Details

Time bar (total: 1.8s)

analyze14.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%18.7%81.3%0
0%18.7%81.3%1
0%18.7%81.3%2
0%18.7%81.3%3
0%18.7%81.3%4
4.7%14%81.3%5
5.3%13.5%81.3%6
18.1%0.6%81.3%7
18.1%0.6%81.3%8
18.6%0.1%81.3%9
18.6%0.1%81.3%10
18.7%0%81.3%11
18.7%0%81.3%12
18.7%0%81.3%13
18.7%0%81.3%14

sample22.0ms (1.2%)

Algorithm
1×intervals
Results
9.0ms256×body80valid
5.0ms256×pre80true

simplify148.0ms (8.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (147.0ms)

IterNodesCost
0489715
1489715

prune10.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.1b

Counts
2 → 1

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
18.9b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
8×associate-/l/
7×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
2 → 42
Calls

2 calls:

12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
4.0ms
(+ (* x x) (* y y))

series16.0ms (0.9%)

Counts
2 → 6
Calls

2 calls:

10.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
6.0ms
(+ (* x x) (* y y))

simplify22.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
05103655

prune70.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New44448
Fresh000
Picked011
Done000
Total44549

Merged error: 0.3b

Counts
49 → 5

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
0.0b
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
18.2b
(sqrt (+ (* x x) (* y y)))
18.2b
(sqrt (+ (* x x) (* y y)))

rewrite61.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Rules
99×add-sqr-sqrt
93×*-un-lft-identity
90×times-frac
55×add-cube-cbrt
54×sqrt-prod
36×associate-*l*
30×associate-*r*
18×add-exp-log add-cbrt-cube
13×distribute-lft-out
10×sqrt-div
9×unswap-sqr
8×pow1
6×flip3-+ associate-/r* associate-/r/ flip-+ distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 175
Calls

4 calls:

35.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
11.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
4.0ms
(sqrt (+ (* x x) (* y y)))
4.0ms
(sqrt (+ (* x x) (* y y)))

series37.0ms (2.1%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
12.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
6.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

simplify40.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
053653657

prune204.0ms (11.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1843187
Fresh033
Picked101
Done101
Total1866192

Merged error: 0.3b

Counts
192 → 6

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.2b
(* (+ x y) (/ 1 (sqrt (+ (* x x) (* y y)))))
18.2b
(sqrt (+ (* x x) (* y y)))
18.2b
(sqrt (+ (* x x) (* y y)))

rewrite38.0ms (2.1%)

Algorithm
1×rewrite-expression-head
Rules
67×add-sqr-sqrt
57×*-un-lft-identity
52×times-frac
39×add-cube-cbrt
35×sqrt-prod
24×associate-*r*
15×add-exp-log
11×add-cbrt-cube
8×pow1 sqrt-div
7×distribute-lft-out-- difference-of-squares
6×flip3-+ associate-/r* flip-+
5×associate-/l* unswap-sqr
4×associate-*l* prod-exp associate-/r/ add-log-exp
3×div-exp
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ cbrt-unprod div-inv associate-/l/
1×rec-exp flip3-- frac-2neg 1-exp div-sub associate-*r/ pow-prod-down clear-num un-div-inv *-commutative flip-- distribute-lft-out
Counts
4 → 142
Calls

4 calls:

15.0ms
(* (+ x y) (/ 1 (sqrt (+ (* x x) (* y y)))))
9.0ms
(/ (- x y) (sqrt (+ (* x x) (* y y))))
5.0ms
(sqrt (+ (* x x) (* y y)))
4.0ms
(sqrt (+ (* x x) (* y y)))

series35.0ms (2%)

Counts
4 → 12
Calls

4 calls:

12.0ms
(* (+ x y) (/ 1 (sqrt (+ (* x x) (* y y)))))
12.0ms
(/ (- x y) (sqrt (+ (* x x) (* y y))))
6.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

simplify64.0ms (3.6%)

Algorithm
1×egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
058182264

prune190.0ms (10.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh055
Picked011
Done000
Total1546160

Merged error: 0.3b

Counts
160 → 6

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms (0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New000
Fresh044
Picked011
Done011
Total066

Merged error: 0.3b

Counts
6 → 6

regimes121.0ms (6.9%)

Accuracy

Total 5.1b remaining (91%)

Threshold costs 0b (0%)

bsearch37.0ms (2.1%)

Steps
ItersRangePoint
6
4.130637735382058e-205
4.8418120782494744e-204
4.755047945101056e-204
7
-1.5335732361285339e-161
-4.4451465724872585e-163
-1.5799804884119341e-162
10
-6.818987673778931e-40
-8.900687591212937e-58
-6.71233735076048e-40

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03942
13942

end0.0ms (0%)

sample581.0ms (32.9%)

Algorithm
1×intervals
Results
299.0ms8000×body80valid
145.0ms8000×pre80true

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