Details

Time bar (total: 9.9s)

sample59.0ms

Algorithm
intervals
Results
18.0ms53×body1280valid
12.0ms49×body640valid
8.0ms129×body80valid
4.0ms20×body320valid
1.0ms5×body160valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03413
17513
213913
320713
437513
5137313
6500113
done500113

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(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)))
9.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
17×add-sqr-sqrt
15×*-un-lft-identity
12×prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×unpow-prod-down sqrt-prod
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow times-frac div-exp hypot-def
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out sqr-pow
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv
Counts
4 → 96
Calls
4 calls:
18.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
20.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
67.0ms
(sqrt (+ 1.0 (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))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
139.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
149.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
196.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify57.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04641076
11988966
25001965
done5001965

prune323.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
9.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*l* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 88
Calls
4 calls:
17.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
18.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
17.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
53.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series699.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
51.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
48.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
509.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify60.0ms

Counts
100 → 100
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0489993
12344770
25001770
done5001770

prune304.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
9.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
9.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*r* sqrt-prod
10×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 85
Calls
4 calls:
179.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
56.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.1s

Counts
4 → 12
Calls
4 calls:
523.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
563.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
508.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
503.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify71.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
03991872
118301509
250021503
done50021503

prune377.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
9.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
9.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
9.2b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1
19×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 122
Calls
4 calls:
19.0ms
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.1s

Counts
4 → 12
Calls
4 calls:
508.0ms
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
521.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
518.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
515.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify184.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02411874
18381729
245491678
350011678
done50011678

prune467.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.6b

regimes282.0ms

Accuracy

0% (0.3b remaining)

Error of 7.7b against oracle of 7.4b and baseline of 7.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414
done2414

end0.0ms

sample1.6s

Algorithm
intervals
Results
539.0ms1505×body1280valid
316.0ms1286×body640valid
293.0ms4277×body80valid
119.0ms631×body320valid
38.0ms304×body160valid