Details

Time bar (total: 15.7s)

sample118.0ms

Algorithm
intervals
Results
43.0ms66×body1280valid
27.0ms60×body640valid
19.0ms196×body80valid
9.0ms26×body320valid
2.0ms11×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
11.1b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.3b
(/ (pow t 3.0) (* l l))

rewrite54.0ms

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))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
22.0ms
(* (* (* (/ (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))

series1.4s

Counts
4 → 12
Calls
4 calls:
325.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
252.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
641.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
182.0ms
(/ (pow t 3.0) (* l l))

simplify122.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune504.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.1b
(* (* (* (/ (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))

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×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:
16.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
30.0ms
(* (* (* (/ (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:
362.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
239.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
198.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
734.0ms
(* (* (* (/ (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
241 → 241
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013473795
150013312

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.1b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
991×prod-exp
289×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
75×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt associate-*r/
26×unpow-prod-down
17×pow-prod-down
16×tan-quot
13×cbrt-undiv cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
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 → 378
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
25.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
43.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
310.0ms
(pow (cbrt t) 3.0)
357.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
231.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
946.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
390 → 390
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018368578
150016656

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.1b

localize43.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
2.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
3.4b
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
11.1b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
3309×add-exp-log
2549×prod-exp
584×div-exp
448×pow-exp
268×pow-to-exp
214×add-cbrt-cube
201×cbrt-unprod
65×pow1
62×associate-*l/
45×pow-prod-down
37×associate-*l*
36×add-sqr-sqrt
34×frac-times times-frac
33×*-un-lft-identity
30×associate-*r/
28×cbrt-undiv add-cube-cbrt
20×unpow-prod-down
16×tan-quot
15×associate-*r*
13×cbrt-prod
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 627
Calls
4 calls:
16.0ms
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
38.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
14.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
61.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
242.0ms
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
362.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
290.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
740.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify187.0ms

Algorithm
egg-herbie
Counts
639 → 639
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0272219380
1500216255

prune1.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 8.9b

regimes708.0ms

Accuracy

15.6% (6.4b remaining)

Error of 16.7b against oracle of 10.2b and baseline of 17.9b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07289
17289

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s2041×body1280valid
816.0ms1752×body640valid
597.0ms5890×body80valid
289.0ms868×body320valid
112.0ms470×body160valid