Details

Time bar (total: 11.5s)

sample136.0ms

Algorithm
intervals
Results
50.0ms66×body1280valid
26.0ms180×body80valid
24.0ms47×body640valid
11.0ms29×body320valid
4.0ms14×body160valid

simplify23.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0508625

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.3b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.8b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.4b
(/ (pow t 3.0) (* l l))
15.2b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite52.0ms

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))
8.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
6.0ms
(/ (pow t 3.0) (* l l))
21.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series329.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
56.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
38.0ms
(/ (pow t 3.0) (* l l))
160.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049712558
149712558

prune313.0ms

Filtered
98 candidates to 156 candidates (-59.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New14511156
Fresh011
Picked101
Done000
Total14612158

Merged error: 21.5b

Counts
158 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
3.7b
(* (sin k) (/ (pow (cbrt t) 3.0) l))
8.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.2b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite77.0ms

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×cbrt-unprod
42×*-un-lft-identity associate-*r*
37×add-cube-cbrt
34×frac-times
33×pow-exp
31×associate-*r/
29×pow1
27×associate-*l/
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
12×cbrt-undiv
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-*l* 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) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
12.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
29.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series369.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
66.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
42.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
181.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify104.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
049485663
149485663

prune509.0ms

Filtered
134 candidates to 241 candidates (-79.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New23011241
Fresh3811
Picked101
Done000
Total23419253

Merged error: 16.9b

Counts
253 → 19

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l)))
2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
3.7b
(* (sin k) (/ (pow (cbrt t) 3.0) l))
15.2b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
1884×add-exp-log
1025×prod-exp
732×div-exp
334×pow-exp
204×times-frac
199×pow-to-exp
151×add-cbrt-cube
105×add-sqr-sqrt associate-*l*
97×*-un-lft-identity
92×add-cube-cbrt
78×cbrt-unprod
54×unpow-prod-down
43×associate-*r*
38×sqr-pow
37×cbrt-undiv
35×frac-times
34×pow1 associate-*r/
28×associate-*l/
20×pow-prod-down
16×tan-quot
10×cbrt-prod
8×flip3-+ flip-+
7×div-inv
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 585
Calls
4 calls:
31.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l)))
26.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
12.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
45.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series390.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l)))
80.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k))
66.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
180.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (sin k) (/ (pow (cbrt t) 3.0) l))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify263.0ms

Algorithm
egg-herbie
Counts
597 → 597
Iterations

Useful iterations: 0 (176.0ms)

IterNodesCost
0712016941

prune1.1s

Filtered
225 candidates to 597 candidates (-165.3%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New58314597
Fresh61218
Picked101
Done000
Total59026616

Merged error: 13.9b

Counts
616 → 26

localize47.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
2.2b
(* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k))
3.7b
(* (sin k) (/ (pow (cbrt t) 3.0) l))
15.2b
(* (* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
8844×add-exp-log
5920×prod-exp
2583×div-exp
752×add-cbrt-cube
638×cbrt-unprod
514×pow-exp
354×pow-to-exp
310×rec-exp 1-exp
253×cbrt-undiv
99×associate-*l/
98×frac-times
79×associate-*r/
65×pow1
46×pow-prod-down
43×add-sqr-sqrt
42×associate-*r*
35×*-un-lft-identity
34×times-frac
32×tan-quot
30×add-cube-cbrt
26×unpow-prod-down
16×flip3-+ flip-+
13×cbrt-prod
5×associate-*l* 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 → 1300
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
63.0ms
(* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k))
12.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
91.0ms
(* (* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series354.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(pow (cbrt t) 3.0)
70.0ms
(* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k))
67.0ms
(* (sin k) (/ (pow (cbrt t) 3.0) l))
170.0ms
(* (* (* (/ 1 (/ (* (cbrt l) (cbrt l)) (* (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (* (* (sin k) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (cbrt (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify498.0ms

Algorithm
egg-herbie
Counts
1312 → 1312
Iterations

Useful iterations: 0 (180.0ms)

IterNodesCost
0495965928
1495965928

prune1.1s

Filtered
160 candidates to 1312 candidates (-720.0%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New130931312
Fresh32225
Picked101
Done000
Total1313251338

Merged error: 13.6b

Counts
1338 → 25

regimes638.0ms

Accuracy

13.9% (4.7b remaining)

Error of 17.1b against oracle of 12.3b and baseline of 17.8b

bsearch205.0ms

Steps
ItersRangePoint
8
2.867518500391327e-72
2.2306025090703958e-69
7.271153522413357e-72
8
-2.6448701877505777e-143
-9.17247791194273e-148
-8.118276423849149e-147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089223
189223

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s2119×body1280valid
934.0ms1736×body640valid
735.0ms5827×body80valid
307.0ms798×body320valid
111.0ms435×body160valid

Profiling

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