Details

Time bar (total: 10.0s)

analyze1.9s

Algorithm
search

sample102.0ms

Algorithm
intervals
Results
46.0ms51×body1280valid
16.0ms29×body640valid
15.0ms136×body80valid
9.0ms24×body320valid
4.0ms16×body160valid

simplify45.0ms

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: 17.2b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.0b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite39.0ms

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))))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
17.0ms
(* (* (* -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)))

series123.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
30.0ms
(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)))

simplify66.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05431085
12466960
25002960

prune239.0ms

Filtered
67 candidates to 102 candidates (-52.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New957102
Fresh000
Picked011
Done000
Total958103

Merged error: 11.2b

Counts
103 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.2b
(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)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(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))))
32.0ms
(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)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
01891016
1461986
21696986
35002962

prune340.0ms

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

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New86288
Fresh156
Picked011
Done011
Total87996

Merged error: 11.2b

Counts
96 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.3b
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

rewrite37.0ms

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:
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)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms
(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))

series184.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
32.0ms
(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))

simplify131.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
03081305
19121272
240371256
350021246

prune342.0ms

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

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1030103
Fresh066
Picked011
Done022
Total1039112

Merged error: 11.2b

Counts
112 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)
0.5b
(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
7.0b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
46×prod-exp
34×add-cbrt-cube
30×div-exp
23×add-sqr-sqrt
21×*-un-lft-identity
20×associate-*r*
19×pow1
17×add-cube-cbrt
15×pow-exp
14×cbrt-unprod
13×times-frac
8×rec-exp 1-exp associate-*l* pow-prod-down sqrt-prod
7×cbrt-undiv
4×sqrt-div add-log-exp
3×pow-unpow associate-*r/
2×pow-pow flip3-+ *-commutative flip-+ div-inv distribute-lft-out unswap-sqr
1×frac-times pow-to-exp unpow-prod-down rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ sqr-pow
Counts
4 → 127
Calls
4 calls:
12.0ms
(pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)
11.0ms
(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
10.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0))))
4.0ms
(sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)
17.0ms
(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
41.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0))))
31.0ms
(sqrt (+ 1.0 (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) 2.0)))

simplify87.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07081437
133861217
250011214

prune226.0ms

Filtered
75 candidates to 139 candidates (-85.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1372139
Fresh055
Picked011
Done123
Total13810148

Merged error: 11.1b

Counts
148 → 10

regimes626.0ms

Accuracy

82.9% (0.9b remaining)

Error of 13.0b against oracle of 12.0b and baseline of 17.6b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05851
15851

end0.0ms

analyze1.8s

Algorithm
search

sample3.2s

Algorithm
intervals
Results
1.2s1510×body1280valid
686.0ms1214×body640valid
495.0ms4293×body80valid
493.0ms675×body320valid
82.0ms308×body160valid
0.0ms3×body80invalid

Profiling

Loading profile data...