Details

Time bar (total: 17.8s)

sample123.0ms

Algorithm
intervals
Results
45.0ms62×body1280valid
29.0ms61×body640valid
19.0ms189×body80valid
10.0ms30×body320valid
4.0ms17×body160valid

simplify28.0ms

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: 32.6b

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.6b
(/ (pow t 3.0) (* l l))
16.1b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

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:
11.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
6.0ms
(/ (pow t 3.0) (* l l))
22.0ms
(* (* (* (/ (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:
253.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
324.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
183.0ms
(/ (pow t 3.0) (* l l))
639.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify118.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08011619
146461348
250021348

prune500.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
16.1b
(* (* (* (/ (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))

rewrite79.0ms

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:
19.0ms
(* (* (/ (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)
29.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
370.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
198.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
744.0ms
(* (* (* (/ (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))

simplify59.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013473795
150013312

prune987.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.1b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite439.0ms

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×*-commutative add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 710
Calls
4 calls:
55.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
44.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
58.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
290.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
371.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
745.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify149.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0272711417
1500110598

prune3.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.6b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
6.9b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
12.8b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
745×add-exp-log
479×prod-exp
210×div-exp
142×add-cbrt-cube
79×cbrt-unprod
75×pow-to-exp pow-exp
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×frac-times flip3-+ flip-+ add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 264
Calls
4 calls:
15.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
40.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
27.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
241.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
714.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
544.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013565415
150024747

prune788.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.7b

regimes607.0ms

Accuracy

56.1% (3.5b remaining)

Error of 10.3b against oracle of 6.8b and baseline of 14.7b

bsearch364.0ms

Steps
ItersRangePoint
9
1.607813371098077e-70
5.205620924581097e-64
3.0002554763073475e-64
11
-0.03898241045545256
-1.4071425044701078e-22
-6.6074907727629425e-21

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075104
175104

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2052×body1280valid
801.0ms1709×body640valid
625.0ms5841×body80valid
296.0ms885×body320valid
104.0ms443×body160valid