Details

Time bar (total: 16.6s)

sample125.0ms

Algorithm
intervals
Results
45.0ms57×body1280valid
27.0ms53×body640valid
24.0ms200×body80valid
8.0ms21×body320valid
4.0ms15×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: 33.6b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
14.3b
(/ (pow t 3.0) (* l l))
14.7b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite63.0ms

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:
12.0ms
(* (* (/ (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))
29.0ms
(* (* (* (/ (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:
316.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
246.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
181.0ms
(/ (pow t 3.0) (* l l))
629.0ms
(* (* (* (/ (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: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune485.0ms

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

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.7b
(* (* (* (/ (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))

rewrite88.0ms

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:
18.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
34.0ms
(* (* (* (/ (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:
363.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
197.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
730.0ms
(* (* (* (/ (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))

simplify63.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013473795
150013312

prune947.0ms

Filtered
241 candidates to 149 candidates (61.8%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New22714241
Fresh3710
Picked101
Done000
Total23121252

Merged error: 10.8b

Counts
252 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 2.0 (* (* (* (/ (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)))
2.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
14.7b
(* (* (* (/ (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))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
687×prod-exp
503×div-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
99×cbrt-unprod
78×associate-*l/
63×frac-times
49×cbrt-undiv
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
29×pow1 add-cube-cbrt
28×tan-quot
25×associate-*r/
23×associate-/r/
20×unpow-prod-down
17×pow-prod-down
16×flip3-+ flip-+
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 → 397
Calls
4 calls:
65.0ms
(/ 2.0 (* (* (* (/ (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)))
51.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
65.0ms
(* (* (* (/ (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))

series2.1s

Counts
4 → 12
Calls
4 calls:
649.0ms
(/ 2.0 (* (* (* (/ (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)))
345.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
231.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
923.0ms
(* (* (* (/ (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))

simplify107.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018718293
150017380

prune1.0s

Filtered
409 candidates to 161 candidates (39.4%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New39613409
Fresh91120
Picked101
Done000
Total40624430

Merged error: 7.4b

Counts
430 → 24

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.2b
(* (/ 2.0 (* (* (* (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)))
11.1b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
658×add-exp-log
423×prod-exp
186×div-exp
120×add-cbrt-cube
75×add-sqr-sqrt
71×times-frac
68×pow-to-exp pow-exp
67×cbrt-unprod
54×*-un-lft-identity associate-*l*
49×add-cube-cbrt
45×associate-*r*
40×unpow-prod-down
29×associate-*l/
26×associate-*r/
24×cbrt-undiv
20×cbrt-prod frac-times
15×pow1
14×tan-quot
11×associate-/r/
10×unswap-sqr
8×flip3-+ flip-+ sqr-pow
6×pow-prod-down
4×*-commutative add-log-exp
3×div-inv distribute-lft-out
1×distribute-rgt-in distribute-lft-in
Counts
4 → 304
Calls
4 calls:
16.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
55.0ms
(* (/ 2.0 (* (* (* (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))

series2.1s

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
239.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
648.0ms
(* (/ 2.0 (* (* (* (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)))
820.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify92.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
017095978
150015341

prune944.0ms

Filtered
316 candidates to 171 candidates (54.1%)
Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New30412316
Fresh41923
Picked101
Done000
Total30931340

Merged error: 6.4b

Counts
340 → 31

regimes695.0ms

Accuracy

61.1% (3.3b remaining)

Error of 10.2b against oracle of 7.0b and baseline of 15.4b

bsearch326.0ms

Steps
ItersRangePoint
9
9.75663645696442e-148
1.1183709739513307e-141
1.1054645625611026e-141
8
-1.8191185095599998e-22
-2.025698590439059e-25
-1.0152271852077127e-24

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06973
16973

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.6s2064×body1280valid
907.0ms1718×body640valid
702.0ms5854×body80valid
329.0ms889×body320valid
110.0ms439×body160valid