Details

Time bar (total: 19.0s)

sample118.0ms

Algorithm
intervals
Results
50.0ms68×body1280valid
23.0ms50×body640valid
17.0ms169×body80valid
9.0ms25×body320valid
3.0ms12×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 2

localize20.0ms

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))

rewrite59.0ms

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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u 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 → 152
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))
9.0ms
(/ (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))

series1.3s

Counts
4 → 12
Calls
4 calls:
241.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
308.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
174.0ms
(/ (pow t 3.0) (* l l))
613.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify122.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08171679
147261405
250011405

prune497.0ms

Filtered
164 candidates to 101 candidates (61.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1559164
Fresh011
Picked101
Done000
Total15610166

Merged error: 17.8b

Counts
166 → 10

localize25.0ms

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))

rewrite81.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 237
Calls
4 calls:
11.0ms
(* (/ (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)
33.0ms
(* (* (* (/ (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:
227.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
347.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
189.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
713.0ms
(* (* (* (/ (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))

simplify68.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013643882
150013394

prune926.0ms

Filtered
249 candidates to 157 candidates (63.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2418249
Fresh279
Picked101
Done000
Total24415259

Merged error: 13.4b

Counts
259 → 15

localize41.0ms

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))

rewrite354.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 996
Calls
4 calls:
70.0ms
(/ 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)))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
37.0ms
(* (* (* (/ (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))
63.0ms
(* (* (* (* (/ (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))

series2.0s

Counts
4 → 12
Calls
4 calls:
652.0ms
(/ 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)))
242.0ms
(* (/ (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))
717.0ms
(* (* (* (* (/ (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))

simplify307.0ms

Algorithm
egg-herbie
Counts
1008 → 1008
Iterations

Useful iterations: 1 (55.0ms)

IterNodesCost
0414131770
1500228892

prune2.0s

Filtered
1008 candidates to 255 candidates (25.3%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New995131008
Fresh6814
Picked101
Done000
Total1002211023

Merged error: 12.0b

Counts
1023 → 21

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)))

rewrite368.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×frac-2neg clear-num associate-/r*
Counts
4 → 1242
Calls
4 calls:
74.0ms
(/ 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))))
18.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
52.0ms
(* (* (* (/ (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:
644.0ms
(/ 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))))
83.0ms
(* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
235.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
695.0ms
(* (* (* (/ (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)))

simplify392.0ms

Algorithm
egg-herbie
Counts
1254 → 1254
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0479741938
1500339919

prune2.1s

Filtered
1254 candidates to 297 candidates (23.7%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New125041254
Fresh21820
Picked101
Done000
Total1253221275

Merged error: 11.3b

Counts
1275 → 22

regimes719.0ms

Accuracy

8.4% (7.0b remaining)

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

bsearch632.0ms

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

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0110210
1110210

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2050×body1280valid
819.0ms1719×body640valid
641.0ms5929×body80valid
297.0ms877×body320valid
101.0ms427×body160valid