Details

Time bar (total: 8.2s)

analyze1.8s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14

sample103.0ms

Algorithm
intervals
Results
44.0ms53×body1280valid
16.0ms143×body80valid
15.0ms26×body640valid
8.0ms19×body320valid
4.0ms15×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0550124

prune15.0ms

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: 17.4b

Counts
2 → 2

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)
7.8b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

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)
14.0ms
(* (* (* -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)))

series125.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
34.0ms
(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))))
38.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049831601
149831601

prune275.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh101
Picked011
Done000
Total90999

Merged error: 13.7b

Counts
99 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

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))))
7.0ms
(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)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(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))))
38.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
35.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049041580
149041580

prune361.0ms

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

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh077
Picked011
Done011
Total871097

Merged error: 13.7b

Counts
97 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
15.0b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
15.0b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×sqrt-prod
12×add-sqr-sqrt
9×add-cube-cbrt
8×cbrt-prod
7×pow1
6×sqrt-div
5×sqrt-pow1
4×add-exp-log cbrt-div flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square pow1/2
2×pow1/3
Counts
4 → 66
Calls
4 calls:
8.0ms
(sqrt (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)))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
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)))
63.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
62.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
048361514
148361514

prune445.0ms

Filtered
58 candidates to 78 candidates (-34.5%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New78078
Fresh077
Picked011
Done022
Total781088

Merged error: 13.7b

Counts
88 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.8b
(* (* (* J (* -2.0 (* (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))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
24×add-exp-log
18×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)))
21.0ms
(* (* (* J (* -2.0 (* (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))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series114.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (cos (/ K 2.0)))
17.0ms
(cbrt (cos (/ K 2.0)))
43.0ms
(* (* (* J (* -2.0 (* (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))))
36.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
051471358

prune235.0ms

Filtered
55 candidates to 83 candidates (-50.9%)
Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New80383
Fresh066
Picked011
Done033
Total801393

Merged error: 13.6b

Counts
93 → 13

regimes722.0ms

Accuracy

91.5% (0.4b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 17.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04599
14599

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1417×body1280valid
745.0ms1261×body640valid
501.0ms4348×body80valid
251.0ms614×body320valid
101.0ms360×body160valid
0.0ms1×body160invalid
0.0ms1×body80invalid

Profiling

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