Details

Time bar (total: 21.3s)

sample127.0ms

Algorithm
intervals
Results
45.0ms134×body80valid
30.0ms49×body1280valid
18.0ms40×body640valid
9.0ms23×body320valid
2.0ms10×body160valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize40.0ms

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)
5.8b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite487.0ms

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:
27.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
43.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
271.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series772.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
197.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
281.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
217.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.9s

Counts
97 → 97
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01932013
15081800
223991625
done50001613

prune470.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
0.9b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite284.0ms

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:
104.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
43.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
66.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
354.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
131.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
368.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
368.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01562277
13562140
213291854
done50001805

prune679.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
0.8b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 J))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×cbrt-prod
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cube-cbrt add-cbrt-cube
7×sqrt-prod
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* pow-prod-down prod-exp cbrt-unprod flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* *-commutative
Counts
4 → 67
Calls
4 calls:
88.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
19.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 J))
66.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
46.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
325.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
74.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* -2.0 J))
328.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
361.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify946.0ms

Counts
79 → 79
Iterations

Useful iterations: done (940.0ms)

IterNodesCost
01402019
13031885
210011679
done50011630

prune549.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
5.8b
(* (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* -2.0 J)) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite746.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
29×add-exp-log
20×add-cbrt-cube
19×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 74
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
676.0ms
(* (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* -2.0 J)) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
65.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
210.0ms
(cbrt (cos (/ K 2.0)))
243.0ms
(cbrt (cos (/ K 2.0)))
355.0ms
(* (* (* (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))) (* -2.0 J)) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
242.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts
86 → 86
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01512457
14012210
220011891
done50011441

prune406.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.0b

regimes594.0ms

Accuracy

90.8% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 18.1b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s1516×body1280valid
954.0ms1252×body640valid
547.0ms4334×body80valid
263.0ms596×body320valid
65.0ms304×body160valid