Details

Time bar (total: 46.5s)

sample103.0ms

Algorithm
intervals
Results
38.0ms87×body1280valid
23.0ms92×body640valid
14.0ms263×body80valid
6.0ms36×body320valid
2.0ms17×body160valid

simplify32.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01415
12315
24115
37615
412815
520915
641015
757815
894515
9315715
done500115

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* J (- (exp l) (exp (- l))))
0.0b
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.2b
(- (exp l) (exp (- l)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
8×associate-*r*
6×add-cube-cbrt
5×add-log-exp
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sub-neg flip3-- flip--
2×distribute-rgt-in distribute-lft-in associate-*l/ *-commutative distribute-lft-out-- difference-of-squares
1×diff-log unswap-sqr
Counts
3 → 60
Calls
3 calls:
21.0ms
(* J (- (exp l) (exp (- l))))
29.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
7.0ms
(- (exp l) (exp (- l)))

series183.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* J (- (exp l) (exp (- l))))
91.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms
(- (exp l) (exp (- l)))

simplify3.8s

Counts
69 → 69
Iterations

Useful iterations: 3 (529.0ms)

IterNodesCost
0114899
1271874
21002738
34694735
done5000735

prune213.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
0.1b
(* 1/60 (pow l 5))
0.1b
(* 1/3 (pow l 3))
0.1b
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×associate-*r*
19×add-exp-log
13×add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
9×pow1 prod-exp
8×unpow-prod-down
7×associate-*l* unswap-sqr
6×add-log-exp
5×cbrt-unprod
4×cube-prod sqr-pow
3×pow-prod-down *-commutative
2×pow-to-exp flip3-+ associate-*r/ associate-*l/ pow-exp flip-+
1×+-commutative cube-mult unpow3 sum-log
Counts
4 → 87
Calls
4 calls:
38.0ms
(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
6.0ms
(* 1/60 (pow l 5))
7.0ms
(* 1/3 (pow l 3))
44.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
349.0ms
(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
51.0ms
(* 1/60 (pow l 5))
50.0ms
(* 1/3 (pow l 3))
170.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify948.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (184.0ms)

IterNodesCost
01801661
14831533
219741379
done50001379

prune347.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/60 (pow l 5))
0.1b
(* 1/3 (pow l 3))
0.1b
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.1b
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×associate-*r*
21×add-exp-log
15×add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×associate-*l*
11×pow1
10×prod-exp
8×unpow-prod-down unswap-sqr
6×cbrt-unprod
4×cube-prod pow-prod-down associate-*l/ *-commutative add-log-exp sqr-pow
2×pow-to-exp flip3-+ associate-*r/ pow-exp flip-+
1×cube-mult unpow3
Counts
4 → 96
Calls
4 calls:
6.0ms
(* 1/60 (pow l 5))
7.0ms
(* 1/3 (pow l 3))
35.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
34.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* 1/60 (pow l 5))
37.0ms
(* 1/3 (pow l 3))
179.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
94.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify805.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
01811751
14641663
219111431
done50001431

prune388.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b
(* 1/3 (pow l 3))
0.1b
(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
29.8b
(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
24×associate-*r*
22×add-cbrt-cube
15×add-cube-cbrt *-un-lft-identity
9×associate-*l* prod-exp
8×pow1
7×cbrt-unprod
6×times-frac unswap-sqr
4×cbrt-undiv unpow-prod-down flip3-- cube-prod div-exp associate-*l/ associate-/r/ flip-- add-log-exp
3×associate-/r* *-commutative
2×pow-prod-down div-inv associate-/l/ sqr-pow
1×cube-mult pow-to-exp frac-2neg unpow3 associate-*r/ pow-exp clear-num associate-/l*
Counts
4 → 105
Calls
4 calls:
13.0ms
(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
10.0ms
(* 1/3 (pow l 3))
40.0ms
(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
19.0ms
(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
46.0ms
(* 1/3 (pow l 3))
394.0ms
(* J (/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))))
161.0ms
(/ (* (- (* 1/9 (pow l 6)) (* (+ (* 1/60 (pow l 5)) (* 2 l)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) (- (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))

simplify1.2s

Counts
117 → 117
Iterations

Useful iterations: 2 (237.0ms)

IterNodesCost
02224635
16174520
229113686
done50013686

prune521.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02224
13024
done3024

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s2639×body1280valid
718.0ms2682×body640valid
496.0ms8405×body80valid
251.0ms1415×body320valid
96.0ms775×body160valid