Details

Time bar (total: 5.7s)

sample112.0ms

Algorithm
intervals
Results
33.0ms76×body1280valid
24.0ms267×body80valid
21.0ms69×body640valid
6.0ms27×body320valid
3.0ms19×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
010513
110513

prune12.0ms

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: 0.4b

Counts
2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.1b
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite27.0ms

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
6×associate-/r*
5×pow1 add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-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))
12.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series57.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
37.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
14.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049651529
149651529

prune178.0ms

Filtered
69 candidates to 103 candidates (-49.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New958103
Fresh101
Picked101
Done000
Total978105

Merged error: 0b

Counts
105 → 8

localize19.0ms

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))))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite55.0ms

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)))
29.0ms
(* (* (/ (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)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
30.0ms
(* (* (/ (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)))

simplify86.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049704143
149704143

prune367.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2121213
Fresh257
Picked011
Done000
Total2147221

Merged error: 0b

Counts
221 → 7

localize13.0ms

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))))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite66.0ms

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:
21.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2)))))
8.0ms
(/ (sqrt 2.0) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series33.0ms

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)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify153.0ms

Algorithm
egg-herbie
Counts
423 → 423
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
0508111244

prune311.0ms

Filtered
162 candidates to 423 candidates (-161.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New4230423
Fresh055
Picked011
Done011
Total4237430

Merged error: 0b

Counts
430 → 7

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)))
0.5b
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.8b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite44.0ms

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
6×associate-*l/ prod-exp associate-/r* cbrt-unprod associate-/l*
5×flip3-+ flip-+
4×add-log-exp
3×cbrt-undiv div-exp pow-prod-down
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-inv associate-/l/
1×sqrt-undiv frac-2neg associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 157
Calls
4 calls:
20.0ms
(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
8.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series50.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* (sqrt (+ (* a1 a1) (* a2 a2))) (cos th)) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0)))
11.0ms
(/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
7.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify54.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
054772865

prune164.0ms

Filtered
100 candidates to 169 candidates (-69.0%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1690169
Fresh044
Picked011
Done022
Total1697176

Merged error: 0b

Counts
176 → 7

regimes391.0ms

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
01932
11932

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s2535×body1280valid
688.0ms2199×body640valid
607.0ms8067×body80valid
226.0ms1000×body320valid
76.0ms496×body160valid

Profiling

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