Details

Time bar (total: 8.3s)

sample106.0ms

Algorithm
intervals
Results
40.0ms92×body1280valid
17.0ms71×body640valid
12.0ms248×body80valid
9.0ms58×body320valid
3.0ms26×body160valid

simplify373.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0239
1419
2839
31739
42719
55339
610239
713959
843699
950029
done50029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
0.0b
(* J (- (exp l) (exp (- l))))
4.2b
(- (exp l) (exp (- l)))

rewrite118.0ms

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:
59.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
45.0ms
(* J (- (exp l) (exp (- l))))
13.0ms
(- (exp l) (exp (- l)))

series196.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
60.0ms
(* J (- (exp l) (exp (- l))))
39.0ms
(- (exp l) (exp (- l)))

simplify35.0ms

Counts
69 → 69
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0264566
11116481
25001475
done5001475

prune204.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
0.0b
(* 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)))

rewrite133.0ms

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 add-log-exp
8×unpow-prod-down
7×associate-*l* unswap-sqr
5×cbrt-unprod
4×cube-prod sqr-pow
3×pow-prod-down sum-log *-commutative
2×pow-to-exp flip3-+ associate-*r/ associate-*l/ pow-exp flip-+
1×+-commutative cube-mult associate-+r+ unpow3
Counts
4 → 89
Calls
4 calls:
20.0ms
(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
11.0ms
(* 1/60 (pow l 5))
14.0ms
(* 1/3 (pow l 3))
85.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))
54.0ms
(* 1/60 (pow l 5))
39.0ms
(* 1/3 (pow l 3))
176.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))

simplify65.0ms

Counts
101 → 101
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0443717
12193619
25001619
done5001619

prune298.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 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))))
0.2b
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

rewrite164.0ms

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:
11.0ms
(* 1/60 (pow l 5))
12.0ms
(* 1/3 (pow l 3))
69.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
68.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* 1/60 (pow l 5))
43.0ms
(* 1/3 (pow l 3))
171.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
88.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))

simplify69.0ms

Counts
108 → 108
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0444856
12079731
25001731
done5001731

prune381.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))) (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))))
14.0b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
14.0b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
14.0b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/ associate-*l/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
94.0ms
(* (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))) (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))))
58.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
58.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
59.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
372.0ms
(* (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))) (cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))))
307.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
312.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
313.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))

simplify62.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04122067
115001890
250021781
done50021781

prune444.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03012
13012
done3012

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2761×body1280valid
609.0ms2559×body640valid
440.0ms8339×body80valid
236.0ms1483×body320valid
74.0ms734×body160valid