Details

Time bar (total: 8.3s)

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

sample107.0ms

Algorithm
intervals
Results
42.0ms52×body1280valid
22.0ms39×body640valid
21.0ms140×body80valid
6.0ms16×body320valid
3.0ms9×body160valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
0694424

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: 19.7b

Counts
2 → 2

localize20.0ms

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)
7.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

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)
15.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

series119.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
32.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
45.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify46.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050301611

prune282.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New871097
Fresh101
Picked011
Done000
Total881199

Merged error: 12.8b

Counts
99 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.3b
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
16.4b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
16.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite30.0ms

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:
8.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (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)))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
37.0ms
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
61.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
64.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049361766
149361766

prune373.0ms

Filtered
64 candidates to 82 candidates (-28.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New80282
Fresh189
Picked101
Done011
Total821193

Merged error: 12.8b

Counts
93 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

7.4b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
11.3b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
11.3b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

rewrite32.0ms

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:
9.0ms
(cbrt (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)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

series161.0ms

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)))
33.0ms
(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)))

simplify62.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049911476
149911476

prune405.0ms

Filtered
59 candidates to 77 candidates (-30.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New77077
Fresh099
Picked011
Done011
Total771188

Merged error: 12.8b

Counts
88 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.1b
(* (* (* 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))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

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)))
23.0ms
(* (* (* 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))))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))
48.0ms
(* (* (* 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))))
35.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049311366
149311366

prune234.0ms

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

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New78583
Fresh268
Picked101
Done022
Total811394

Merged error: 12.7b

Counts
94 → 13

regimes751.0ms

Accuracy

89.2% (0.6b remaining)

Error of 13.0b against oracle of 12.4b and baseline of 17.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
011999
111999

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.3s1493×body1280valid
771.0ms1327×body640valid
509.0ms4260×body80valid
238.0ms594×body320valid
87.0ms326×body160valid
0.0ms2×body80invalid

Profiling

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