Details

Time bar (total: 6.0s)

sample117.0ms

Algorithm
intervals
Results
49.0ms61×body1280valid
20.0ms36×body640valid
14.0ms125×body80valid
10.0ms26×body320valid
2.0ms8×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0550124

prune14.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.4b

Counts
2 → 2

localize16.0ms

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)
6.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite39.0ms

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:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
17.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
31.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049831601
149831601

prune239.0ms

Filtered
69 candidates to 97 candidates (-40.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New90797
Fresh101
Picked011
Done000
Total91899

Merged error: 11.0b

Counts
99 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series190.0ms

Counts
4 → 12
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))))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049041580
149041580

prune336.0ms

Filtered
62 candidates to 88 candidates (-41.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh156
Picked011
Done011
Total88896

Merged error: 11.0b

Counts
96 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×sqrt-prod
12×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-div
7×pow1 cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 65
Calls
4 calls:
10.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

series163.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
36.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
048521476
148521476

prune414.0ms

Filtered
57 candidates to 77 candidates (-35.1%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New77077
Fresh055
Picked011
Done022
Total77885

Merged error: 11.0b

Counts
85 → 8

localize10.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-exp-log add-cbrt-cube
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1×associate-*l* *-commutative add-log-exp
Counts
1 → 18
Calls
1 calls:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))

series9.0ms

Counts
1 → 3
Calls
1 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
05075180

prune33.0ms

Filtered
14 candidates to 21 candidates (-50.0%)
Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New14721
Fresh224
Picked011
Done033
Total161329

Merged error: 11.0b

Counts
29 → 13

regimes654.0ms

Accuracy

92.3% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04599
14599

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s1515×body1280valid
691.0ms1204×body640valid
497.0ms4303×body80valid
264.0ms644×body320valid
92.0ms337×body160valid

Profiling

Loading profile data...