Details

Time bar (total: 18.8s)

sample138.0ms

Algorithm
intervals
Results
59.0ms71×body1280valid
29.0ms55×body640valid
23.0ms188×body80valid
7.0ms19×body320valid
3.0ms11×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

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: 30.1b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.3b
(/ (pow t 3.0) (* l l))
14.0b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite61.0ms

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:
10.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
14.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
6.0ms
(/ (pow t 3.0) (* l l))
24.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
259.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
331.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
188.0ms
(/ (pow t 3.0) (* l l))
660.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify117.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune480.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New14511156
Fresh000
Picked101
Done000
Total14611157

Merged error: 15.8b

Counts
157 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.0b
(* (* (* (/ (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))

rewrite87.0ms

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:
20.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
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))

series1.6s

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
257.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
207.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
761.0ms
(* (* (* (/ (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))

simplify62.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013473795
150013312

prune933.0ms

Filtered
241 candidates to 150 candidates (62.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New22912241
Fresh4610
Picked101
Done000
Total23418252

Merged error: 11.6b

Counts
252 → 18

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
3.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.0b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
5034×add-exp-log
3200×prod-exp
1557×div-exp
709×pow-exp
424×pow-to-exp
340×add-cbrt-cube
246×cbrt-unprod
125×associate-*l/
103×frac-times
85×cbrt-undiv
61×pow1
41×pow-prod-down
40×add-sqr-sqrt
37×associate-*l*
34×times-frac
33×associate-*r/
32×tan-quot *-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down
16×flip3-+ flip-+
12×associate-*r*
10×cbrt-prod
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 → 939
Calls
4 calls:
29.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
46.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
66.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
326.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
403.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
258.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
786.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify264.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0319327225
1500123594

prune1.5s

Filtered
951 candidates to 201 candidates (21.1%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New94110951
Fresh51217
Picked101
Done000
Total94722969

Merged error: 10.7b

Counts
969 → 22

localize47.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.0b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
5799×add-exp-log
3701×prod-exp
1809×div-exp
718×pow-exp
427×pow-to-exp
406×add-cbrt-cube
288×cbrt-unprod
179×frac-times
178×associate-*l/
112×cbrt-undiv
81×associate-*r/
56×tan-quot
47×associate-/r/
42×add-sqr-sqrt
40×pow1
37×times-frac
36×associate-*l*
34×*-un-lft-identity
32×flip3-+ flip-+
29×add-cube-cbrt
26×pow-prod-down
20×unpow-prod-down
11×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 998
Calls
4 calls:
77.0ms
(/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
43.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
17.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
69.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
917.0ms
(/ 2.0 (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
406.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
251.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
781.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify315.0ms

Algorithm
egg-herbie
Counts
1010 → 1010
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0408732151
1500131215

prune1.7s

Filtered
1010 candidates to 243 candidates (24.1%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New998121010
Fresh91221
Picked101
Done000
Total1008241032

Merged error: 8.3b

Counts
1032 → 24

regimes737.0ms

Accuracy

0.4% (8.0b remaining)

Error of 16.0b against oracle of 7.9b and baseline of 16.0b

bsearch332.0ms

Steps
ItersRangePoint
0
6.247535745489316e+110
6.464535686127643e+110
6.356035715808479e+110
7
2.2426584992196937e-24
5.136678226021711e-22
3.061078201938046e-22
5
-17909.48569475165
-5885.016217463414
-17485.46349436262
8
-5.486826032289836e+141
-6.54581261410613e+138
-5.198030982564454e+141

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097135
197135

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.6s2069×body1280valid
945.0ms1750×body640valid
726.0ms5779×body80valid
327.0ms859×body320valid
111.0ms433×body160valid