Details

Time bar (total: 21.2s)

sample140.0ms

Algorithm
intervals
Results
56.0ms51×body1280valid
26.0ms47×body640valid
17.0ms127×body80valid
8.0ms22×body320valid
3.0ms9×body160valid

simplify2.7s

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize52.0ms

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)
7.1b
(* (* (* -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
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:
28.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
31.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
144.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
103.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
222.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
314.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify1.4s

Counts
97 → 97
Iterations
IterNodes
done5002
22368
1508
0192

prune614.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.9b

localize32.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
7.1b
(sqrt (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)))
9.9b
(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

rewrite350.0ms

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:
77.0ms
(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
82.0ms
(sqrt (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)))
77.0ms
(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
282.0ms
(sqrt (sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0))))
339.0ms
(sqrt (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)))
204.0ms
(sqrt (+ 1.0 (pow (/ (/ U 2.0) (* J (cos (/ K 2.0)))) 2.0)))

simplify689.0ms

Counts
88 → 88
Iterations
IterNodes
done5000
31462
2471
1194
097

prune757.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.1b
(* (* (* (* -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))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
16×add-cbrt-cube
15×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 → 71
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
997.0ms
(* (* (* (* -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))))
52.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series902.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(cbrt (cos (/ K 2.0)))
219.0ms
(cbrt (cos (/ K 2.0)))
274.0ms
(* (* (* (* -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)))

simplify1.1s

Counts
83 → 83
Iterations
IterNodes
done5000
21891
1382
0147

prune660.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.9b

localize87.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0))) (* (* -2.0 J) (cos (/ K 2.0))))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
9.9b
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))

rewrite530.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×pow1 sqrt-prod
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-div
7×associate-*l*
6×pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/
1×associate-*r* *-commutative
Counts
4 → 75
Calls
4 calls:
274.0ms
(* (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0))) (* (* -2.0 J) (cos (/ K 2.0))))
76.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
94.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
82.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))

series952.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(* (sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0))) (* (* -2.0 J) (cos (/ K 2.0))))
193.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
200.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))
226.0ms
(sqrt (+ 1.0 (pow (/ U (* (cos (/ K 2.0)) (* 2.0 J))) 2.0)))

simplify1.2s

Counts
87 → 87
Iterations
IterNodes
done5000
2965
1268
0104

prune781.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.9b

regimes835.0ms

Accuracy

78.5% (1.2b remaining)

Error of 13.4b against oracle of 12.2b and baseline of 17.7b

bsearch4.0ms

simplify7.0ms

Iterations
IterNodes
done44
144
032

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s1469×body1280valid
838.0ms1311×body640valid
649.0ms4324×body80valid
262.0ms602×body320valid
168.0ms296×body160valid