Details

Time bar (total: 29.1s)

sample151.0ms

Algorithm
intervals
Results
50.0ms139×body80valid
32.0ms40×body1280valid
25.0ms43×body640valid
9.0ms22×body320valid
4.0ms12×body160valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite509.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
43.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
39.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
278.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
267.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
369.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
262.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.3s

Counts
102 → 102
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02142168
16011954
228131741
done50021735

prune890.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.0b

localize70.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.1b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite378.0ms

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:
132.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
98.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
68.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
75.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
439.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
213.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
448.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
439.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01562277
13562140
213291854
done50001805

prune980.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.0b

localize85.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
6.9b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log add-cbrt-cube
11×cbrt-prod
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
6×pow-prod-down prod-exp cbrt-unprod
4×cbrt-div sqrt-div add-log-exp
3×flip3-+ associate-*l* flip-+ distribute-lft-out
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 68
Calls
4 calls:
100.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
65.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
128.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
78.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
210.0ms
(* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (* (* -2.0 J) (cos (/ K 2.0))))
432.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
284.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
433.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts
80 → 80
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01702243
13822097
214431820
done50001802

prune953.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize106.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite206.0ms

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:
2.0ms
(sqrt (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
63.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
69.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
68.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
387.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
389.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
420.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.6s

Counts
67 → 67
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0951672
11951542
25361425
326321401
done50001392

prune793.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.0b

regimes951.0ms

Accuracy

87.8% (0.7b remaining)

Error of 13.4b against oracle of 12.7b and baseline of 18.1b

bsearch7.0ms

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.0s1542×body1280valid
1.4s4303×body80valid
888.0ms1237×body640valid
424.0ms595×body320valid
107.0ms330×body160valid