Details

Time bar (total: 19.0s)

sample118.0ms

Algorithm
intervals
Results
47.0ms68×body1280valid
26.0ms50×body640valid
17.0ms169×body80valid
8.0ms25×body320valid
3.0ms12×body160valid

simplify31.0ms

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: 32.2b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
4.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.2b
(/ (pow t 3.0) (* l l))
15.3b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite64.0ms

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))
12.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan 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:
254.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
323.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
185.0ms
(/ (pow t 3.0) (* l l))
658.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify120.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune477.0ms

Filtered
156 candidates to 93 candidates (59.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1479156
Fresh000
Picked101
Done000
Total1489157

Merged error: 17.8b

Counts
157 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
8.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.3b
(* (* (* (/ (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))

rewrite84.0ms

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:
14.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
18.0ms
(* (* (/ (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)
32.0ms
(* (* (* (/ (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:
239.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
365.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
195.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
725.0ms
(* (* (* (/ (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))

simplify64.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013473795
150013312

prune906.0ms

Filtered
241 candidates to 149 candidates (61.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2338241
Fresh268
Picked101
Done000
Total23614250

Merged error: 13.4b

Counts
250 → 14

localize44.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 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)))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.4b
(* (* (* (/ (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))
15.3b
(* (* (* (* (/ (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))

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
5733×add-exp-log
3663×prod-exp
1790×div-exp
709×pow-exp
424×pow-to-exp
412×add-cbrt-cube
291×cbrt-unprod
206×associate-*l/
179×frac-times
109×cbrt-undiv
56×tan-quot
53×associate-*r/
49×pow1
47×associate-/r/
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
33×pow-prod-down
32×flip3-+ flip-+
29×add-cube-cbrt
20×unpow-prod-down
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 → 988
Calls
4 calls:
76.0ms
(/ 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)))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms
(* (* (* (/ (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))
62.0ms
(* (* (* (* (/ (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))

series2.2s

Counts
4 → 12
Calls
4 calls:
669.0ms
(/ 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)))
233.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
371.0ms
(* (* (* (/ (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))
919.0ms
(* (* (* (* (/ (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))

simplify325.0ms

Algorithm
egg-herbie
Counts
1000 → 1000
Iterations

Useful iterations: 1 (58.0ms)

IterNodesCost
0411831583
1500128649

prune1.8s

Filtered
1000 candidates to 246 candidates (24.6%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New987131000
Fresh6713
Picked101
Done000
Total994201014

Merged error: 12.0b

Counts
1014 → 20

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 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))))
1.2b
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
19.0b
(* (* (* (/ (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)))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
7634×add-exp-log
4727×prod-exp
2538×div-exp
945×pow-exp
565×pow-to-exp
541×add-cbrt-cube
371×cbrt-unprod
164×frac-times
158×cbrt-undiv
140×associate-*l/
80×associate-*r/
51×tan-quot
49×pow1
47×associate-/r/
44×add-sqr-sqrt
38×associate-*l*
37×times-frac
34×*-un-lft-identity flip3-+ flip-+
33×pow-prod-down
29×add-cube-cbrt
20×unpow-prod-down
10×cbrt-prod
9×associate-*r*
6×unswap-sqr
5×distribute-rgt-in distribute-lft-in
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×frac-2neg clear-num associate-/r*
Counts
4 → 1234
Calls
4 calls:
78.0ms
(/ 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))))
15.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
58.0ms
(* (* (* (/ (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
665.0ms
(/ 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))))
84.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
232.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
722.0ms
(* (* (* (/ (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)))

simplify397.0ms

Algorithm
egg-herbie
Counts
1246 → 1246
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0477341791
1500239655

prune2.1s

Filtered
1246 candidates to 289 candidates (23.2%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New124241246
Fresh21719
Picked101
Done000
Total1245211266

Merged error: 11.3b

Counts
1266 → 21

regimes549.0ms

Accuracy

8.4% (7.0b remaining)

Error of 16.5b against oracle of 9.5b and baseline of 17.1b

bsearch648.0ms

Steps
ItersRangePoint
4
1.5056127507307748e+113
2.245460825297648e+113
1.8346047238911825e+113
10
1.30412499104367e+31
1.0035707230662013e+44
3.89008926846833e+36
11
1.1975473842644465e-107
3.3025596874127677e-87
5.166165813271737e-107
2
-4.623623525107348e-183
-4.042508657112577e-183
-4.550984166608002e-183
7
-9.834161795002263e-26
-5.183361901796283e-27
-9.747363755682131e-26
7
-4.706237202987014e+161
-2.943775557298342e+159
-5.71240151429869e+159

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116212
1116212

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2050×body1280valid
814.0ms1719×body640valid
625.0ms5929×body80valid
288.0ms877×body320valid
104.0ms427×body160valid