Details

Time bar (total: 1.7s)

analyze73.0ms

Algorithm
search

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
0.0ms6×body80invalid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1203
2223
3223

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 6.3b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.9b
(* x (+ 1.0 (* y y)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (+ 1.0 (* y y)))

series10.0ms

Counts
1 → 3
Calls
1 calls:
9.0ms
(* x (+ 1.0 (* y y)))

simplify78.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune38.0ms

Filtered
17 candidates to 25 candidates (-47.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New21425
Fresh000
Picked011
Done000
Total21526

Merged error: 6.1b

Counts
26 → 5

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
17×add-sqr-sqrt
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 83
Calls
4 calls:
6.0ms
(* x (sqrt (+ 1.0 (* y y))))
9.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))

series28.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* x (sqrt (+ 1.0 (* y y))))
10.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
4.0ms
(sqrt (+ 1.0 (* y y)))

simplify44.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0306681
11316604
25002594

prune143.0ms

Filtered
67 candidates to 95 candidates (-41.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New92395
Fresh123
Picked101
Done011
Total946100

Merged error: 6.1b

Counts
100 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-+ flip-+
28×frac-times
26×associate-*r/
18×sqrt-prod
16×pow1
14×associate-*l/
13×add-exp-log add-sqr-sqrt add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 98
Calls
4 calls:
17.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
2.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))

series23.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))

simplify59.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04481458
117471223
250011105

prune215.0ms

Filtered
77 candidates to 110 candidates (-42.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1100110
Fresh044
Picked011
Done011
Total1106116

Merged error: 6.1b

Counts
116 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1 sqrt-div
19×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×rem-sqrt-square
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
12.0ms
(* (sqrt (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
2.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))

series14.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
4.0ms
(sqrt (+ 1.0 (* y y)))

simplify48.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0255894
11077840
25001816

prune190.0ms

Filtered
78 candidates to 140 candidates (-79.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1400140
Fresh033
Picked011
Done022
Total1406146

Merged error: 6.1b

Counts
146 → 6

regimes221.0ms

Accuracy

0% (0.2b remaining)

Error of 5.4b against oracle of 5.2b and baseline of 5.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

analyze67.0ms

Algorithm
search

sample287.0ms

Algorithm
intervals
Results
169.0ms8000×body80valid
3.0ms172×body80invalid

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