Details

Time bar (total: 56.6s)

sample776.0ms

Algorithm
intervals
Results
221.0ms125×body1280valid
211.0ms69×body2560valid
162.0ms20×body5120valid
88.0ms83×body640valid
24.0ms32×body320valid
15.0ms63×body80valid
7.0ms17×body160valid

simplify829.0ms

Counts
1 → 1
Iterations

Useful iterations: done (828.0ms)

IterNodesCost
01925
14425
214625
384823
done500121

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.8b
(/ (pow t 3.0) (* l l))
27.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×pow-prod-down add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 354
Calls
4 calls:
34.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
94.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
25.0ms
(/ (pow t 3.0) (* l l))
177.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
350.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
507.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
310.0ms
(/ (pow t 3.0) (* l l))
827.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify769.0ms

Counts
366 → 366
Iterations

Useful iterations: done (747.0ms)

IterNodesCost
066210242
117649771
done50009289

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.6b
(* (pow k 2.0) (pow t 1.0))
14.6b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
21.0ms
(* (pow k 2.0) (pow t 1.0))
86.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
547.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
109.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
460.0ms
(* (pow k 2.0) (pow t 1.0))
1.2s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify771.0ms

Counts
612 → 612
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
048315017
1135513309
done500013047

prune981.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite742.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1460
Calls
4 calls:
8.0ms
(pow (sin k) 2)
100.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
32.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
251.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow (sin k) 2)
545.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
129.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.0s

Counts
1472 → 1472
Iterations

Useful iterations: done (950.0ms)

IterNodesCost
059750343
1180834674
done500132849

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.6b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
3.7b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
5.4b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.7b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
22030×add-exp-log
15939×prod-exp
12558×pow-exp
9152×div-exp
6078×pow-to-exp
1300×rec-exp 1-exp
34×unpow-prod-down
32×add-cbrt-cube
27×associate-*l*
26×times-frac
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
13×cbrt-unprod
12×associate-*r*
8×associate-/r* sqr-pow
6×cbrt-undiv
5×pow1
4×div-inv unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×associate-*l/ *-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 4425
Calls
4 calls:
7.0ms
(pow (sin k) 2)
247.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
120.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
21.0ms
(pow (sin k) 2)
620.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
124.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
557.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify2.5s

Counts
4437 → 4437
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01155192116
13810162904
done5000153323

prune1.7s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.6b

regimes617.0ms

Accuracy

13.6% (6.2b remaining)

Error of 17.6b against oracle of 11.3b and baseline of 18.5b

bsearch911.0ms

Steps
ItersRangePoint
10
2.169088006431291e+144
2.28798361624408e+157
1.1675553419995746e+154

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
04383
15278
25478
35678
done5678

end0.0ms

sample32.2s

Algorithm
intervals
Results
9.5s4121×body1280valid
9.3s2306×body2560valid
7.6s923×body5120valid
2.8s2524×body640valid
1.2s982×body320valid
626.0ms2047×body80valid
184.0ms407×body160valid