Details

Time bar (total: 16.4s)

analyze2.2s

Algorithm
search

sample132.0ms

Algorithm
intervals
Results
51.0ms64×body1280valid
29.0ms52×body640valid
13.0ms100×body80valid
12.0ms31×body320valid
5.0ms9×body640invalid
4.0ms32×body80invalid
2.0ms9×body160valid
1.0ms3×body320invalid
1.0ms2×body160invalid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.1b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.6b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.3b
(/ (pow t 3.0) (* l l))

rewrite56.0ms

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))
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))

series345.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
78.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
164.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
43.0ms
(/ (pow t 3.0) (* l l))

simplify120.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08571728
147841448
250011444

prune316.0ms

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: 23.2b

Counts
157 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
9.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.6b
(* (* (* (/ (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))

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:
13.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
36.0ms
(* (* (* (/ (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))

series374.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
82.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
45.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
190.0ms
(* (* (* (/ (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))

simplify60.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014303890
150023397

prune586.0ms

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

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New23110241
Fresh2911
Picked101
Done000
Total23419253

Merged error: 15.9b

Counts
253 → 19

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.4b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
14.6b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
2085×add-exp-log
1365×prod-exp
627×div-exp
253×add-cbrt-cube
210×pow-to-exp pow-exp
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 → 518
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
39.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
61.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series375.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(pow (cbrt t) 3.0)
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
88.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
182.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify147.0ms

Algorithm
egg-herbie
Counts
530 → 530
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0261512493
1500111859

prune1.0s

Filtered
189 candidates to 530 candidates (-180.4%)
Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New51614530
Fresh31518
Picked101
Done000
Total52029549

Merged error: 15.4b

Counts
549 → 29

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
3.3b
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
3.4b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
14.6b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
2085×add-exp-log
1365×prod-exp
627×div-exp
253×add-cbrt-cube
210×pow-to-exp pow-exp
187×cbrt-unprod
116×associate-*l/
98×frac-times
57×cbrt-undiv
50×pow1
34×add-sqr-sqrt
33×pow-prod-down
32×tan-quot
30×associate-*r/
29×*-un-lft-identity
27×associate-*l*
24×add-cube-cbrt times-frac
16×unpow-prod-down flip3-+ flip-+
11×associate-*r*
5×sqr-pow
4×add-log-exp unswap-sqr
3×cbrt-prod pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 508
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
10.0ms
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
43.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
59.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series397.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(pow (cbrt t) 3.0)
49.0ms
(* (/ (pow t (* 1/3 3.0)) l) (sin k))
96.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k))
202.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow t (* 1/3 3.0)) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify147.0ms

Algorithm
egg-herbie
Counts
520 → 520
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0263212420
1500311786

prune832.0ms

Filtered
178 candidates to 520 candidates (-192.1%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New5137520
Fresh101828
Picked101
Done000
Total52425549

Merged error: 15.4b

Counts
549 → 25

regimes803.0ms

Accuracy

1.6% (2.5b remaining)

Error of 17.9b against oracle of 15.4b and baseline of 18.0b

bsearch1.7s

Steps
ItersRangePoint
7
-2.47274128784708e-56
-1.1920129468087678e-58
-3.131759569927817e-57
6
-8.134996166999984e+165
-1.6594154864528906e+165
-1.6759904213731208e+165

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05844
15844

end0.0ms

analyze2.2s

Algorithm
search

sample4.0s

Algorithm
intervals
Results
1.6s2022×body1280valid
915.0ms1635×body640valid
430.0ms3271×body80valid
300.0ms724×body320valid
189.0ms1358×body80invalid
100.0ms348×body160valid
81.0ms152×body640invalid
47.0ms122×body320invalid
21.0ms24×body1280invalid
19.0ms72×body160invalid

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