Details

Time bar (total: 7.0s)

analyze747.0ms

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

sample92.0ms

Algorithm
intervals
Results
21.0ms48×body1280valid
19.0ms43×body1280invalid
11.0ms37×body640valid
10.0ms141×body80valid
7.0ms24×body640invalid
5.0ms21×body320valid
3.0ms11×body320invalid
1.0ms9×body160valid
1.0ms16×body80invalid
1.0ms6×body160invalid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
010513
110513

prune14.0ms

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: 0.3b

Counts
2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
1×frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num *-commutative flip-+
Counts
2 → 83
Calls
2 calls:
10.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series47.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
10.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
057121398

prune150.0ms

Filtered
59 candidates to 89 candidates (-50.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New82789
Fresh011
Picked101
Done000
Total83891

Merged error: 0b

Counts
91 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ a1 (sqrt 2.0)) a1)
0.2b
(* (/ a2 (sqrt 2.0)) a2)
0.4b
(/ a2 (sqrt 2.0))
0.4b
(/ a1 (sqrt 2.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
76×times-frac
62×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
18×add-exp-log add-cbrt-cube
12×associate-/r*
8×pow1
6×associate-*r* associate-/l* unswap-sqr
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv add-log-exp
2×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 162
Calls
4 calls:
8.0ms
(* (/ a1 (sqrt 2.0)) a1)
8.0ms
(* (/ a2 (sqrt 2.0)) a2)
4.0ms
(/ a2 (sqrt 2.0))
4.0ms
(/ a1 (sqrt 2.0))

series23.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (/ a1 (sqrt 2.0)) a1)
6.0ms
(* (/ a2 (sqrt 2.0)) a2)
6.0ms
(/ a2 (sqrt 2.0))
6.0ms
(/ a1 (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
051451286

prune257.0ms

Filtered
116 candidates to 174 candidates (-50.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1731174
Fresh167
Picked011
Done000
Total1748182

Merged error: 0b

Counts
182 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
0.5b
(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0b
(sqrt (+ (* a1 a1) (* a2 a2)))
5.0b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
540×times-frac
429×sqrt-prod
297×add-sqr-sqrt
295×add-cube-cbrt *-un-lft-identity
48×associate-/r*
22×sqrt-div
17×associate-/r/
12×associate-/l*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×sqrt-undiv
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 411
Calls
4 calls:
18.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
7.0ms
(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
10.0ms
(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
12.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify124.0ms

Algorithm
egg-herbie
Counts
423 → 423
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
0513411244

prune302.0ms

Filtered
164 candidates to 423 candidates (-157.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4230423
Fresh066
Picked011
Done011
Total4238431

Merged error: 0b

Counts
431 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.3b
(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
5.0b
(sqrt (+ (* a1 a1) (* a2 a2)))
5.0b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
102×sqrt-prod
86×add-sqr-sqrt
84×add-cube-cbrt *-un-lft-identity
78×cbrt-prod
58×associate-*r*
38×add-exp-log
29×add-cbrt-cube
16×prod-exp cbrt-unprod
11×pow1
9×cbrt-undiv div-exp associate-/r*
6×sqrt-div associate-/l*
4×add-log-exp
3×flip3-+ pow-prod-down associate-*l/ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
1×frac-times frac-2neg associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 201
Calls
4 calls:
8.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
27.0ms
(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series64.0ms

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

simplify83.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049664143
149664143

prune348.0ms

Filtered
128 candidates to 213 candidates (-66.4%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2130213
Fresh055
Picked011
Done022
Total2138221

Merged error: 0b

Counts
221 → 8

regimes661.0ms

Accuracy

0% (0.4b 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
01616
11616

end0.0ms

analyze735.0ms

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

sample3.0s

Algorithm
intervals
Results
755.0ms1244×body1280invalid
602.0ms1353×body1280valid
345.0ms4716×body80valid
325.0ms1021×body640invalid
321.0ms1056×body640valid
136.0ms594×body320valid
100.0ms446×body320invalid
42.0ms517×body80invalid
42.0ms281×body160valid
35.0ms239×body160invalid

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