Details

Time bar (total: 9.6s)

sample100.0ms

Algorithm
intervals
Results
35.0ms80×body1280valid
19.0ms269×body80valid
16.0ms52×body640valid
6.0ms27×body320valid
3.0ms21×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune11.0ms

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: 0.5b

Counts
2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series43.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (cos th) (sqrt 2.0))
6.0ms
(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05041284
120091156
250011136

prune316.0ms

Filtered
180 candidates to 116 candidates (35.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1719180
Fresh101
Picked101
Done000
Total1739182

Merged error: 0.0b

Counts
182 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
1149×sqrt-prod
1137×times-frac
626×add-sqr-sqrt
592×add-cube-cbrt *-un-lft-identity
283×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
24×associate-/r*
23×div-inv
13×unswap-sqr
11×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×frac-2neg pow-prod-down clear-num
1×associate-*r* associate-*l/ *-commutative associate-/l/
Counts
4 → 744
Calls
4 calls:
44.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

series42.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
5.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
14.0ms
(/ (cos th) (sqrt 2.0))

simplify112.0ms

Algorithm
egg-herbie
Counts
756 → 756
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015449868
150028666

prune1.5s

Filtered
756 candidates to 353 candidates (53.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New7551756
Fresh088
Picked011
Done000
Total75510765

Merged error: 0b

Counts
765 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a1 a1)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
1426×sqrt-prod
977×times-frac
520×add-sqr-sqrt
515×add-cube-cbrt *-un-lft-identity
506×associate-*l*
135×add-exp-log
89×add-cbrt-cube
61×prod-exp
44×div-exp
39×cbrt-unprod
25×cbrt-undiv
18×pow1
16×div-inv
15×associate-/r*
9×pow-prod-down
6×associate-/l*
5×rec-exp 1-exp
4×associate-*l/ add-log-exp
3×unswap-sqr
2×frac-2neg associate-*r* clear-num *-commutative
1×frac-times associate-*r/
Counts
4 → 674
Calls
4 calls:
9.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
84.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a1 a1)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
7.0ms
(/ (cos th) (sqrt 2.0))

series49.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
15.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (* a1 a1)))
8.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt 2.0))

simplify112.0ms

Algorithm
egg-herbie
Counts
686 → 686
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0173710264
150019192

prune2.8s

Filtered
686 candidates to 382 candidates (44.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New6860686
Fresh088
Picked011
Done011
Total68610696

Merged error: 0b

Counts
696 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
44×times-frac
43×add-sqr-sqrt
37×add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
28×sqrt-prod
25×associate-*l*
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down
4×associate-/l* add-log-exp unswap-sqr
3×div-inv
2×frac-2neg associate-*r* clear-num *-commutative
1×associate-*l/
Counts
4 → 132
Calls
4 calls:
5.0ms
(* (cos th) (* a2 a2))
11.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
8.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

series44.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos th) (* a2 a2))
14.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms
(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0501987
12125864
25002850

prune181.0ms

Filtered
144 candidates to 91 candidates (36.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1422144
Fresh347
Picked101
Done022
Total1468154

Merged error: 0b

Counts
154 → 8

regimes474.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01815
11815

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s2492×body1280valid
661.0ms2118×body640valid
585.0ms8043×body80valid
242.0ms1058×body320valid
83.0ms549×body160valid

Profiling

Loading profile data...