Details

Time bar (total: 6.2s)

sample103.0ms

Algorithm
intervals
Results
31.0ms33×body1280valid
22.0ms40×body640valid
16.0ms149×body80valid
9.0ms23×body320valid
3.0ms11×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.2b

Counts
2 → 1

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)
7.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

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)
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series117.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
31.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
41.0ms
(* (* (* -2.0 J) (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)))

simplify55.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04531006
11965898
25001898

prune248.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New851297
Fresh000
Picked011
Done000
Total851398

Merged error: 12.7b

Counts
98 → 13

localize15.0ms

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)
7.4b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r/ associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
12.0ms
(* (* -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)))

series115.0ms

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)))

simplify55.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0488988
12020866
25001866

prune227.0ms

Filtered
59 candidates to 94 candidates (-59.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New93194
Fresh01111
Picked101
Done011
Total9413107

Merged error: 12.7b

Counts
107 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.4b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite31.0ms

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

series187.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
58.0ms
(sqrt (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)))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune340.0ms

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

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh01111
Picked011
Done011
Total8714101

Merged error: 12.7b

Counts
101 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.7b
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
26×cbrt-prod
25×*-un-lft-identity
19×add-sqr-sqrt
15×add-cube-cbrt
12×sqrt-div
10×unpow-prod-down cube-prod
8×pow1
6×sqrt-pow1
5×distribute-lft-out
4×add-exp-log rem-sqrt-square flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 91
Calls
4 calls:
7.0ms
(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)))
6.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
10.0ms
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

series186.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (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)))
35.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
58.0ms
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

simplify130.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
03081305
19121272
240371256
350021246

prune312.0ms

Filtered
63 candidates to 103 candidates (-63.5%)
Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New1030103
Fresh01111
Picked011
Done022
Total10314117

Merged error: 12.7b

Counts
117 → 14

regimes796.0ms

Accuracy

91.7% (0.4b remaining)

Error of 12.7b against oracle of 12.3b and baseline of 17.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s1487×body1280valid
702.0ms1236×body640valid
480.0ms4301×body80valid
267.0ms651×body320valid
84.0ms326×body160valid

Profiling

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