Details

Time bar (total: 20.4s)

sample106.0ms

Algorithm
intervals
Results
37.0ms45×body640valid
27.0ms46×body1280valid
18.0ms144×body80valid
4.0ms15×body320valid
1.0ms6×body160valid

simplify2.1s

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize59.0ms

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)
8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite294.0ms

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:
23.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
169.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
80.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
207.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
252.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
243.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts
97 → 97
Iterations
IterNodes
done5002
22368
1508
0192

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* J (cos (/ K 2.0)))
0.2b
(pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)
8.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))))
9.9b
(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
22×times-frac
20×pow1
19×add-sqr-sqrt
18×*-un-lft-identity add-cbrt-cube
17×unpow-prod-down
16×add-cube-cbrt
11×prod-exp
9×pow-prod-down cbrt-unprod
6×div-exp
5×pow-exp
4×sqrt-div associate-*r* associate-*l* associate-*r/ sqrt-prod add-log-exp
3×pow-unpow
2×flip3-+ *-commutative flip-+ div-inv
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 93
Calls
4 calls:
13.0ms
(* J (cos (/ K 2.0)))
25.0ms
(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)))))
111.0ms
(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series749.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* J (cos (/ K 2.0)))
163.0ms
(pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)
301.0ms
(* (* -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)))

simplify1.2s

Counts
105 → 105
Iterations
IterNodes
done5002
22385
1708
0254

prune799.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.9b

localize66.0ms

Local error

Found 4 expressions with local error:

1.7b
(sqrt (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
8.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (fabs (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))))))
16.8b
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
16.8b
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
25×add-cbrt-cube add-exp-log
15×pow-prod-down prod-exp cbrt-unprod
14×*-un-lft-identity
13×cbrt-prod
10×add-sqr-sqrt
8×cbrt-div add-cube-cbrt
7×sqrt-prod
4×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
3×pow1/3 distribute-lft-out
2×rem-sqrt-square sqrt-pow1
1×pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 79
Calls
4 calls:
73.0ms
(sqrt (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
189.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (fabs (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))))))
53.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
35.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
384.0ms
(sqrt (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
380.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (fabs (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))))))
407.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
336.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

simplify1.0s

Counts
91 → 91
Iterations
IterNodes
done5001
21791
1438
0179

prune874.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.9b

localize95.0ms

Local error

Found 4 expressions with local error:

1.7b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.9b
(* (* (fabs (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0))) (* -2.0 J))
16.8b
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
16.8b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-cbrt-cube add-exp-log
14×*-un-lft-identity
13×cbrt-prod
10×add-sqr-sqrt
8×pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
7×sqrt-prod
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 71
Calls
4 calls:
78.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
21.0ms
(* (* (fabs (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0))) (* -2.0 J))
54.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
45.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
383.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
199.0ms
(* (* (fabs (cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))) (cos (/ K 2.0))) (* -2.0 J))
428.0ms
(cbrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))
322.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify804.0ms

Counts
83 → 83
Iterations
IterNodes
done5000
21452
1404
0180

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 14.9b

regimes731.0ms

Accuracy

92.6% (0.4b remaining)

Error of 13.4b against oracle of 13.0b and baseline of 18.4b

bsearch3.0ms

simplify5.0ms

Iterations
IterNodes
done48
148
036

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.6s1520×body1280valid
785.0ms1296×body640valid
589.0ms4242×body80valid
267.0ms623×body320valid
114.0ms324×body160valid