Details

Time bar (total: 8.3s)

analyze1.9s (22.7%)

Algorithm
1×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

sample101.0ms (1.2%)

Algorithm
1×intervals
Results
34.0ms41×body1280valid
25.0ms45×body640valid
14.0ms127×body80valid
13.0ms33×body320valid
3.0ms10×body160valid

simplify65.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0550124

prune13.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 20.7b

Counts
2 → 1

localize16.0ms (0.2%)

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)
8.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms (0.4%)

Algorithm
1×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:

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)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))

series123.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

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)))
33.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))

simplify82.0ms (1%)

Algorithm
1×egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
049831601
149831601

prune335.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh000
Picked011
Done000
Total89998

Merged error: 14.7b

Counts
98 → 9

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

9.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms (0.4%)

Algorithm
1×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)))

series199.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

63.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
62.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
39.0ms
(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)))

simplify68.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049041580
149041580

prune437.0ms (5.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh077
Picked011
Done011
Total88997

Merged error: 14.7b

Counts
97 → 9

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
8.9b
(* (* (* (* 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))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
30×pow1
29×add-exp-log
20×add-cbrt-cube
19×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 → 74
Calls

4 calls:

22.0ms
(* (* (* (* 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)))
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))

series120.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

45.0ms
(* (* (* (* 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))))
39.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))

simplify50.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
054041433

prune357.0ms (4.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New84286
Fresh066
Picked011
Done022
Total841195

Merged error: 14.6b

Counts
95 → 11

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
8.9b
(* (* (* (* J -2.0) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (log (exp (cbrt (cos (/ K 2.0)))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite36.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
30×pow1
29×add-exp-log
25×add-cbrt-cube
19×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 → 74
Calls

4 calls:

24.0ms
(* (* (* (* J -2.0) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (log (exp (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)))
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))

series119.0ms (1.4%)

Counts
4 → 12
Calls

4 calls:

45.0ms
(* (* (* (* J -2.0) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (log (exp (cbrt (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)))
18.0ms
(cbrt (cos (/ K 2.0)))
18.0ms
(cbrt (cos (/ K 2.0)))

simplify52.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
055581433

prune337.0ms (4.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New85186
Fresh077
Picked101
Done033
Total861197

Merged error: 14.6b

Counts
97 → 11

regimes640.0ms (7.8%)

Accuracy

Total 0.5b remaining (4%)

Threshold costs 0.5b (4%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04599
14599

end0.0ms (0%)

sample3.1s (37%)

Algorithm
1×intervals
Results
1.2s1461×body1280valid
730.0ms1268×body640valid
496.0ms4311×body80valid
257.0ms645×body320valid
85.0ms315×body160valid
0.0ms1×body80invalid

Profiling

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