Details

Time bar (total: 21.5s)

sample88.0ms

Algorithm
intervals
Results
28.0ms47×body1280valid
13.0ms145×body80valid
12.0ms35×body640valid
7.0ms22×body320valid
1.0ms7×body160valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
21.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
32.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
278.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
95.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series838.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
204.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
283.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
216.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts
102 → 102
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02142168
16011954
228131741
done50021735

prune486.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite446.0ms

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:
128.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
102.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
83.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
130.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
286.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
293.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
226.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
212.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify919.0ms

Counts
88 → 88
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
0971968
11951666
24701604
314521598
done50011592

prune992.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.5b

localize46.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.8b
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

rewrite467.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
26×cbrt-prod
25×*-un-lft-identity
19×add-sqr-sqrt
15×add-cube-cbrt
12×sqrt-div
10×unpow-prod-down cube-prod
8×pow1
6×sqrt-pow1
5×distribute-lft-out
4×add-exp-log rem-sqrt-square flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 91
Calls
4 calls:
134.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
92.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
101.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
134.0ms
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
344.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
203.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
179.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
353.0ms
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: 2 (303.0ms)

IterNodesCost
01422815
13422146
216452112
done50012112

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.4b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.5b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
13.9b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.9b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite278.0ms

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:
97.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
70.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
44.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
65.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
315.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
180.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
367.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
320.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify832.0ms

Counts
82 → 82
Iterations

Useful iterations: done (827.0ms)

IterNodesCost
01562277
13562140
213291854
done50001805

prune559.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.5b

regimes455.0ms

Accuracy

92.1% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 17.7b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample3.2s

Algorithm
intervals
Results
959.0ms1448×body1280valid
857.0ms4429×body80valid
567.0ms1227×body640valid
284.0ms590×body320valid
101.0ms309×body160valid