Details

Time bar (total: 52.4s)

sample883.0ms

Algorithm
intervals
Results
334.0ms90×body2560valid
212.0ms120×body1280valid
178.0ms32×body5120valid
74.0ms76×body640valid
23.0ms35×body320valid
14.0ms65×body80valid
6.0ms12×body160valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01925
14425
214825
384123
done500121

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.5b
(/ (pow t 3.0) (* l l))
29.0b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite363.0ms

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×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 362
Calls
4 calls:
36.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
99.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.0ms
(/ (pow t 3.0) (* l l))
165.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
319.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
417.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
275.0ms
(/ (pow t 3.0) (* l l))
878.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify840.0ms

Counts
374 → 374
Iterations

Useful iterations: done (821.0ms)

IterNodesCost
067010352
117859880
done50019414

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b
(* (pow k 2.0) (pow t 1.0))
16.6b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 575
Calls
4 calls:
4.0ms
(pow (sin k) 2)
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
19.0ms
(* (pow k 2.0) (pow t 1.0))
105.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
24.0ms
(pow (sin k) 2)
96.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
432.0ms
(* (pow k 2.0) (pow t 1.0))
966.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify602.0ms

Counts
587 → 587
Iterations

Useful iterations: done (580.0ms)

IterNodesCost
044614510
1135512991
done500012210

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.6b
(* (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)))

rewrite511.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1468
Calls
4 calls:
64.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(pow (sin k) 2)
21.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
174.0ms
(* (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)))

series1.6s

Counts
4 → 12
Calls
4 calls:
460.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
24.0ms
(pow (sin k) 2)
135.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
966.0ms
(* (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)))

simplify967.0ms

Counts
1480 → 1480
Iterations

Useful iterations: done (895.0ms)

IterNodesCost
060550477
1205133540
done500031701

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.2b
(/ (pow l 2) (sin k))
2.7b
(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
16.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
4561×add-exp-log
3350×prod-exp
1881×pow-exp
1593×div-exp
1044×pow-to-exp
310×rec-exp 1-exp
77×add-sqr-sqrt
76×times-frac
48×add-cube-cbrt *-un-lft-identity
45×add-cbrt-cube
30×unpow-prod-down
29×associate-*r*
24×associate-*l*
16×cbrt-unprod
12×cbrt-undiv
11×associate-/l*
10×unswap-sqr sqr-pow
9×unpow2
7×pow1
5×associate-*r/ div-inv
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down inv-pow
Counts
4 → 1139
Calls
4 calls:
61.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
10.0ms
(/ (pow l 2) (sin k))
54.0ms
(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
256.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

series1.6s

Counts
4 → 12
Calls
4 calls:
487.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
65.0ms
(/ (pow l 2) (sin k))
105.0ms
(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
917.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

simplify1.3s

Counts
1151 → 1151
Iterations

Useful iterations: done (1.3s)

IterNodesCost
068338631
1231824976
done500024482

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.7b

regimes698.0ms

Accuracy

51.5% (3.6b remaining)

Error of 12.8b against oracle of 9.3b and baseline of 16.6b

bsearch3.0ms

simplify32.0ms

Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
059122
174116
277114
380114
done80114

end0.0ms

sample31.8s

Algorithm
intervals
Results
9.4s2303×body2560valid
8.0s3994×body1280valid
7.5s939×body5120valid
3.9s2569×body640valid
1.3s1007×body320valid
657.0ms2048×body80valid
199.0ms432×body160valid