Details

Time bar (total: 11.9s)

analyze748.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
25%74.9%0.1%8
25%74.9%0.1%9
25%64%11.1%10
31.2%54.6%14.2%11
39%44.1%16.9%12
39%41.5%19.5%13
42.9%37%20.1%14

sample88.0ms

Algorithm
intervals
Results
18.0ms42×body1280valid
15.0ms28×body1280invalid
12.0ms148×body80valid
11.0ms35×body640valid
8.0ms27×body640invalid
3.0ms16×body320valid
3.0ms12×body320invalid
2.0ms15×body160valid
1.0msbody160invalid
1.0ms14×body80invalid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
010513
110513

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize219.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
associate-/r*
pow1 add-log-exp
associate-*l* associate-/l* unswap-sqr
cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 94
Calls
3 calls:
4.0ms
(+ (* a1 a1) (* a2 a2))
11.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series53.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
37.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049651529
149651529

prune210.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New967103
Fresh101
Picked011
Done000
Total978105

Merged error: 0b

Counts
105 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.2b
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
625×add-sqr-sqrt
578×add-cube-cbrt *-un-lft-identity
283×associate-*r*
34×associate-/l*
22×div-inv
20×add-exp-log add-cbrt-cube
18×associate-/r*
13×unswap-sqr
cbrt-undiv div-exp
pow1 add-log-exp
associate-*l* prod-exp cbrt-unprod associate-/l/
frac-2neg flip3-+ clear-num flip-+
+-commutative associate-*r/ pow-prod-down sum-log *-commutative
Counts
4 → 713
Calls
4 calls:
4.0ms
(+ (* a1 a1) (* a2 a2))
68.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
17.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
41.0ms
(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
11.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))

simplify160.0ms

Algorithm
egg-herbie
Counts
725 → 725
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0538416199

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New7241725
Fresh156
Picked011
Done011
Total7258733

Merged error: 0b

Counts
733 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b
(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
1116×sqrt-prod
1098×times-frac
581×add-sqr-sqrt
579×add-cube-cbrt *-un-lft-identity
286×associate-*r*
54×add-exp-log
34×add-cbrt-cube associate-/l*
25×pow1
22×div-inv
20×sqrt-pow1 div-exp
18×associate-/r*
16×prod-exp
14×pow-flip
10×cbrt-undiv pow1/2 cbrt-unprod pow-div
associate-*l/
rec-exp 1-exp associate-*l* pow-prod-down add-log-exp
flip3-+ flip-+
frac-times frac-2neg clear-num *-commutative inv-pow
associate-*r/ associate-/l/ unswap-sqr
Counts
4 → 740
Calls
4 calls:
6.0ms
(* (+ (* a1 a1) (* a2 a2)) (cos th))
56.0ms
(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
16.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ 1 (sqrt (sqrt 2.0)))

series50.0ms

Counts
4 → 8
Calls
4 calls:
16.0ms
(* (+ (* a1 a1) (* a2 a2)) (cos th))
34.0ms
(* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify172.0ms

Algorithm
egg-herbie
Counts
748 → 748
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
0497711970
1497711970

prune3.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New7480748
Fresh055
Picked011
Done022
Total7488756

Merged error: 0b

Counts
756 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
0.4b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
8.8b
(sqrt (+ (* a1 a1) (* a2 a2)))
8.8b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
72×times-frac
61×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
40×associate-*r*
18×add-exp-log add-cbrt-cube
11×pow1
10×sqrt-div
associate-*l/ prod-exp associate-/r* cbrt-unprod associate-/l*
flip3-+ flip-+
add-log-exp
cbrt-undiv div-exp pow-prod-down
frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
sqrt-undiv frac-2neg associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 157
Calls
4 calls:
17.0ms
(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
7.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series48.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
10.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify51.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
054772865

prune259.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New1690169
Fresh044
Picked011
Done033
Total1698177

Merged error: 0b

Counts
177 → 8

regimes388.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01920
11920

end0.0ms

sample2.7s

Algorithm
intervals
Results
590.0ms1344×body1280valid
498.0ms1140×body1280invalid
351.0ms1141×body640valid
345.0ms4680×body80valid
286.0ms939×body640invalid
122.0ms537×body320valid
111.0ms487×body320invalid
44.0ms298×body160valid
39.0ms507×body80invalid
36.0ms240×body160invalid

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