ms (0.4%)

Algorithm
1×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:

23.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
6.0ms
(/ (pow t 3.0) (* l l))

series341.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

163.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
77.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
57.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
44.0ms
(/ (pow t 3.0) (* l l))

simplify57.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049972562
149972562

prune472.0ms (3.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New14115156
Fresh000
Picked101
Done000
Total14215157

Merged error: 17.4b

Counts
157 → 15

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.5b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
10.5b
(* (* (* (/ (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))

rewrite79.0ms (0.5%)

Algorithm
1×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:

33.0ms
(* (* (* (/ (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))
16.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)

series373.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

187.0ms
(* (* (* (/ (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))
85.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
55.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
46.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)

simplify85.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049665639
149665639

prune859.0ms (5.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New22615241
Fresh6814
Picked101
Done000
Total23323256

Merged error: 12.0b

Counts
256 → 23

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.5b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.5b
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite131.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
1050×add-exp-log
734×prod-exp
255×div-exp
151×add-cbrt-cube
145×pow-to-exp pow-exp
96×cbrt-unprod
47×associate-*l/
40×add-sqr-sqrt
37×associate-*l*
35×frac-times
34×pow1 times-frac
33×associate-*r/
32×*-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down pow-prod-down
19×cbrt-undiv
16×tan-quot
12×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 366
Calls

4 calls:

41.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
23.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
22.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))

series390.0ms (2.6%)

Counts
4 → 12
Calls

4 calls:

186.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
84.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
63.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))

simplify105.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
378 → 378
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049597485
149597485

prune1.4s (9.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New36711378
Fresh91322
Picked101
Done000
Total37724401

Merged error: 11.6b

Counts
401 → 24

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))
1.1b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.6b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))

rewrite170.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
1938×add-exp-log
1285×prod-exp
556×div-exp
275×add-cbrt-cube
241×pow-to-exp pow-exp
167×cbrt-unprod
65×associate-*r/
59×frac-times
54×associate-*l/
52×cbrt-undiv
40×add-sqr-sqrt
37×times-frac
36×associate-*l*
32×pow1
27×add-cube-cbrt *-un-lft-identity
24×tan-quot
23×associate-/r/
20×unpow-prod-down
19×pow-prod-down
16×flip3-+ flip-+
10×cbrt-prod
5×associate-*r* unswap-sqr
4×distribute-rgt-in distribute-lft-in add-log-exp sqr-pow
3×*-commutative associate-/l*
2×div-inv
1×frac-2neg clear-num associate-/r*
Counts
4 → 536
Calls

4 calls:

41.0ms
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))
36.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))
21.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))

series483.0ms (3.2%)

Counts
4 → 12
Calls

4 calls:

188.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))
175.0ms
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))
63.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))

simplify160.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
548 → 548
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
0497913458
1497913458

prune2.0s (13.3%)

Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New5426548
Fresh22123
Picked101
Done000
Total54527572

Merged error: 9.7b

Counts
572 → 27

regimes1.0s (6.9%)

Accuracy

Total 3.4b remaining (21.3%)

Threshold costs 0b (0%)

bsearch155.0ms (1%)

Steps
ItersRangePoint
9
1.8632901516714905e-233
3.090447047155586e-227
3.0479605309600283e-227
9
-4.352593571526155e-161
-1.2097687850078278e-170
-4.242279192446241e-161

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04890
14890

end0.0ms (0%)

sample4.2s (27.6%)

Algorithm
1×intervals
Results
1.7s2036×body1280valid
899.0ms1542×body640valid
456.0ms3285×body80valid
335.0ms809×body320valid
184.0ms1342×body80invalid
97.0ms328×body160valid
72.0ms129×body640invalid
52.0ms129×body320invalid
24.0ms84×body160invalid
23.0ms30×body1280invalid

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