Details

analyze228.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
1.0ms	28×	body	80	invalid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	82	11
1	82	11

prune10.0ms (0.1%)

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: 6.0b

Counts

2 → 1

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

3.4b	(* y (+ 1.0 (* z z)))
3.7b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `unswap-sqr`

Counts

2 → 70

Calls

2 calls:

13.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
8.0ms	(* y (+ 1.0 (* z z)))

series43.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
15.0ms	(* y (+ 1.0 (* z z)))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune192.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 4.3b

Counts

77 → 9

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(/ (/ 1.0 x) y)
5.5b	(/ (/ (/ 1.0 x) y) (+ 1.0 (* z z)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

468×	`times-frac`
228×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
56×	`associate-/l*`
22×	`div-inv`
16×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r/` `associate-/l/` `add-log-exp`
1×	`flip3-+` `flip-+`

Counts

2 → 264

Calls

2 calls:

15.0ms	(/ (/ (/ 1.0 x) y) (+ 1.0 (* z z)))
5.0ms	(/ (/ 1.0 x) y)

series20.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ (/ (/ 1.0 x) y) (+ 1.0 (* z z)))
3.0ms	(/ (/ 1.0 x) y)

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4981	5243
1	4981	5243

prune542.0ms (8.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	270	9	279

Merged error: 4.3b

Counts

279 → 9

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 x))
1.9b	(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
2.3b	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))))
2.8b	(/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

rewrite114.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

1496×	`times-frac`
635×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
455×	`cbrt-prod`
224×	`associate-/r*`
50×	`div-inv`
32×	`add-exp-log`
26×	`associate-/r/`
22×	`add-cbrt-cube`
20×	`associate-/l*`
16×	`cbrt-undiv` `div-exp`
11×	`flip3-+` `flip-+`
6×	`cbrt-div`
4×	`pow1` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`frac-times` `pow1/3` `associate-r/` `associate-l/`

Counts

4 → 699

Calls

4 calls:

34.0ms	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))))
14.0ms	(/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))
7.0ms	(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
2.0ms	(cbrt (/ 1.0 x))

series137.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))
33.0ms	(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
24.0ms	(cbrt (/ 1.0 x))
24.0ms	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ y (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))))

simplify124.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5296	19279

prune3.4s (52.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	710	1	711
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	710	10	720

Merged error: 4.3b

Counts

720 → 10

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.7b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
16.1b	(sqrt (+ 1.0 (* z z)))
16.1b	(sqrt (+ 1.0 (* z z)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

13.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
9.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series37.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
10.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
6.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4991	1716
1	4991	1716

prune241.0ms (3.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	129	10	139

Merged error: 4.3b

Counts

139 → 10

regimes570.0ms (8.8%)

Accuracy

Total 1.7b remaining (25.9%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

end0.0ms (0%)

sample465.0ms (7.1%)

Algorithm

1×

intervals

Results

279.0ms	8000×	body	80	valid
19.0ms	505×	body	80	invalid

Details

analyze228.0ms (3.5%)

sample26.0ms (0.4%)

simplify5.0ms (0.1%)

prune10.0ms (0.1%)

localize12.0ms (0.2%)

rewrite25.0ms (0.4%)

series43.0ms (0.7%)

simplify67.0ms (1%)

prune192.0ms (2.9%)

localize7.0ms (0.1%)

rewrite36.0ms (0.5%)

series20.0ms (0.3%)

simplify67.0ms (1%)

prune542.0ms (8.3%)

localize11.0ms (0.2%)

rewrite114.0ms (1.8%)

series137.0ms (2.1%)

simplify124.0ms (1.9%)

prune3.4s (52.7%)

localize10.0ms (0.1%)

rewrite31.0ms (0.5%)

series37.0ms (0.6%)

simplify56.0ms (0.9%)

prune241.0ms (3.7%)

regimes570.0ms (8.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample465.0ms (7.1%)

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