Details

Time bar (total: 30.8s)

sample121.0ms

Algorithm
intervals
Results
46.0ms50×body640valid
29.0ms48×body1280valid
13.0ms127×body80valid
6.0ms21×body320valid
2.0ms10×body160valid

simplify9.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
14324
213624
329224
done500024

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize40.0ms

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)
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite443.0ms

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-*r/ associate-*l* *-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:
40.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
47.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
241.0ms
(* (* (* -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)))

series847.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
227.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
318.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01932013
110701799
done50001613

prune477.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.4b

localize50.0ms

Local error

Found 4 expressions with local error:

1.3b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.3b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
17.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
17.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite256.0ms

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:
85.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
55.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
62.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
52.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
337.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
175.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
378.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
285.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01562277
16962137
done50001845

prune621.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.4b

localize38.0ms

Local error

Found 4 expressions with local error:

1.3b
(sqrt (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
17.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
17.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
17.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-div
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 sqrt-prod flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 55
Calls
4 calls:
1.0ms
(sqrt (fabs (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)))
35.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
44.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
352.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
349.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
351.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0951672
14071539
done50001413

prune597.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.4b

localize63.0ms

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))))
10.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite975.0ms

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:
2.0ms
(cbrt (cos (/ K 2.0)))
2.0ms
(cbrt (cos (/ K 2.0)))
854.0ms
(* (* (* (* -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))))
112.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
247.0ms
(cbrt (cos (/ K 2.0)))
257.0ms
(cbrt (cos (/ K 2.0)))
314.0ms
(* (* (* (* -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))))
207.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify3.6s

Counts
86 → 86
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01512457
17252210
done50001441

prune345.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.4b

regimes669.0ms

Accuracy

91.3% (0.5b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 18.0b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.2s1486×body1280valid
1.2s4321×body80valid
1.0s1232×body640valid
223.0ms654×body320valid
76.0ms314×body160valid