Details

analyze547.0ms (13.4%)

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
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample148.0ms (3.6%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
2.0ms	36×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	3.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series15.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 40

Calls

1 calls:

5.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

552×	`distribute-rgt-in_binary64`
532×	`distribute-lft-in_binary64`
426×	`fma-def_binary64`
406×	`times-frac_binary64`
357×	`div-sub_binary64`

Counts

76 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1438
1	224	1392
2	495	1134
3	1230	1134
4	4511	1134
5	4991	1134

prune60.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Error

0.0b

Counts

72 → 6

Alt Table

Status	Error	Program
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	33.8b	(fabs.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (fma.f64 x z -4))) (cbrt.f64 (-.f64 x (fma.f64 x z -4)))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (-.f64 x (fma.f64 x z -4))) (sqrt.f64 y))))
	4.3b	(fabs.f64 (/.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)))
▶	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	33.4b	(fabs.f64 (/.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) (sqrt.f64 y)) (sqrt.f64 y)))
	3.2b	(fabs.f64 (/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4)))))

Compiler

Compiled 1451 to 879 computations (39.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (/.f64 1 y))
✓	0.0b	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
✓	0.0b	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
✓	7.4b	(/.f64 (*.f64 z x) y)

series41.0ms (1%)

Counts

4 → 66

Calls

4 calls:

18.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
13.0ms	(/.f64 (*.f64 z x) y)
7.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
1.0ms	(*.f64 4 (/.f64 1 y))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`
28×	`prod-diff_binary64`

Counts

4 → 150

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
6.0ms	(*.f64 4 (/.f64 1 y))
5.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
3.0ms	(/.f64 (*.f64 z x) y)

simplify129.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-def_binary64`
584×	`times-frac_binary64`
413×	`fma-neg_binary64`
247×	`cancel-sign-sub-inv_binary64`
200×	`distribute-rgt-neg-in_binary64`

Counts

216 → 231

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	246	3440
1	602	3020
2	1945	2741
3	4148	2727
4	4969	2710
5	4977	2710

prune171.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	232	5	237

Error

Counts

237 → 5

Alt Table

Status	Error	Program
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	33.8b	(fabs.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (fma.f64 x z -4))) (cbrt.f64 (-.f64 x (fma.f64 x z -4)))) (sqrt.f64 y)) (/.f64 (cbrt.f64 (-.f64 x (fma.f64 x z -4))) (sqrt.f64 y))))
	33.7b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
▶	3.2b	(fabs.f64 (/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4)))))

Compiler

Compiled 6212 to 2754 computations (55.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4))))
✓	2.9b	(/.f64 y (-.f64 x (fma.f64 x z -4)))

series54.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

38.0ms	(/.f64 y (-.f64 x (fma.f64 x z -4)))
16.0ms	(/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4))))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 149

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4))))
4.0ms	(/.f64 y (-.f64 x (fma.f64 x z -4)))

simplify146.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

707×	`times-frac_binary64`
407×	`fma-neg_binary64`
237×	`cancel-sign-sub-inv_binary64`
140×	`distribute-neg-in_binary64`
135×	`associate-r_binary64`

Counts

221 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	5376
1	731	5069
2	2613	4865
3	4582	4865
4	5119	4865

prune156.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	219	5	224

Error

Counts

224 → 5

Alt Table

Status	Error	Program
▶	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	33.7b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	16.0b	(fabs.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 x (fma.f64 x z -4))))) (/.f64 y (sqrt.f64 (-.f64 x (fma.f64 x z -4))))))
✓	3.2b	(fabs.f64 (/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4)))))

Compiler

Compiled 5478 to 3414 computations (37.7% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	5.3b	(*.f64 (/.f64 x y) z)

series30.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
11.0ms	(*.f64 (/.f64 x y) z)

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
4.0ms	(*.f64 (/.f64 x y) z)

simplify128.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
414×	`associate-l_binary64`
348×	`associate-*l/_binary64`
343×	`associate-r_binary64`
327×	`fma-def_binary64`

Counts

154 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2469
1	383	2220
2	1060	1685
3	3521	1673
4	4720	1673
5	4999	1673
6	4896	1673

prune108.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Error

Counts

143 → 5

Alt Table

Status	Error	Program
✓	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	3.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	16.0b	(fabs.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 x (fma.f64 x z -4))))) (/.f64 y (sqrt.f64 (-.f64 x (fma.f64 x z -4))))))
	3.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	3.2b	(fabs.f64 (/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4)))))

Compiler

Compiled 2833 to 1294 computations (54.3% saved)

regimes1.3s (31.1%)

Accuracy

Total 0.7b remaining (98%)

Threshold costs 0.7b (98%)

Counts

135 → 3

Compiler

Compiled 12837 to 8926 computations (30.5% saved)

bsearch17.0ms (0.4%)

Steps

Iters	Range		Point
1	7.630791711714039e-102	6.27408636819691e-98	7.17864311788996e-100
5	-4.19378435762958e+155	-1.1027265248738358e+151	-1.5209272263734793e+151

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
15×	`*-commutative_binary64`
15×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	72
1	54	72
2	80	72
3	107	72
4	129	72
5	138	72
6	140	72
7	137	72

end1.0ms (0%)

Compiler: Compiled 51 to 34 computations (33.3% saved)

sample800.0ms (19.6%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
58.0ms	1239×	body	128	invalid

Compiler

Compiled 158 to 109 computations (31% saved)

Details

analyze547.0ms (13.4%)

sample148.0ms (3.6%)

simplify64.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.4%)

rewrite8.0ms (0.2%)

simplify70.0ms (1.7%)

prune60.0ms (1.5%)

localize12.0ms (0.3%)

series41.0ms (1%)

rewrite35.0ms (0.9%)

simplify129.0ms (3.2%)

prune171.0ms (4.2%)

localize8.0ms (0.2%)

series54.0ms (1.3%)

rewrite26.0ms (0.6%)

simplify146.0ms (3.6%)

prune156.0ms (3.8%)

localize8.0ms (0.2%)

series30.0ms (0.7%)

rewrite18.0ms (0.4%)

simplify128.0ms (3.1%)

prune108.0ms (2.6%)

regimes1.3s (31.1%)

bsearch17.0ms (0.4%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample800.0ms (19.6%)

Profiling