Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample12.0ms (0.8%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	69	5
1	69	5

prune5.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt (fabs (- x y)))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

1.0ms

(sqrt (fabs (- x y)))

series5.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

5.0ms

(sqrt (fabs (- x y)))

simplify107.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4784	96
1	4784	96

prune24.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	3	17

Merged error: 0.0b

Counts

17 → 3

localize7.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- x y)))
0.1b	(sqrt (sqrt (fabs (- x y))))
0.1b	(sqrt (sqrt (fabs (- x y))))
0.5b	(* (sqrt (sqrt (fabs (- x y)))) (sqrt (sqrt (fabs (- x y)))))

rewrite22.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`sqrt-prod`
56×	`add-sqr-sqrt`
41×	`sqrt-pow1`
32×	`pow1`
21×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
4×	`add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

13.0ms	(* (sqrt (sqrt (fabs (- x y)))) (sqrt (sqrt (fabs (- x y)))))
2.0ms	(sqrt (sqrt (fabs (- x y))))
2.0ms	(sqrt (sqrt (fabs (- x y))))
1.0ms	(sqrt (fabs (- x y)))

series32.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (sqrt (fabs (- x y))))
12.0ms	(sqrt (sqrt (fabs (- x y))))
4.0ms	(* (sqrt (sqrt (fabs (- x y)))) (sqrt (sqrt (fabs (- x y)))))
4.0ms	(sqrt (fabs (- x y)))

simplify57.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4912	906
1	4912	906

prune137.0ms (9.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	4	141

Merged error: 0.0b

Counts

141 → 4

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (sqrt (fabs (- x y))))) (cbrt (sqrt (sqrt (fabs (- x y))))))
0.5b	(cbrt (sqrt (sqrt (fabs (- x y)))))
0.5b	(cbrt (sqrt (sqrt (fabs (- x y)))))
0.6b	(cbrt (fabs (- x y)))

rewrite20.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`cbrt-prod`
90×	`sqrt-prod`
71×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr`
16×	`unswap-sqr`
12×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

9.0ms	(* (cbrt (sqrt (sqrt (fabs (- x y))))) (cbrt (sqrt (sqrt (fabs (- x y))))))
2.0ms	(cbrt (sqrt (sqrt (fabs (- x y)))))
2.0ms	(cbrt (sqrt (sqrt (fabs (- x y)))))
1.0ms	(cbrt (fabs (- x y)))

series49.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (cbrt (sqrt (sqrt (fabs (- x y))))) (cbrt (sqrt (sqrt (fabs (- x y))))))
12.0ms	(cbrt (sqrt (sqrt (fabs (- x y)))))
12.0ms	(cbrt (fabs (- x y)))
11.0ms	(cbrt (sqrt (sqrt (fabs (- x y)))))

simplify55.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5150	1843

prune136.0ms (9.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	132	5	137

Merged error: 0b

Counts

137 → 5

localize15.0ms (1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))
0.5b	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))
0.6b	(cbrt (fabs (- x y)))
1.1b	(pow (cbrt (cbrt (sqrt (sqrt (fabs (- x y)))))) 5)

rewrite16.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod`
27×	`sqrt-prod`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

5.0ms	(pow (cbrt (cbrt (sqrt (sqrt (fabs (- x y)))))) 5)
4.0ms	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))
2.0ms	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))
1.0ms	(cbrt (fabs (- x y)))

series58.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (cbrt (cbrt (sqrt (sqrt (fabs (- x y)))))) 5)
12.0ms	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))
12.0ms	(cbrt (fabs (- x y)))
12.0ms	(cbrt (cbrt (sqrt (sqrt (fabs (- x y))))))

simplify54.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4860	1147
1	4860	1147

prune133.0ms (9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	93	5	98

Merged error: 0b

Counts

98 → 5

regimes231.0ms (15.5%)

Accuracy

Total 0.0b remaining (58.6%)

Threshold costs 0.0b (58.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	15	5

end0.0ms (0%)

sample288.0ms (19.4%)

Algorithm

1×

intervals

Results

170.0ms

8000×

body

valid

Details

analyze2.0ms (0.1%)

sample12.0ms (0.8%)

simplify4.0ms (0.3%)

prune5.0ms (0.4%)

localize4.0ms (0.3%)

rewrite2.0ms (0.1%)

series5.0ms (0.4%)

simplify107.0ms (7.2%)

prune24.0ms (1.6%)

localize7.0ms (0.5%)

rewrite22.0ms (1.5%)

series32.0ms (2.1%)

simplify57.0ms (3.8%)

prune137.0ms (9.2%)

localize11.0ms (0.7%)

rewrite20.0ms (1.3%)

series49.0ms (3.3%)

simplify55.0ms (3.7%)

prune136.0ms (9.2%)

localize15.0ms (1%)

rewrite16.0ms (1.1%)

series58.0ms (3.9%)

simplify54.0ms (3.6%)

prune133.0ms (9%)

regimes231.0ms (15.5%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample288.0ms (19.4%)

Profiling