Details

Time bar (total: 50.1s)

sample231.0ms

Algorithm
intervals
Results
59.0ms79×body1280valid
49.0ms49×body320valid
42.0ms84×body640valid
32.0ms291×body80valid
5.0ms24×body160valid

simplify25.0s

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01415
12414
24514
39014
418914
528114
635814
749314
864614
9103114
10180014
11258614
12324314
13356414
14364814
done364814

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.0b
(- (exp l) (exp (- l)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- fma-udef distribute-lft-out-- difference-of-squares
Counts
2 → 38
Calls
2 calls:
0.0ms
(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
39.0ms
(- (exp l) (exp (- l)))

series302.0ms

Counts
2 → 6
Calls
2 calls:
259.0ms
(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
43.0ms
(- (exp l) (exp (- l)))

simplify3.2s

Counts
44 → 44
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0108792
1227645
2548509
32017452
done5000443

prune196.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b
(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0ms
(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series459.0ms

Counts
2 → 6
Calls
2 calls:
107.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
352.0ms
(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify1.2s

Counts
26 → 26
Iterations

Useful iterations: 3 (237.0ms)

IterNodesCost
055559
1102551
2292482
31267468
done5001468

prune167.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.5b
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.5b
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
0.6b
(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
1.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
15.0ms
(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))

series3.4s

Counts
4 → 12
Calls
4 calls:
666.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
639.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
672.0ms
(cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U))
1.4s
(* (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)) (cbrt (fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)))

simplify1.5s

Counts
93 → 93
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01363978
12953721
27193404
319862881
done50002693

prune704.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (- (exp l) (exp (- l)))) (cbrt (- (exp l) (exp (- l)))))
6.0b
(- (exp l) (exp (- l)))
6.0b
(- (exp l) (exp (- l)))
6.0b
(- (exp l) (exp (- l)))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×*-un-lft-identity
33×add-cube-cbrt
28×cbrt-prod
27×prod-diff
12×cbrt-div
11×pow1
10×swap-sqr add-log-exp
9×flip3-- fma-neg flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log pow1/3
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u unswap-sqr
3×sub-neg diff-log
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 142
Calls
4 calls:
146.0ms
(* (cbrt (- (exp l) (exp (- l)))) (cbrt (- (exp l) (exp (- l)))))
33.0ms
(- (exp l) (exp (- l)))
17.0ms
(- (exp l) (exp (- l)))
31.0ms
(- (exp l) (exp (- l)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (cbrt (- (exp l) (exp (- l)))) (cbrt (- (exp l) (exp (- l)))))
71.0ms
(- (exp l) (exp (- l)))
40.0ms
(- (exp l) (exp (- l)))
71.0ms
(- (exp l) (exp (- l)))

simplify3.4s

Counts
154 → 154
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01522968
13042361
27292011
321931685
done50011627

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes358.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01921
12121
done2121

end0.0ms

sample8.1s

Algorithm
intervals
Results
2.9s2697×body1280valid
1.8s2569×body640valid
1.3s8369×body80valid
685.0ms1382×body320valid
293.0ms756×body160valid