Details

Time bar (total: 18.0s)

analyze2.1s

Algorithm
search

sample134.0ms

Algorithm
intervals
Results
55.0ms70×body1280valid
30.0ms55×body640valid
17.0ms105×body80valid
6.0ms46×body80invalid
6.0ms14×body320valid
3.0ms12×body160valid
1.0ms1×body1280invalid
1.0ms2×body160invalid
0.0ms1×body640invalid
0.0ms1×body320invalid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.2b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
15.7b
(/ (pow t 3.0) (* l l))
15.7b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

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

series334.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
40.0ms
(/ (pow t 3.0) (* l l))
162.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify119.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08571728
147841448
250011444

prune325.0ms

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: 22.1b

Counts
157 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.7b
(* (* (* (/ (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))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
30.0ms
(* (* (* (/ (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))

series360.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (/ (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))
44.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
180.0ms
(* (* (* (/ (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))

simplify65.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014303890
150023397

prune609.0ms

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

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New22813241
Fresh3811
Picked101
Done000
Total23221253

Merged error: 17.3b

Counts
253 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.8b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.7b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 710
Calls
4 calls:
63.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
46.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
58.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series386.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
82.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
186.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify146.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0278811518
1500210775

prune2.6s

Filtered
480 candidates to 722 candidates (-50.4%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New70814722
Fresh81220
Picked101
Done000
Total71726743

Merged error: 14.2b

Counts
743 → 26

localize25.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.9b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
11.7b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
576×add-exp-log
347×prod-exp
183×div-exp
128×times-frac
103×add-cbrt-cube
80×add-sqr-sqrt
72×*-un-lft-identity
67×pow-to-exp add-cube-cbrt pow-exp
56×unpow-prod-down
53×cbrt-unprod
36×associate-*l*
34×associate-/r*
28×cbrt-prod associate-*l/
25×associate-*r/
23×cbrt-undiv
19×frac-times
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 320
Calls
4 calls:
14.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
36.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
30.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series514.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
182.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (cbrt t) 3.0)))
198.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify87.0ms

Algorithm
egg-herbie
Counts
332 → 332
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
018426305
150015784

prune736.0ms

Filtered
192 candidates to 332 candidates (-72.9%)
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New32111332
Fresh52025
Picked101
Done000
Total32731358

Merged error: 13.1b

Counts
358 → 31

regimes1.1s

Accuracy

-9.1% (2.9b remaining)

Error of 15.2b against oracle of 12.3b and baseline of 15.0b

bsearch1.5s

Steps
ItersRangePoint
9
1.814233999060795e-273
5.926977963214794e-266
2.8157859008423338e-273
8
-1.1581530594619724e-138
-8.318082899494175e-142
-1.0595693242055032e-141

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072102
172102

end0.0ms

analyze2.3s

Algorithm
search

sample3.9s

Algorithm
intervals
Results
1.6s2020×body1280valid
884.0ms1613×body640valid
429.0ms3293×body80valid
296.0ms736×body320valid
187.0ms1372×body80invalid
88.0ms338×body160valid
70.0ms126×body640invalid
49.0ms128×body320invalid
20.0ms26×body1280invalid
20.0ms74×body160invalid

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