Details

Time bar (total: 28.2s)

sample138.0ms

Algorithm
intervals
Results
41.0ms40×body640valid
39.0ms49×body1280valid
21.0ms140×body80valid
5.0ms13×body320valid
4.0ms14×body160valid

simplify3.4s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize62.0ms

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)
7.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite227.0ms

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:
14.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
126.0ms
(* (* (* -2.0 J) (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)))

series767.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
209.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
270.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
233.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts
97 → 97
Iterations
IterNodes
done5002
22368
1508
0192

prune803.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.4b

localize65.0ms

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)
7.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp associate-*r/ sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
14.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
27.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
109.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
90.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
201.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
262.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (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)))

simplify1.9s

Counts
94 → 94
Iterations
IterNodes
done5002
22427
1544
0199

prune709.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.4b

localize101.0ms

Local error

Found 4 expressions with local error:

7.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
60.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
61.0ms
(sqrt (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)))
92.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
327.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
296.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
194.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
225.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.0s

Counts
88 → 88
Iterations
IterNodes
done5000
31471
2475
1195
097

prune683.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.4b

localize139.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
5.4b
(sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0))))
7.6b
(* (* -2.0 J) (* (cos (/ K 2.0)) (/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))))
19.6b
(/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))

rewrite921.0ms

Algorithm
rewrite-expression-head
Rules
59×sqrt-prod
42×times-frac
38×add-sqr-sqrt
36×*-un-lft-identity add-cube-cbrt
27×add-cbrt-cube add-exp-log
18×pow1
13×prod-exp cbrt-unprod
8×sqrt-div cube-unmult pow3 pow-prod-down sum-cubes
7×associate-/l*
6×associate-/r*
4×flip3-+ flip-+ add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-/r/ associate-/l/
1×sqrt-undiv clear-num frac-2neg associate-*r* associate-*l* *-commutative div-inv
Counts
4 → 130
Calls
4 calls:
209.0ms
(sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
10.0ms
(sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0))))
352.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))))
345.0ms
(/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))

series3.4s

Counts
4 → 12
Calls
4 calls:
253.0ms
(sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0)))))
854.0ms
(sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0))))
1.0s
(* (* -2.0 J) (* (cos (/ K 2.0)) (/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))))
1.2s
(/ (sqrt (+ (* (* 1.0 1.0) 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0))))) (sqrt (+ (* 1.0 1.0) (* (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) (- (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) 2.0) 1.0)))))

simplify2.6s

Counts
142 → 142
Iterations
IterNodes
done5000
22854
1614
0259

prune1.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.4b

regimes821.0ms

Accuracy

89.1% (0.6b remaining)

Error of 13.2b against oracle of 12.6b and baseline of 18.0b

bsearch4.0ms

simplify11.0ms

Iterations
IterNodes
done45
145
032

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s1487×body1280valid
1.3s1300×body640valid
736.0ms4239×body80valid
412.0ms647×body320valid
81.0ms330×body160valid