Details

Time bar (total: 6.7s)

sample108.0ms

Algorithm
intervals
Results
40.0ms49×body1280valid
17.0ms28×body640valid
16.0ms144×body80valid
13.0ms23×body320valid
3.0ms12×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0550124

prune16.0ms

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: 20.4b

Counts
2 → 2

localize21.0ms

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)
8.0b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

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)))
6.0ms
(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)))

series116.0ms

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)))

simplify69.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049751601
149751601

prune266.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89897
Fresh101
Picked011
Done000
Total90999

Merged error: 15.1b

Counts
99 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.1b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
11.0b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
11.0b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite32.0ms

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))))
9.0ms
(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)))

series185.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
60.0ms
(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)))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
055711572

prune348.0ms

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

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New86288
Fresh077
Picked011
Done011
Total861197

Merged error: 15.1b

Counts
97 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

8.1b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
11.0b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
17.1b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
17.1b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×sqrt-prod
12×add-sqr-sqrt
9×add-cube-cbrt
8×cbrt-prod
7×pow1
6×sqrt-div
5×sqrt-pow1
4×add-exp-log cbrt-div flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square pow1/2
2×pow1/3
Counts
4 → 66
Calls
4 calls:
7.0ms
(sqrt (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)))
6.0ms
(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)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (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
(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)))

simplify77.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
048771514
148771514

prune414.0ms

Filtered
58 candidates to 78 candidates (-34.5%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New78078
Fresh088
Picked011
Done022
Total781189

Merged error: 15.1b

Counts
89 → 11

localize31.0ms

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))))
2.4b
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
17.1b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
17.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite28.0ms

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:
7.0ms
(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)))))))
6.0ms
(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)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
36.0ms
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
58.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
63.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049701766
149701766

prune327.0ms

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

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New79382
Fresh257
Picked011
Done123
Total821193

Merged error: 15.1b

Counts
93 → 11

regimes714.0ms

Accuracy

82.5% (0.9b remaining)

Error of 13.2b against oracle of 12.3b and baseline of 17.6b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04599
14599

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s1456×body1280valid
745.0ms1300×body640valid
504.0ms4317×body80valid
245.0ms598×body320valid
89.0ms331×body160valid

Profiling

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