Details

Time bar (total: 13.9s)

sample56.0ms

Algorithm
intervals
Results
17.0ms48×body1280valid
10.0ms39×body640valid
9.0ms142×body80valid
4.0ms19×body320valid
1.0ms8×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
312724
416924
527224
677424
7313724
done500024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
7.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
57.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
27.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
138.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
201.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
149.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify918.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (386.0ms)

IterNodesCost
01932013
14551800
216301613
done50011613

prune290.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

localize19.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
26.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
24.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
26.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series725.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
218.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
144.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
144.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify697.0ms

Counts
88 → 88
Iterations

Useful iterations: 3 (173.0ms)

IterNodesCost
0971968
11921666
24501604
314141598
done50011598

prune347.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.7b

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.0b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
16.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log cbrt-prod add-cbrt-cube
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* *-commutative
Counts
4 → 70
Calls
4 calls:
24.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
17.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
15.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series777.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
102.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
229.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
222.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: 3 (489.0ms)

IterNodesCost
01562277
13552140
211031854
349561796
done50001796

prune358.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
16.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
13×pow1 add-exp-log add-cbrt-cube
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+ distribute-lft-out
1×associate-*r* *-commutative
Counts
4 → 63
Calls
4 calls:
17.0ms
(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series784.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (fabs (* (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))) (* (* -2.0 J) (cos (/ K 2.0))))
225.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
230.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
224.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: 3 (457.0ms)

IterNodesCost
01322668
13212050
210341748
347211724
done50001724

prune349.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.7b

regimes258.0ms

Accuracy

87.7% (0.7b remaining)

Error of 12.7b against oracle of 12.0b and baseline of 17.4b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample1.6s

Algorithm
intervals
Results
574.0ms1513×body1280valid
314.0ms1218×body640valid
300.0ms4355×body80valid
115.0ms593×body320valid
46.0ms323×body160valid