Details

analyze376.0ms (16.4%)

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
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	32×	body	80	invalid

simplify64.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4930	9
1	4930	9

prune12.0ms (0.5%)

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 → 2

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) z)
0.0b	(- (* x (/ (+ y 1.0) z)) x)
4.5b	(* x (/ (+ y 1.0) z))

rewrite22.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
16×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `add-log-exp`
4×	`associate-/l*`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `flip-+`

Counts

3 → 79

Calls

3 calls:

8.0ms	(* x (/ (+ y 1.0) z))
7.0ms	(- (* x (/ (+ y 1.0) z)) x)
5.0ms	(/ (+ y 1.0) z)

series22.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (* x (/ (+ y 1.0) z)) x)
8.0ms	(* x (/ (+ y 1.0) z))
4.0ms	(/ (+ y 1.0) z)

simplify58.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5158	804

prune141.0ms (6.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0b

Counts

90 → 5

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y 1.0))
0.0b	(- (/ (* x (+ y 1.0)) z) x)
2.5b	(/ (* x (+ y 1.0)) z)

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`associate-r/` `associate-r*`
3×	`times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

7.0ms	(- (/ (* x (+ y 1.0)) z) x)
6.0ms	(/ (* x (+ y 1.0)) z)
6.0ms	(* x (+ y 1.0))

series25.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (/ (* x (+ y 1.0)) z) x)
8.0ms	(/ (* x (+ y 1.0)) z)
8.0ms	(* x (+ y 1.0))

simplify47.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4972	588
1	4972	588

prune98.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 0b

Counts

73 → 5

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* x (+ y 1.0))
0.0b	(- (/ 1 (/ z (* x (+ y 1.0)))) x)
0.4b	(/ 1 (/ z (* x (+ y 1.0))))
2.5b	(/ z (* x (+ y 1.0)))

rewrite39.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`times-frac`
35×	`add-sqr-sqrt`
32×	`add-exp-log` `*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`div-exp`
12×	`associate-*r/`
11×	`associate-/r/`
10×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-inv`
6×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
5×	`prod-exp`
4×	`associate-r`
3×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod` `difference-of-squares`
2×	`frac-2neg` `clear-num` `distribute-lft-out--`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-flip` `distribute-lft-in` `diff-log` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 126

Calls

4 calls:

16.0ms	(- (/ 1 (/ z (* x (+ y 1.0)))) x)
8.0ms	(/ 1 (/ z (* x (+ y 1.0))))
6.0ms	(/ z (* x (+ y 1.0)))
5.0ms	(* x (+ y 1.0))

series32.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ z (* x (+ y 1.0)))
9.0ms	(/ 1 (/ z (* x (+ y 1.0))))
9.0ms	(- (/ 1 (/ z (* x (+ y 1.0)))) x)
5.0ms	(* x (+ y 1.0))

simplify73.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	1463
1	4969	1463

prune192.0ms (8.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	138	5	143

Merged error: 0b

Counts

143 → 5

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/ z (+ y 1.0))
0.0b	(- (/ 1 (* (/ 1 x) (/ z (+ y 1.0)))) x)
0.4b	(/ 1 (* (/ 1 x) (/ z (+ y 1.0))))
4.4b	(* (/ 1 x) (/ z (+ y 1.0)))

rewrite50.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-exp-log`
51×	`div-exp`
50×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
43×	`times-frac`
36×	`add-cbrt-cube`
32×	`prod-exp`
30×	`add-cube-cbrt`
18×	`associate-r`
17×	`rec-exp` `1-exp`
14×	`cbrt-undiv`
13×	`associate-l`
9×	`pow1`
8×	`associate-/r/` `cbrt-unprod`
7×	`distribute-lft-out`
6×	`associate-/l*` `add-log-exp` `unswap-sqr`
5×	`associate-/r*` `div-inv`
3×	`associate-*l/`
2×	`frac-times` `pow-flip` `frac-2neg` `flip3-+` `associate-*r/` `pow-prod-down` `clear-num` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `*-commutative` `flip--` `inv-pow` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

13.0ms	(- (/ 1 (* (/ 1 x) (/ z (+ y 1.0)))) x)
13.0ms	(* (/ 1 x) (/ z (+ y 1.0)))
13.0ms	(/ 1 (* (/ 1 x) (/ z (+ y 1.0))))
5.0ms	(/ z (+ y 1.0))

series32.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (/ 1 x) (/ z (+ y 1.0)))
9.0ms	(/ 1 (* (/ 1 x) (/ z (+ y 1.0))))
9.0ms	(- (/ 1 (* (/ 1 x) (/ z (+ y 1.0)))) x)
5.0ms	(/ z (+ y 1.0))

simplify58.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4965	1611
1	4965	1611

prune238.0ms (10.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	176	5	181

Merged error: 0b

Counts

181 → 5

regimes153.0ms (6.7%)

Accuracy

Total 1.7b remaining (98.4%)

Threshold costs 0b (0%)

bsearch17.0ms (0.7%)

Steps

Iters	Range		Point
9	28364741821615.03	2.01458529633393e+18	2592826044157362.5

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms (0%)

sample480.0ms (20.9%)

Algorithm

1×

intervals

Results

247.0ms	8000×	body	80	valid
35.0ms	1086×	body	80	invalid

Details

analyze376.0ms (16.4%)

sample19.0ms (0.8%)

simplify64.0ms (2.8%)

prune12.0ms (0.5%)

localize6.0ms (0.3%)

rewrite22.0ms (1%)

series22.0ms (0.9%)

simplify58.0ms (2.5%)

prune141.0ms (6.1%)

localize6.0ms (0.3%)

rewrite21.0ms (0.9%)

series25.0ms (1.1%)

simplify47.0ms (2%)

prune98.0ms (4.3%)

localize10.0ms (0.4%)

rewrite39.0ms (1.7%)

series32.0ms (1.4%)

simplify73.0ms (3.2%)

prune192.0ms (8.4%)

localize9.0ms (0.4%)

rewrite50.0ms (2.2%)

series32.0ms (1.4%)

simplify58.0ms (2.5%)

prune238.0ms (10.3%)

regimes153.0ms (6.7%)

bsearch17.0ms (0.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample480.0ms (20.9%)

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