Details

Time bar (total: 1.7s)

analyze67.0ms (3.9%)

Algorithm
1×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
25%74.9%0.1%5
25%50%25.1%6
25%31.2%43.8%7
31.2%25%43.8%8
39%17.2%43.8%9
42.9%13.3%43.8%10
47.2%9%43.8%11
49.4%6.8%43.8%12
51.6%4.6%43.8%13
52.7%3.5%43.8%14

sample14.0ms (0.9%)

Algorithm
1×intervals
Results
7.0ms256×body80valid

simplify4.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0389
1389

prune6.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.1b

Counts
2 → 1

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* y y))
0.1b
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite21.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
2×associate-+l+
Counts
3 → 38
Calls

3 calls:

9.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* y y))
4.0ms
(+ (* x x) (* y y))

series23.0ms (1.3%)

Counts
3 → 9
Calls

3 calls:

8.0ms
(+ (* x x) (* y y))
7.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
7.0ms
(+ (+ (* x x) (* y y)) (* y y))

simplify58.0ms (3.4%)

Algorithm
1×egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05136513

prune87.0ms (5.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New371047
Fresh000
Picked101
Done000
Total381048

Merged error: 0.0b

Counts
48 → 10

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(+ (+ (* x x) (* y y)) (* y (+ y y)))

rewrite12.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
9×add-log-exp
6×flip3-+ flip-+
4×associate-*r/ frac-add sum-log
2×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+r+ *-un-lft-identity add-cbrt-cube
1×distribute-rgt-in associate-+l+ distribute-lft-in
Counts
2 → 30
Calls

2 calls:

8.0ms
(+ (+ (* x x) (* y y)) (* y (+ y y)))
4.0ms
(+ (* x x) (* y y))

series13.0ms (0.8%)

Counts
2 → 6
Calls

2 calls:

7.0ms
(+ (+ (* x x) (* y y)) (* y (+ y y)))
6.0ms
(+ (* x x) (* y y))

simplify75.0ms (4.4%)

Algorithm
1×egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
04809423
14809423

prune65.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New33336
Fresh549
Picked011
Done000
Total38846

Merged error: 0.0b

Counts
46 → 8

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
0.3b
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))
5.8b
(sqrt (+ (* x x) (* y (+ y y))))
5.8b
(sqrt (+ (* x x) (* y (+ y y))))

rewrite34.0ms (2%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls

4 calls:

12.0ms
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
12.0ms
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))
4.0ms
(sqrt (+ (* x x) (* y (+ y y))))
4.0ms
(sqrt (+ (* x x) (* y (+ y y))))

series30.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

8.0ms
(sqrt (+ (* x x) (* y (+ y y))))
7.0ms
(sqrt (+ (* x x) (* y (+ y y))))
7.0ms
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
7.0ms
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))

simplify60.0ms (3.6%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049591363
149591363

prune150.0ms (8.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1100110
Fresh066
Picked011
Done011
Total1108118

Merged error: 0.0b

Counts
118 → 8

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b
(* (* y y) 3)
0.3b
(* (sqrt (+ (* x x) (* (* y y) 3))) (sqrt (+ (* x x) (* (* y y) 3))))
5.8b
(sqrt (+ (* x x) (* (* y y) 3)))
5.8b
(sqrt (+ (* x x) (* (* y y) 3)))

rewrite32.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Rules
30×add-sqr-sqrt
26×pow1
24×sqrt-prod
16×sqrt-div
15×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r*
8×flip3-+ swap-sqr flip-+
7×associate-*l*
6×pow-prod-down
5×pow-prod-up unswap-sqr
4×frac-times prod-exp cbrt-unprod add-log-exp
3×pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/ *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 106
Calls

4 calls:

14.0ms
(* (sqrt (+ (* x x) (* (* y y) 3))) (sqrt (+ (* x x) (* (* y y) 3))))
6.0ms
(* (* y y) 3)
4.0ms
(sqrt (+ (* x x) (* (* y y) 3)))
4.0ms
(sqrt (+ (* x x) (* (* y y) 3)))

series26.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

8.0ms
(sqrt (+ (* x x) (* (* y y) 3)))
8.0ms
(sqrt (+ (* x x) (* (* y y) 3)))
7.0ms
(* (sqrt (+ (* x x) (* (* y y) 3))) (sqrt (+ (* x x) (* (* y y) 3))))
3.0ms
(* (* y y) 3)

simplify93.0ms (5.5%)

Algorithm
1×egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
048811300
148811300

prune199.0ms (11.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1144118
Fresh325
Picked101
Done022
Total1188126

Merged error: 0.0b

Counts
126 → 8

regimes242.0ms (14.3%)

Accuracy

Total 0.1b remaining (87.7%)

Threshold costs 0.1b (87.7%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01113
11113

end0.0ms (0%)

sample343.0ms (20.4%)

Algorithm
1×intervals
Results
222.0ms8000×body80valid
0.0ms10×body80invalid

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