Details

Time bar (total: 5.8s)

sample87.0ms

Algorithm
intervals
Results
24.0ms41×body1280valid
19.0ms44×body640valid
12.0ms146×body80valid
5.0ms16×body320valid
2.0ms9×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.7b

Counts
2 → 1

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)
7.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite36.0ms

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:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
6.0ms
(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)))
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series114.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms
(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)))
41.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (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

prune406.0ms

Filtered
97 candidates to 62 candidates (36.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh000
Picked011
Done000
Total89998

Merged error: 11.8b

Counts
98 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite28.0ms

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:
6.0ms
(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)))
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))))

series183.0ms

Counts
4 → 12
Calls
4 calls:
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)))
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
59.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune310.0ms

Filtered
88 candidates to 62 candidates (29.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh077
Picked011
Done011
Total871097

Merged error: 11.7b

Counts
97 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

7.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
19×*-un-lft-identity
18×add-sqr-sqrt
14×sqrt-div
13×sqrt-pow1
11×pow1 add-cube-cbrt
7×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 82
Calls
4 calls:
6.0ms
(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 (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))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
56.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
59.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
01891114
14611083
216961083
350021051

prune426.0ms

Filtered
94 candidates to 65 candidates (30.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New94094
Fresh077
Picked011
Done022
Total9410104

Merged error: 11.7b

Counts
104 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.7b
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
13.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.2b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-exp-log add-cbrt-cube
14×*-un-lft-identity
13×cbrt-prod
10×add-sqr-sqrt
8×add-cube-cbrt pow-prod-down prod-exp cbrt-unprod
7×sqrt-prod
6×cbrt-div
4×add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 71
Calls
4 calls:
7.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
6.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
6.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
34.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
59.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
57.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03471291
112061104
250011096

prune368.0ms

Filtered
83 candidates to 63 candidates (24.1%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New83083
Fresh066
Picked011
Done033
Total831093

Merged error: 11.7b

Counts
93 → 10

regimes626.0ms

Accuracy

83.4% (1.0b remaining)

Error of 13.0b against oracle of 12.1b and baseline of 17.9b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample2.4s

Algorithm
intervals
Results
907.0ms1531×body1280valid
549.0ms1294×body640valid
361.0ms4220×body80valid
198.0ms643×body320valid
63.0ms314×body160valid

Profiling

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