Details

Time bar (total: 46.1s)

sample270.0ms

Algorithm
intervals
Results
72.0ms31×body320valid
70.0ms66×body1280valid
54.0ms54×body640valid
34.0ms209×body80valid
6.0ms17×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
14.6b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
16.4b
(/ (pow t 3.0) (* l l))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
59×times-frac add-cbrt-cube
49×prod-exp
43×div-exp
39×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
19×cbrt-undiv
17×associate-/l*
16×associate-*l/
12×associate-*l* associate-/r/
11×pow1
10×tan-quot unpow-prod-down
8×pow-to-exp pow-exp
7×div-inv
6×associate-*r*
5×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u add-log-exp unswap-sqr sqr-pow
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 178
Calls
4 calls:
117.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
62.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
155.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
12.0ms
(/ (pow t 3.0) (* l l))

series2.3s

Counts
4 → 12
Calls
4 calls:
533.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
433.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
1.1s
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
312.0ms
(/ (pow t 3.0) (* l l))

simplify2.2s

Counts
190 → 190
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03714464
19304301
233093731
done50013730

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.9b

localize41.0ms

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))
7.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
14.6b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite675.0ms

Algorithm
rewrite-expression-head
Rules
333×add-exp-log
157×prod-exp
132×div-exp
103×times-frac
88×add-cbrt-cube
72×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
46×associate-*l/
36×cbrt-unprod
35×associate-*l*
33×pow-exp
29×cbrt-undiv
28×associate-/r/
25×frac-times
24×unpow-prod-down
22×pow-to-exp
20×tan-quot
19×associate-/l*
15×pow1 associate-*r/
10×cbrt-prod
8×sqr-pow
7×pow-prod-down div-inv
6×associate-*r* associate-/r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
239.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
66.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
19.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
329.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.2s

Counts
4 → 12
Calls
4 calls:
541.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
336.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
283.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.0s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify3.0s

Counts
278 → 278
Iterations

Useful iterations: done (3.0s)

IterNodesCost
05638511
114168094
248247039
done50007038

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.1b

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (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))
14.6b
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite855.0ms

Algorithm
rewrite-expression-head
Rules
1993×add-exp-log
947×div-exp
918×prod-exp
334×pow-exp
258×times-frac
199×pow-to-exp
164×add-cbrt-cube
135×associate-*l*
127×add-sqr-sqrt
114×add-cube-cbrt *-un-lft-identity
67×cbrt-unprod
60×cbrt-undiv
54×unpow-prod-down
49×associate-*l/
38×sqr-pow
29×associate-/r/
26×frac-times
20×tan-quot pow1
16×associate-*r/
14×associate-/l*
12×div-inv
10×cbrt-prod pow-prod-down
7×associate-*r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 622
Calls
4 calls:
97.0ms
(* (/ (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)))
320.0ms
(* (* (/ (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))
43.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
323.0ms
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.8s

Counts
4 → 12
Calls
4 calls:
877.0ms
(* (/ (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)))
522.0ms
(* (* (/ (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))
291.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(/ (/ 2.0 (* (* (/ (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))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.6s

Counts
634 → 634
Iterations

Useful iterations: done (1.6s)

IterNodesCost
091427064
1238324810
done500022632

prune3.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.2b

localize96.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.4b
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0)))
13.1b
(* (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1119×add-exp-log
600×prod-exp
435×div-exp
263×times-frac
159×add-sqr-sqrt
147×pow-exp
131×add-cube-cbrt *-un-lft-identity
127×add-cbrt-cube
88×pow-to-exp
67×associate-*r*
56×cbrt-unprod
45×associate-*l*
42×unpow-prod-down
41×cbrt-undiv
26×sqr-pow
19×associate-/l*
11×div-inv
10×pow1 cbrt-prod unswap-sqr
8×associate-*l/
7×associate-*r/
4×tan-quot expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times pow-prod-down associate-/r* associate-/r/ *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 448
Calls
4 calls:
33.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
185.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
21.0ms
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0)))
829.0ms
(* (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0))))

series2.3s

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
536.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
444.0ms
(/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0)))
1.1s
(* (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify1.0s

Counts
460 → 460
Iterations

Useful iterations: done (986.0ms)

IterNodesCost
071720114
1191218624
done500016742

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.9b

regimes997.0ms

Accuracy

61.8% (0.8b remaining)

Error of 12.2b against oracle of 11.3b and baseline of 13.5b

bsearch497.0ms

Steps
ItersRangePoint
9
3.3294204820464926e-135
5.9441740639567975e-127
1.4720658533520247e-129
5
-6.145090426699763e-123
-2.198741206744628e-123
-2.75256788644924e-123

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
044170
156119
done56119

end0.0ms

sample11.1s

Algorithm
intervals
Results
4.3s2072×body1280valid
3.0s1714×body640valid
1.6s5844×body80valid
1.2s873×body320valid
249.0ms430×body160valid