Details

Time bar (total: 6.5s)

sample115.0ms

Algorithm
intervals
Results
49.0ms54×body1280valid
22.0ms38×body640valid
15.0ms135×body80valid
7.0ms18×body320valid
3.0ms12×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

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: 19.4b

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)
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite42.0ms

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:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms
(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)))
15.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
37.0ms
(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)))
48.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
049671601
149671601

prune284.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh011
Picked011
Done000
Total891099

Merged error: 14.7b

Counts
99 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* J (* 2.0 (cos (/ K 2.0))))
0.2b
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
8.3b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
10.0b
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
16×pow1
14×add-cbrt-cube
12×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt
9×prod-exp
7×unpow-prod-down
6×associate-*l* pow-prod-down cbrt-unprod
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 78
Calls
4 calls:
6.0ms
(* J (* 2.0 (cos (/ K 2.0))))
8.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
7.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
13.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* J (* 2.0 (cos (/ K 2.0))))
35.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
41.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
45.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))

simplify28.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
053051399

prune254.0ms

Filtered
60 candidates to 90 candidates (-50.0%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New86490
Fresh178
Picked011
Done011
Total8713100

Merged error: 14.7b

Counts
100 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
9.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-div
30×pow1
28×sqrt-prod
25×add-exp-log add-cbrt-cube
15×*-un-lft-identity pow-prod-down prod-exp cbrt-unprod
14×add-sqr-sqrt
10×associate-*r/
9×add-cube-cbrt sqrt-pow1 flip3-+ flip-+
5×rem-sqrt-square pow1/2
4×frac-times add-log-exp
3×distribute-lft-out
2×associate-*l/
1×associate-*r* associate-*l* *-commutative
Counts
4 → 96
Calls
4 calls:
7.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
33.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
11.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
50.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))))
66.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))
69.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
049762308
149762308

prune391.0ms

Filtered
65 candidates to 108 candidates (-66.2%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1080108
Fresh01010
Picked011
Done022
Total10813121

Merged error: 14.7b

Counts
121 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0b
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

rewrite36.0ms

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 (+ 1.0 (pow (/ U (* J (* 2.0 (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 (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

series215.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))
38.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
70.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
057201572

prune317.0ms

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

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New88088
Fresh099
Picked011
Done033
Total8813101

Merged error: 14.7b

Counts
101 → 13

regimes714.0ms

Accuracy

88.6% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 18.4b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04999
14999

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s1515×body1280valid
757.0ms1268×body640valid
494.0ms4323×body80valid
258.0ms596×body320valid
87.0ms308×body160valid

Profiling

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