Details

analyze19.0ms (0.9%)

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

sample14.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	243×	body	80	valid
1.0ms	5×	body	2560	valid
0.0ms	4×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	320	valid

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	181	8
1	181	8

prune6.0ms (0.3%)

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

localize11.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.3%)

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:

6.0ms

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

series6.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify62.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	171
1	4944	171

prune31.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.0b

Counts

16 → 4

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (1.9%)

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:

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

series86.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
22.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
20.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
20.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify64.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5106	1940

prune264.0ms (13.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

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))))

rewrite36.0ms (1.8%)

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

series40.0ms (2%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
14.0ms	(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))

simplify33.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4979	1678
1	4979	1678

prune217.0ms (10.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	116	6	122

Merged error: 0.0b

Counts

122 → 6

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.3b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite40.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`sqrt-div`
13×	`associate-r`
12×	`cbrt-prod` `add-cube-cbrt` `sqrt-prod`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-*l/`
9×	`flip3-+` `flip-+`
8×	`associate-l`
4×	`frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out` `add-log-exp`
2×	`pow1/3` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

17.0ms	(* (* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
9.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
6.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series115.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
32.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
22.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
20.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify47.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5039	2860

prune313.0ms (15.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	97	7	104

Merged error: 0.0b

Counts

104 → 7

regimes180.0ms (8.9%)

Accuracy

Total 0.0b remaining (59%)

Threshold costs 0.0b (59%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms (0%)

sample344.0ms (17%)

Algorithm

1×

intervals

Results

184.0ms	7672×	body	80	valid
14.0ms	128×	body	1280	valid
7.0ms	53×	body	2560	valid
7.0ms	81×	body	640	valid
3.0ms	42×	body	320	valid
1.0ms	24×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze19.0ms (0.9%)

sample14.0ms (0.7%)

simplify13.0ms (0.6%)

prune6.0ms (0.3%)

localize11.0ms (0.6%)

rewrite6.0ms (0.3%)

series6.0ms (0.3%)

simplify62.0ms (3.1%)

prune31.0ms (1.5%)

localize10.0ms (0.5%)

rewrite38.0ms (1.9%)

series86.0ms (4.2%)

simplify64.0ms (3.2%)

prune264.0ms (13.1%)

localize8.0ms (0.4%)

rewrite36.0ms (1.8%)

series40.0ms (2%)

simplify33.0ms (1.6%)

prune217.0ms (10.8%)

localize14.0ms (0.7%)

rewrite40.0ms (2%)

series115.0ms (5.7%)

simplify47.0ms (2.3%)

prune313.0ms (15.5%)

regimes180.0ms (8.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample344.0ms (17%)

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