Details

Time bar (total: 10.6s)

sample83.0ms

Algorithm
intervals
Results
26.0ms44×body1280valid
17.0ms42×body640valid
12.0ms142×body80valid
6.0ms22×body320valid
1.0ms6×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune6.0ms

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: 16.4b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
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)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
162.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
231.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
174.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify64.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05431086
12465960
25001960

prune772.0ms

Filtered
102 candidates to 67 candidates (34.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New957102
Fresh000
Picked011
Done000
Total958103

Merged error: 11.7b

Counts
103 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite34.0ms

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

series838.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
252.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
170.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
168.0ms
(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 (45.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune295.0ms

Filtered
88 candidates to 62 candidates (29.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh066
Picked011
Done011
Total88896

Merged error: 11.7b

Counts
96 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×pow1 sqrt-prod
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-div
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*r/
1×associate-*l* *-commutative
Counts
4 → 75
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
(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)))

series729.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
170.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
171.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
167.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02541060
11124971
25001961

prune296.0ms

Filtered
87 candidates to 58 candidates (33.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New87087
Fresh055
Picked011
Done022
Total87895

Merged error: 11.7b

Counts
95 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

2.8b
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
4.2b
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
13.0b
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
19.7b
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-exp-log sqrt-prod add-cbrt-cube
12×add-sqr-sqrt
10×add-cube-cbrt
8×sqrt-div
6×pow1 times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
5×distribute-lft-out
4×cbrt-undiv unpow-prod-down flip3-+ cube-prod div-exp flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-/r/ associate-/l/
1×sub-neg flip3-- distribute-rgt-out-- frac-2neg diff-log clear-num sum-cubes flip-- div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
22.0ms
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
11.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
44.0ms
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
156.0ms
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
576.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
561.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
1.4s
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07033111
135142792
250012792

prune540.0ms

Filtered
96 candidates to 69 candidates (28.1%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New94296
Fresh044
Picked101
Done033
Total959104

Merged error: 11.7b

Counts
104 → 9

regimes668.0ms

Accuracy

92.2% (0.4b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 17.8b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample2.4s

Algorithm
intervals
Results
901.0ms1499×body1280valid
540.0ms1236×body640valid
372.0ms4298×body80valid
203.0ms656×body320valid
62.0ms311×body160valid

Profiling

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