Details

Time bar (total: 15.5s)

sample125.0ms

Algorithm
intervals
Results
50.0ms67×body1280valid
27.0ms57×body640valid
21.0ms212×body80valid
6.0ms17×body320valid
3.0ms15×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.6b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.6b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.3b
(/ (pow t 3.0) (* l l))

rewrite58.0ms

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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u 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 → 152
Calls
4 calls:
14.0ms
(* (* (/ (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))

series1.4s

Counts
4 → 12
Calls
4 calls:
327.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
245.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
642.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
184.0ms
(/ (pow t 3.0) (* l l))

simplify119.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08171679
147261405
250011405

prune491.0ms

Filtered
164 candidates to 101 candidates (61.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15410164
Fresh011
Picked101
Done000
Total15511166

Merged error: 16.8b

Counts
166 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.6b
(* (* (* (/ (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×expm1-log1p-u log1p-expm1-u 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 → 237
Calls
4 calls:
17.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
14.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms
(* (* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
368.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
240.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
198.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
734.0ms
(* (* (* (/ (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
249 → 249
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013643882
150013394

prune951.0ms

Filtered
249 candidates to 157 candidates (63.1%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New2409249
Fresh1910
Picked101
Done000
Total24218260

Merged error: 12.5b

Counts
260 → 18

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.9b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.6b
(* (* (* (* (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))

rewrite129.0ms

Algorithm
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×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 374
Calls
4 calls:
18.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
27.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (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))
39.0ms
(* (* (* (* (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))

series1.8s

Counts
4 → 12
Calls
4 calls:
487.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
370.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
242.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
745.0ms
(* (* (* (* (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))

simplify91.0ms

Algorithm
egg-herbie
Counts
386 → 386
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
014976684
150015489

prune846.0ms

Filtered
386 candidates to 144 candidates (37.3%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New3797386
Fresh41317
Picked101
Done000
Total38420404

Merged error: 12.0b

Counts
404 → 20

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k))))
2.6b
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
2.9b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
13.6b
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
2600×add-exp-log
1975×prod-exp
510×div-exp
290×pow-to-exp pow-exp
271×add-cbrt-cube
253×cbrt-unprod
70×pow1
65×associate-*l/
49×pow-prod-down
38×cbrt-undiv
37×associate-*l*
35×frac-times
34×add-sqr-sqrt times-frac
33×associate-*r/
31×*-un-lft-identity
26×add-cube-cbrt
20×unpow-prod-down
16×tan-quot
10×cbrt-prod associate-*r*
8×flip3-+ flip-+
5×unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 607
Calls
4 calls:
28.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k))))
15.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
36.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
57.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
288.0ms
(* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k))))
290.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
353.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
724.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify160.0ms

Algorithm
egg-herbie
Counts
619 → 619
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0212015463
1500112415

prune1.0s

Filtered
619 candidates to 165 candidates (26.7%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New60910619
Fresh51419
Picked101
Done000
Total61524639

Merged error: 11.1b

Counts
639 → 24

regimes675.0ms

Accuracy

20.2% (6.0b remaining)

Error of 16.5b against oracle of 10.5b and baseline of 18.0b

bsearch272.0ms

Steps
ItersRangePoint
9
3.1784587658123057e-152
1.2481259428041416e-144
5.915023705663655e-151
4
-7.303440592003602e-233
-4.3855165870465935e-233
-6.300404215299631e-233

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07860
17860

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.5s2086×body1280valid
839.0ms1727×body640valid
619.0ms5876×body80valid
297.0ms853×body320valid
94.0ms419×body160valid