Details

Time bar (total: 9.3s)

sample89.0ms

Algorithm
intervals
Results
28.0ms43×body1280valid
20.0ms46×body640valid
13.0ms134×body80valid
8.0ms26×body320valid
1.0ms7×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5135213
6500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.9b

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)
6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*l*
5×*-commutative
4×sqrt-div
2×flip3-+ associate-*r/ flip-+
1×pow-to-exp unpow-prod-down pow1/2 div-inv sqr-pow
Counts
4 → 16
Calls
4 calls:
4.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
3.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
4.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
130.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
185.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify40.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (36.0ms)

IterNodesCost
0199238
1507238
21486238
35002234

prune112.0ms

Filtered
28 candidates to 25 candidates (89.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New24428
Fresh000
Picked011
Done000
Total24529

Merged error: 12.7b

Counts
29 → 5

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)
6.9b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
5×*-commutative
4×sqrt-div associate-*r/ associate-*l*
2×flip3-+ associate-*r* flip-+
1×pow-to-exp unpow-prod-down pow1/2 div-inv sqr-pow
Counts
4 → 16
Calls
4 calls:
4.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
3.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
4.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series507.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
129.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
187.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
142.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
0206231
1517231
21485231
35002227

prune102.0ms

Filtered
28 candidates to 24 candidates (85.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New28028
Fresh033
Picked011
Done011
Total28533

Merged error: 12.7b

Counts
33 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
5.6b
(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)))))
15.0b
(- (* (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)))
21.3b
(/ (* (* (* -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))))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
8×sqrt-div
7×*-commutative associate-/l*
6×associate-*l*
5×associate-*r*
4×distribute-rgt-out-- flip3-+ flip-+
3×div-inv
2×unpow-prod-down pow1/2 associate-*r/ sqrt-prod associate-/r/ sum-cubes associate-/l/ distribute-lft-out-- sqr-pow
1×sub-neg flip3-- frac-2neg clear-num flip--
Counts
4 → 31
Calls
4 calls:
6.0ms
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
18.0ms
(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)))))
15.0ms
(- (* (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)))
28.0ms
(/ (* (* (* -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))))))

series2.6s

Counts
4 → 12
Calls
4 calls:
134.0ms
(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
492.0ms
(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)))))
493.0ms
(- (* (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)))
1.5s
(/ (* (* (* -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))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05051149
119401117
250021115

prune276.0ms

Filtered
43 candidates to 38 candidates (88.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New39443
Fresh022
Picked101
Done022
Total40848

Merged error: 12.7b

Counts
48 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (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)))))) (/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.0b
(- (* (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)))
15.0b
(- (* (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)))
16.6b
(/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*l*
22×sqrt-div
21×associate-/r/
20×*-commutative
18×times-frac
13×div-inv
11×flip3-+ flip-+
8×distribute-rgt-out-- associate-*r*
6×associate-/l/ associate-/l*
4×unpow-prod-down distribute-lft-out-- sqr-pow
3×frac-2neg clear-num associate-/r*
2×sub-neg flip3-- associate-*r/ flip--
1×sqrt-undiv
Counts
4 → 65
Calls
4 calls:
44.0ms
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (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)))))) (/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
16.0ms
(- (* (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)))
16.0ms
(- (* (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)))
21.0ms
(/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (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)))))) (/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
486.0ms
(- (* (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)))
493.0ms
(- (* (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)))
819.0ms
(/ (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))))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify75.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05662745
121652373
250012372

prune407.0ms

Filtered
77 candidates to 65 candidates (84.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New75277
Fresh235
Picked011
Done112
Total78785

Merged error: 12.7b

Counts
85 → 7

regimes263.0ms

Accuracy

90.2% (0.5b remaining)

Error of 13.3b against oracle of 12.7b and baseline of 18.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample1.8s

Algorithm
intervals
Results
683.0ms1514×body1280valid
413.0ms1261×body640valid
323.0ms4278×body80valid
144.0ms640×body320valid
52.0ms310×body160valid