Details

Time bar (total: 4.5s)

analyze570.0ms (12.5%)

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
3.1%90.5%6.3%6
4.7%85.9%9.5%7
21.1%64%14.9%8
23.4%58.9%17.7%9
27.7%51.3%21%10
28.9%48.5%22.6%11
31.1%44.4%24.5%12
31.7%42.9%25.4%13
32.7%41%26.3%14

sample63.0ms (1.4%)

Algorithm
intervals
Results
22.0ms45×body1280valid
10.0ms32×body640valid
8.0ms148×body80valid
4.0msbody640invalid
4.0ms19×body320valid
2.0ms12×body160valid
1.0msbody320invalid
1.0msbody1280invalid
1.0msbody160invalid
0.0msbody80invalid
0.0msbody80nan

simplify34.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049859
149859

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 11.8b

Counts
2 → 1

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/ (pow (/ x (+ x y)) x) x)
0.0b
(/ x (+ x y))
8.1b
(pow (/ x (+ x y)) x)

rewrite29.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
138×times-frac
118×*-un-lft-identity
90×unpow-prod-down
80×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
19×distribute-lft-out
16×add-exp-log
12×associate-/r/
div-exp associate-/r* add-cbrt-cube div-inv
flip3-+ flip-+
sqr-pow
pow1 pow-exp
pow-unpow add-log-exp
cbrt-undiv pow-to-exp frac-2neg clear-num
pow-pow
Counts
3 → 172
Calls

3 calls:

10.0ms
(/ (pow (/ x (+ x y)) x) x)
6.0ms
(pow (/ x (+ x y)) x)
5.0ms
(/ x (+ x y))

series47.0ms (1%)

Counts
3 → 9
Calls

3 calls:

21.0ms
(/ (pow (/ x (+ x y)) x) x)
21.0ms
(pow (/ x (+ x y)) x)
5.0ms
(/ x (+ x y))

simplify62.0ms (1.4%)

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050112849

prune231.0ms (5.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1756181
Fresh000
Picked101
Done000
Total1766182

Merged error: 0.4b

Counts
182 → 6

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.0b
(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
7.3b
(cbrt (/ x (+ x y)))
7.3b
(cbrt (/ x (+ x y)))
7.3b
(cbrt (/ x (+ x y)))

rewrite30.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
47×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×pow1
pow-pow pow1/3 distribute-lft-out
add-exp-log
associate-/r/
add-cbrt-cube add-log-exp
pow-unpow cbrt-div flip3-+ flip-+ div-inv
pow-prod-down pow-exp pow-sqr pow-prod-up
pow2 pow-to-exp unpow-prod-down pow-plus prod-exp sqr-pow
Counts
4 → 105
Calls

4 calls:

13.0ms
(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
5.0ms
(cbrt (/ x (+ x y)))
5.0ms
(cbrt (/ x (+ x y)))
4.0ms
(cbrt (/ x (+ x y)))

series113.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

36.0ms
(pow (* (cbrt (/ x (+ x y))) (cbrt (/ x (+ x y)))) x)
28.0ms
(cbrt (/ x (+ x y)))
25.0ms
(cbrt (/ x (+ x y)))
25.0ms
(cbrt (/ x (+ x y)))

simplify47.0ms (1%)

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050831475

prune165.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1170117
Fresh055
Picked011
Done000
Total1176123

Merged error: 0.4b

Counts
123 → 6

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
8.1b
(pow (/ x (+ x y)) x)

rewrite13.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
18×unpow-prod-down
16×add-sqr-sqrt add-cube-cbrt
12×times-frac
cbrt-prod
add-exp-log
pow1
add-cbrt-cube add-log-exp
pow-unpow pow1/3 distribute-lft-out
pow-exp associate-/r/
pow-to-exp pow-pow flip3-+ div-exp flip-+ div-inv sqr-pow
Counts
4 → 66
Calls

4 calls:

8.0ms
(pow (/ x (+ x y)) x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series86.0ms (1.9%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(cbrt x)
22.0ms
(cbrt x)
21.0ms
(cbrt x)
18.0ms
(pow (/ x (+ x y)) x)

simplify46.0ms (1%)

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04995738
14995738

prune118.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New76278
Fresh044
Picked101
Done011
Total77784

Merged error: 0.4b

Counts
84 → 7

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt x) (sqrt (+ x y)))
0.1b
(/ (sqrt x) (sqrt (+ x y)))
0.5b
(pow (/ (sqrt x) (sqrt (+ x y))) x)
0.5b
(pow (/ (sqrt x) (sqrt (+ x y))) x)

rewrite51.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
194×sqrt-prod
172×*-un-lft-identity
168×times-frac
120×add-sqr-sqrt add-cube-cbrt
96×unpow-prod-down
26×distribute-lft-out
14×add-exp-log associate-/r*
12×associate-/l*
sqrt-div associate-/r/ add-cbrt-cube
pow1 pow-unpow
sqrt-undiv flip3-+ div-exp pow-exp flip-+ div-inv add-log-exp
cbrt-undiv pow-to-exp pow-pow frac-2neg clear-num sqrt-pow2 sqr-pow
Counts
4 → 268
Calls

4 calls:

11.0ms
(pow (/ (sqrt x) (sqrt (+ x y))) x)
10.0ms
(pow (/ (sqrt x) (sqrt (+ x y))) x)
7.0ms
(/ (sqrt x) (sqrt (+ x y)))
7.0ms
(/ (sqrt x) (sqrt (+ x y)))

series95.0ms (2.1%)

Counts
4 → 12
Calls

4 calls:

33.0ms
(pow (/ (sqrt x) (sqrt (+ x y))) x)
33.0ms
(pow (/ (sqrt x) (sqrt (+ x y))) x)
15.0ms
(/ (sqrt x) (sqrt (+ x y)))
13.0ms
(/ (sqrt x) (sqrt (+ x y)))

simplify56.0ms (1.2%)

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
050064636

prune301.0ms (6.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2800280
Fresh055
Picked011
Done011
Total2807287

Merged error: 0.4b

Counts
287 → 7

regimes142.0ms (3.1%)

Accuracy

Total 5.2b remaining (88.8%)

Threshold costs 0b (0%)

bsearch256.0ms (5.6%)

Steps
ItersRangePoint
9
2.336597948207047e+110
6.666682236957987e+116
3.955643581924325e+113
8
2.2190731447670528e+85
1.4801716519397095e+88
3.2195260757207784e+85
6
7.95612707699845e+47
4.685558298635802e+48
2.397614431801766e+48
10
1.0788903632013352e-10
871665.6756045957
317.3168173800605
9
-7.670017091762728e+169
-6.345468355134889e+161
-6.463475984187357e+161

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0120131
1120131

end0.0ms (0%)

sample1.9s (42.6%)

Algorithm
intervals
Results
733.0ms1443×body1280valid
368.0ms1203×body640valid
243.0ms4351×body80valid
134.0ms636×body320valid
80.0ms267×body640invalid
47.0ms367×body160valid
47.0ms103×body1280invalid
39.0ms202×body320invalid
13.0ms103×body160invalid
12.0ms155×body80invalid
7.0ms167×body80nan

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