Details

analyze19.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	248×	body	80	valid
1.0ms	5×	body	1280	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	181	8
1	181	8

prune5.0ms (0.2%)

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: 0.1b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 12

Calls

1 calls:

9.0ms

(+ x (/ (fabs (- y x)) 2.0))

series5.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

5.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify51.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	171
1	4944	171

prune32.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Merged error: 0.0b

Counts

16 → 5

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite35.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

14.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
7.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series81.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
19.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
18.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify65.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5106	1940

prune310.0ms (13.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Merged error: 0.0b

Counts

112 → 7

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite35.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `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 → 106

Calls

4 calls:

15.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
6.0ms	(+ x (/ (fabs (- y x)) 2.0))
5.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))

series38.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
4.0ms	(+ x (/ (fabs (- y x)) 2.0))

simplify37.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4979	1678
1	4979	1678

prune226.0ms (10.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	117	8	125

Merged error: 0.0b

Counts

125 → 8

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite43.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

19.0ms	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
6.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
6.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
6.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series81.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
20.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify77.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4946	2704
1	4946	2704

prune510.0ms (22.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	132	8	140

Merged error: 0.0b

Counts

140 → 8

regimes185.0ms (8.2%)

Accuracy

Total 0.0b remaining (63.6%)

Threshold costs 0.0b (63.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms (0%)

sample341.0ms (15.2%)

Algorithm

1×

intervals

Results

184.0ms	7679×	body	80	valid
14.0ms	102×	body	1280	valid
8.0ms	92×	body	640	valid
6.0ms	47×	body	2560	valid
4.0ms	55×	body	320	valid
1.0ms	25×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze19.0ms (0.8%)

sample13.0ms (0.6%)

simplify11.0ms (0.5%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite9.0ms (0.4%)

series5.0ms (0.2%)

simplify51.0ms (2.3%)

prune32.0ms (1.4%)

localize9.0ms (0.4%)

rewrite35.0ms (1.6%)

series81.0ms (3.6%)

simplify65.0ms (2.9%)

prune310.0ms (13.8%)

localize8.0ms (0.4%)

rewrite35.0ms (1.5%)

series38.0ms (1.7%)

simplify37.0ms (1.7%)

prune226.0ms (10.1%)

localize12.0ms (0.5%)

rewrite43.0ms (1.9%)

series81.0ms (3.6%)

simplify77.0ms (3.4%)

prune510.0ms (22.7%)

regimes185.0ms (8.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample341.0ms (15.2%)

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