Details

Time bar (total: 27.8s)

sample129.0ms

Algorithm
intervals
Results
49.0ms60×body1280valid
27.0ms51×body640valid
22.0ms198×body80valid
10.0ms28×body320valid
2.0ms9×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01925
14825
215725
384225
4465725
done500125

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
9.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
20.3b
(/ (pow t 3.0) (* l l))

rewrite627.0ms

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:
75.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
31.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
501.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
339.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
259.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
654.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
191.0ms
(/ (pow t 3.0) (* l l))

simplify1.7s

Counts
156 → 156
Iterations

Useful iterations: 2 (513.0ms)

IterNodesCost
02553209
17543070
234902565
done50002565

prune504.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
9.9b
(* (* (* (/ (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))

rewrite920.0ms

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:
142.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
723.0ms
(* (* (* (/ (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:
379.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
251.0ms
(* (/ (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))

simplify614.0ms

Counts
241 → 241
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
04296958
112506583
done50005619

prune916.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.3b

localize38.0ms

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)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.9b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.3s

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
136×associate-*l*
105×add-sqr-sqrt
97×*-un-lft-identity
92×add-cube-cbrt
78×cbrt-unprod
54×unpow-prod-down
47×associate-*l/
38×sqr-pow
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r*
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:
91.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
183.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
880.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (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:
300.0ms
(* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
379.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
244.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
749.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify772.0ms

Counts
597 → 597
Iterations

Useful iterations: done (747.0ms)

IterNodesCost
073624822
1213622690
done500120620

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.1b

localize32.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.4b
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
7.7b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
966×add-exp-log
593×prod-exp
294×div-exp
145×pow-exp
103×add-cbrt-cube
87×pow-to-exp
83×times-frac
58×add-sqr-sqrt
53×cbrt-unprod
50×*-un-lft-identity
45×add-cube-cbrt
36×associate-*l*
28×associate-*l/
26×unpow-prod-down
25×associate-*r/
23×cbrt-undiv
19×frac-times associate-/r*
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×cbrt-prod sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 343
Calls
4 calls:
131.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
570.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
669.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (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:
377.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
247.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
751.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
845.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify625.0ms

Counts
355 → 355
Iterations

Useful iterations: done (610.0ms)

IterNodesCost
054415144
1152113905
done500112441

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 4.3b

regimes814.0ms

Accuracy

-2% (6.7b remaining)

Error of 14.8b against oracle of 8.1b and baseline of 14.7b

bsearch1.2s

Steps
ItersRangePoint
9
1.9725328048955509e-184
3.537376337853017e-175
2.0078384353861574e-184
10
-4.9594321442529094e-287
-8.214583886015286e-301
-8.381505698861731e-301
9
-1.970119453595179e-261
-2.4983850756070044e-266
-1.889101273676245e-261
9
-1.0646804711485327e-228
-1.3542017881429095e-235
-3.3963588428902944e-234
6
-2.5615213219586237e-118
-2.6508022011786007e-119
-2.7131965443643853e-119

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
089375
1112375
done112375

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s2104×body1280valid
947.0ms1726×body640valid
706.0ms5938×body80valid
322.0ms872×body320valid
126.0ms463×body160valid