Details

Time bar (total: 12.2s)

sample131.0ms

Algorithm
intervals
Results
47.0ms65×body1280valid
25.0ms179×body80valid
24.0ms47×body640valid
12.0ms31×body320valid
4.0ms17×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.4b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.2b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.5b
(/ (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:
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
22.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
9.0ms
(/ (pow t 3.0) (* l l))

series329.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
74.0ms
(* (* (/ (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))
38.0ms
(/ (pow t 3.0) (* l l))

simplify121.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08571728
147841448
250011444

prune331.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New14412156
Fresh000
Picked101
Done000
Total14512157

Merged error: 19.6b

Counts
157 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.2b
(* (* (* (/ (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

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)
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))

series362.0ms

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))
55.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
182.0ms
(* (* (* (/ (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))

simplify61.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014303890
150023397

prune594.0ms

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

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New23011241
Fresh2911
Picked101
Done000
Total23320253

Merged error: 14.6b

Counts
253 → 20

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
3.2b
(* (* (* (/ (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))
3.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.2b
(* (* (* (* (/ (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))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
3594×add-exp-log
2366×prod-exp
1039×div-exp
474×pow-exp
284×pow-to-exp
253×add-cbrt-cube
187×cbrt-unprod
116×associate-*l/
98×frac-times
57×cbrt-undiv
50×pow1
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×times-frac
33×pow-prod-down
32×tan-quot
30×add-cube-cbrt associate-*r/
26×unpow-prod-down
16×flip3-+ flip-+
13×cbrt-prod
11×associate-*r*
5×unswap-sqr sqr-pow
4×add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 688
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
37.0ms
(* (* (* (/ (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))
14.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
57.0ms
(* (* (* (* (/ (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))

series368.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(pow (cbrt t) 3.0)
85.0ms
(* (* (* (/ (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))
53.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
182.0ms
(* (* (* (* (/ (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))

simplify198.0ms

Algorithm
egg-herbie
Counts
700 → 700
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0325820167
1500117787

prune1.0s

Filtered
189 candidates to 700 candidates (-270.4%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New68911700
Fresh41519
Picked101
Done000
Total69426720

Merged error: 13.8b

Counts
720 → 26

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 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))))
0.7b
(pow (cbrt t) 3.0)
3.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.8b
(* (* (* (/ (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))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite533.0ms

Algorithm
rewrite-expression-head
Rules
7633×add-exp-log
4726×prod-exp
2538×div-exp
946×pow-exp
566×pow-to-exp
539×add-cbrt-cube
370×cbrt-unprod
162×frac-times
158×cbrt-undiv
139×associate-*l/
78×associate-*r/
48×tan-quot pow1
47×associate-/r/
43×add-sqr-sqrt
37×times-frac
35×associate-*l*
32×flip3-+ pow-prod-down flip-+
30×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
13×cbrt-prod
5×unswap-sqr sqr-pow
4×distribute-rgt-in distribute-lft-in associate-*r* add-log-exp
3×pow-unpow associate-/l*
2×pow-pow *-commutative div-inv
1×frac-2neg pow1/3 clear-num associate-/r*
Counts
4 → 1228
Calls
4 calls:
73.0ms
(/ 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))))
3.0ms
(pow (cbrt t) 3.0)
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
56.0ms
(* (* (* (/ (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)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ 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))))
46.0ms
(pow (cbrt t) 3.0)
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
187.0ms
(* (* (* (/ (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)))

simplify380.0ms

Algorithm
egg-herbie
Counts
1240 → 1240
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0483241708
1500339701

prune1.9s

Filtered
289 candidates to 1240 candidates (-329.1%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New123281240
Fresh71825
Picked101
Done000
Total1240261266

Merged error: 12.2b

Counts
1266 → 26

regimes855.0ms

Accuracy

12.1% (3.9b remaining)

Error of 17.0b against oracle of 13.1b and baseline of 17.5b

bsearch66.0ms

Steps
ItersRangePoint
9
2.151363062123758e-164
3.696518815383503e-159
1.0767155855803018e-160

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050127
150127

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s2025×body1280valid
861.0ms1658×body640valid
717.0ms6011×body80valid
322.0ms887×body320valid
110.0ms432×body160valid

Profiling

Loading profile data...