Details

analyze603.0ms (15.3%)

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)

sample33.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
2.0ms	41×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify70.0ms (1.8%)

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
	3.9b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	2.9b	(*.f64 (/.f64 x y) z)

series58.0ms (1.5%)

Counts

3 → 96

Calls

3 calls:

29.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
15.0ms	(/.f64 (+.f64 x 4) y)
13.0ms	(*.f64 (/.f64 x y) z)

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

16.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
8.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

simplify137.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune176.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Error

Counts

179 → 8

Alt Table

Status	Error	Program
	3.9b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	32.7b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
▶	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	29.8b	(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
	31.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	32.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
	30.9b	(fabs.f64 (-.f64 (/.f64 (/.f64 (+.f64 x 4) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 3780 to 1805 computations (52.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series188.0ms (4.8%)

Counts

4 → 48

Calls

4 calls:

71.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
41.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
41.0ms	(cbrt.f64 x)
35.0ms	(cbrt.f64 y)

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
38×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
10.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 x)

simplify177.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
708×	`log-prod_binary64`
594×	`unswap-sqr_binary64`
324×	`exp-prod_binary64`
238×	`*-commutative_binary64`

Counts

158 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1220
1	174	1108
2	558	1032
3	895	1004
4	2346	820
5	4061	820
6	4265	820
7	4815	820

prune278.0ms (7.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	220	8	228

Error

Counts

228 → 8

Alt Table

Status	Error	Program
	3.9b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	32.7b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))
▶	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	29.8b	(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
	31.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	32.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
	30.9b	(fabs.f64 (-.f64 (/.f64 (/.f64 (+.f64 x 4) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 6878 to 2335 computations (66.1% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
✓	7.5b	(*.f64 x (/.f64 z y))

series78.0ms (2%)

Counts

2 → 72

Calls

2 calls:

50.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
28.0ms	(*.f64 x (/.f64 z y))

rewrite45.0ms (1.2%)

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:

21.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
11.0ms	(*.f64 x (/.f64 z y))

simplify173.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-r_binary64`
373×	`associate-*r/_binary64`
365×	`associate-*l/_binary64`
350×	`fma-def_binary64`
341×	`fma-neg_binary64`

Counts

154 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2478
1	386	2346
2	1212	1703
3	3481	1689
4	4636	1689
5	4914	1689

prune194.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	171	8	179

Error

Counts

179 → 8

Alt Table

Status	Error	Program
▶	3.9b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 x z) (/.f64 1 y))))
	31.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 z (sqrt.f64 y)))))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))
✓	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	29.8b	(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
	32.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
	30.9b	(fabs.f64 (-.f64 (/.f64 (/.f64 (+.f64 x 4) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 3571 to 1725 computations (51.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.6b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series24.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

24.0ms

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

rewrite12.0ms (0.3%)

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:

9.0ms

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

simplify101.0ms (2.6%)

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

prune113.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	70	8	78

Error

Counts

78 → 8

Alt Table

Status	Error	Program
✓	3.9b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	3.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 x z) (/.f64 1 y))))
	31.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 z (sqrt.f64 y)))))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))
✓	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	29.8b	(fabs.f64 (*.f64 (/.f64 x y) (-.f64 1 z)))
	32.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))
	30.9b	(fabs.f64 (-.f64 (/.f64 (/.f64 (+.f64 x 4) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 1362 to 821 computations (39.7% saved)

regimes411.0ms (10.4%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Counts

57 → 1

Compiler

Compiled 5397 to 3526 computations (34.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	28	40
2	42	40
3	61	40
4	82	40
5	96	40
6	103	40
7	105	40
8	104	40

end1.0ms (0%)

Compiler: Compiled 28 to 17 computations (39.3% saved)

sample930.0ms (23.6%)

Algorithm

1×

intervals

Results

429.0ms	8000×	body	128	valid
64.0ms	1181×	body	128	invalid

Compiler

Compiled 190 to 123 computations (35.3% saved)

Details

analyze603.0ms (15.3%)

sample33.0ms (0.8%)

simplify70.0ms (1.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series58.0ms (1.5%)

rewrite40.0ms (1%)

simplify137.0ms (3.5%)

prune176.0ms (4.5%)

localize16.0ms (0.4%)

series188.0ms (4.8%)

rewrite35.0ms (0.9%)

simplify177.0ms (4.5%)

prune278.0ms (7.1%)

localize16.0ms (0.4%)

series78.0ms (2%)

rewrite45.0ms (1.2%)

simplify173.0ms (4.4%)

prune194.0ms (4.9%)

localize8.0ms (0.2%)

series24.0ms (0.6%)

rewrite12.0ms (0.3%)

simplify101.0ms (2.6%)

prune113.0ms (2.9%)

regimes411.0ms (10.4%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample930.0ms (23.6%)

Profiling