Details

Time bar (total: 24.6s)

sample125.0ms

Algorithm
intervals
Results
44.0ms54×body1280valid
29.0ms55×body640valid
24.0ms218×body80valid
6.0ms17×body320valid
4.0ms18×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
14725
215325
376425
4390425
done500025

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.4b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
13.9b
(/ (pow t 3.0) (* l l))

rewrite376.0ms

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:
18.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
36.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
310.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
255.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
319.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
636.0ms
(* (* (* (/ (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))

simplify1.7s

Counts
156 → 156
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
02553209
18053070
242562565
done50002565

prune549.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.3b

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.2b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.4b
(* (* (* (/ (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))

rewrite600.0ms

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:
82.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
4.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
480.0ms
(* (* (* (/ (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))
238.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
199.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
748.0ms
(* (* (* (/ (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))

simplify446.0ms

Counts
241 → 241
Iterations

Useful iterations: done (437.0ms)

IterNodesCost
04296958
113526583
done50016450

prune1.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (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)))
3.4b
(* (* (* (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))
5.2b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.4b
(* (* (* (* (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))

rewrite886.0ms

Algorithm
rewrite-expression-head
Rules
1884×add-exp-log
1325×prod-exp
432×div-exp
334×pow-exp
199×pow-to-exp
151×add-cbrt-cube
96×cbrt-unprod
47×associate-*l/
40×add-sqr-sqrt
37×associate-*l*
35×frac-times
34×pow1 times-frac
33×associate-*r/
32×*-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down pow-prod-down
19×cbrt-undiv
16×tan-quot
12×associate-*r*
10×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 → 486
Calls
4 calls:
39.0ms
(* (* (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)))
128.0ms
(* (* (* (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))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
640.0ms
(* (* (* (* (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (* (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)))
365.0ms
(* (* (* (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))
248.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
727.0ms
(* (* (* (* (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))

simplify851.0ms

Counts
498 → 498
Iterations

Useful iterations: done (830.0ms)

IterNodesCost
052621737
1181216089
done500015851

prune974.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (/ (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)))
3.4b
(* (* (/ (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))
5.2b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.4b
(* (* (* (/ (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))

rewrite865.0ms

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:
59.0ms
(* (/ (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)))
116.0ms
(* (* (/ (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))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
597.0ms
(* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
293.0ms
(* (/ (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)))
368.0ms
(* (* (/ (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))
235.0ms
(* (/ (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))

simplify1.0s

Counts
597 → 597
Iterations

Useful iterations: done (991.0ms)

IterNodesCost
073624822
1250422690
done500018902

prune1.8s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 8.2b

regimes894.0ms

Accuracy

16.2% (4.9b remaining)

Error of 13.6b against oracle of 8.7b and baseline of 14.6b

bsearch356.0ms

Steps
ItersRangePoint
9
4.651424770938929e-210
1.8276054982907742e-201
2.6035027352513706e-209
7
-6.584027504711929e-248
-3.8939625330993975e-249
-5.610783428824226e-248

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
047143
16395
done6395

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s2038×body1280valid
1.2s1738×body640valid
703.0ms5940×body80valid
316.0ms836×body320valid
117.0ms447×body160valid