Details

Time bar (total: 26.7s)

sample93.0ms

Algorithm
intervals
Results
26.0ms44×body1280valid
20.0ms45×body640valid
15.0ms137×body80valid
6.0ms19×body320valid
3.0ms11×body160valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
63236
5492
4208
3135
271
134
017

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite285.0ms

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-*l* associate-*r/ *-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:
15.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
155.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
93.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
219.0ms
(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))))
171.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.1s

Counts
97 → 97
Iterations
IterNodes
done5002
22368
1508
0192

prune670.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.5b

localize79.0ms

Local error

Found 4 expressions with local error:

10.2b
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×cbrt-prod pow1
9×sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log add-log-exp
3×distribute-lft-out
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 69
Calls
4 calls:
75.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
50.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
29.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
40.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
345.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
343.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
360.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
356.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts
81 → 81
Iterations
IterNodes
done5001
31220
2441
1214
0116

prune840.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.5b

localize155.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.2b
(sqrt (* (* (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-div
58×cbrt-div
30×flip3-+ flip-+
28×frac-times
14×associate-*l/
13×*-un-lft-identity
11×pow1
8×cbrt-prod add-sqr-sqrt associate-*r/
7×add-cube-cbrt
5×sqrt-pow1 pow1/3 pow-prod-down sqrt-prod
4×add-cbrt-cube add-exp-log add-log-exp
3×distribute-lft-out
2×pow1/2
1×rem-sqrt-square
Counts
4 → 83
Calls
4 calls:
55.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
385.0ms
(sqrt (* (* (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
25.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
50.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
250.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
363.0ms
(sqrt (* (* (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
341.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
344.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.9s

Counts
95 → 95
Iterations
IterNodes
done5000
31635
2703
1376
0200

prune1.4s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.9b
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite636.0ms

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)))
2.0ms
(cbrt (cos (/ K 2.0)))
554.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
74.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series948.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(cbrt (cos (/ K 2.0)))
212.0ms
(cbrt (cos (/ K 2.0)))
294.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
208.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.2s

Counts
86 → 86
Iterations
IterNodes
done5000
22020
1400
0150

prune524.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 12.4b

regimes869.0ms

Accuracy

88.5% (0.6b remaining)

Error of 13.0b against oracle of 12.4b and baseline of 17.7b

bsearch4.0ms

simplify16.0ms

Iterations
IterNodes
done45
145
032

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.6s1475×body1280valid
807.0ms1305×body640valid
803.0ms4308×body80valid
455.0ms633×body320valid
83.0ms282×body160valid