Details

analyze448.0ms (14.1%)

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)

sample152.0ms (4.8%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
2.0ms	32×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify63.0ms (2%)

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
	4.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.2b	(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))
✓	2.8b	(*.f64 (/.f64 x y) z)

series40.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

21.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
14.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.8%)

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:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
5.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

simplify120.0ms (3.8%)

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

prune171.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Error

0.0b

Counts

179 → 6

Alt Table

Status	Error	Program
	32.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 y)) z))))
	4.6b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	30.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
▶	1.3b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z))))
	15.1b	(fabs.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z))))
	33.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))

Compiler

Compiled 3710 to 1763 computations (52.5% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z)))
	2.8b	(*.f64 (/.f64 x y) z)

series21.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

21.0ms

(fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z)))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

412×	`times-frac_binary64`
399×	`distribute-rgt-in_binary64`
380×	`distribute-lft-in_binary64`
378×	`unsub-neg_binary64`
369×	`associate-l_binary64`

Counts

46 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	890
1	98	791
2	234	621
3	626	519
4	3056	519
5	4454	519
6	5347	519

prune84.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Error

0.0b

Counts

93 → 6

Alt Table

Status	Error	Program
	32.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 y)) z))))
▶	4.6b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
	30.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.3b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z))))
	15.1b	(fabs.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z))))
	33.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))

Compiler

Compiled 1828 to 961 computations (47.4% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1 z) 4)
✓	4.3b	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)

series21.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
4.0ms	(fma.f64 x (-.f64 1 z) 4)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 1 z) 4) y)
0.0ms	(fma.f64 x (-.f64 1 z) 4)

simplify73.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

488×	`unsub-neg_binary64`
437×	`fma-neg_binary64`
317×	`times-frac_binary64`
313×	`distribute-rgt-in_binary64`
302×	`distribute-lft-in_binary64`

Counts

99 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1544
1	172	1481
2	394	1286
3	824	1193
4	3792	1193
5	5192	1193

prune52.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	66	6	72

Error

0.0b

Counts

72 → 6

Alt Table

Status	Error	Program
	32.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 y)) z))))
✓	4.6b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
	30.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.3b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z))))
▶	15.1b	(fabs.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z))))
	33.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))

Compiler

Compiled 1132 to 749 computations (33.8% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (+.f64 x 4)) y)
✓	0.0b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z)))
	2.8b	(*.f64 (/.f64 x y) z)

series59.0ms (1.9%)

Counts

2 → 46

Calls

2 calls:

41.0ms	(fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z)))
17.0ms	(/.f64 (sqrt.f64 (+.f64 x 4)) y)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`sqrt-prod_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 (sqrt.f64 (+.f64 x 4)) y)
0.0ms	(fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z)))

simplify85.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

421×	`fma-def_binary64`
383×	`associate-/l*_binary64`
371×	`associate-*l/_binary64`
327×	`div-sub_binary64`
296×	`associate-*r/_binary64`

Counts

103 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1695
1	262	1543
2	556	1481
3	1413	1444
4	4375	1444
5	5266	1444

prune142.0ms (4.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	159	6	165

Error

0.0b

Counts

165 → 6

Alt Table

Status	Error	Program
	32.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 y)) z))))
✓	4.6b	(fabs.f64 (/.f64 (fma.f64 x (-.f64 1 z) 4) y))
	30.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.3b	(fabs.f64 (fma.f64 (+.f64 x 4) (/.f64 1 y) (neg.f64 (*.f64 (/.f64 x y) z))))
✓	15.1b	(fabs.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 x 4)) 1) (/.f64 (sqrt.f64 (+.f64 x 4)) y) (neg.f64 (*.f64 (/.f64 x y) z))))
	33.1b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))

Compiler

Compiled 4249 to 2477 computations (41.7% saved)

regimes498.0ms (15.7%)

Accuracy

Total 0.2b remaining (89.9%)

Threshold costs 0.2b (89.9%)

Counts

69 → 3

Compiler

Compiled 6554 to 4318 computations (34.1% saved)

bsearch32.0ms (1%)

Steps

Iters	Range		Point
10	0.00026646965904089084	49675348452.25999	48880875414.55884
4	-1.532516418195955e-48	-1.058745966519706e-53	-3.7938758802322557e-50

Compiler

Compiled 4 to 3 computations (25% saved)

simplify31.0ms (1%)

Algorithm

1×	egg-herbie

Rules

36×	`distribute-rgt-neg-in_binary64`
33×	`cancel-sign-sub-inv_binary64`
29×	`sub-neg_binary64`
22×	`distribute-lft-neg-in_binary64`
22×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	60
1	52	60
2	78	60
3	94	60
4	107	60
5	120	60
6	130	60
7	148	60
8	173	60
9	195	60
10	223	60
11	239	60
12	253	60
13	259	60
14	258	60
15	250	60

end1.0ms (0%)

Compiler: Compiled 43 to 29 computations (32.6% saved)

sample926.0ms (29.1%)

Algorithm

1×

intervals

Results

452.0ms	8000×	body	128	valid
87.0ms	1185×	body	128	invalid

Compiler

Compiled 174 to 117 computations (32.8% saved)

Iter	Nodes	Cost
0	28	60
1	52	60
2	78	60
3	94	60
4	107	60
5	120	60
6	130	60
7	148	60
8	173	60
9	195	60
10	223	60
11	239	60
12	253	60
13	259	60
14	258	60
15	250	60

Iter	Nodes	Cost
0	28	60
1	52	60
2	78	60
3	94	60
4	107	60
5	120	60
6	130	60
7	148	60
8	173	60
9	195	60
10	223	60
11	239	60
12	253	60
13	259	60
14	258	60
15	250	60

Details

analyze448.0ms (14.1%)

sample152.0ms (4.8%)

simplify63.0ms (2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series40.0ms (1.3%)

rewrite26.0ms (0.8%)

simplify120.0ms (3.8%)

prune171.0ms (5.4%)

localize12.0ms (0.4%)

series21.0ms (0.7%)

rewrite1.0ms (0%)

simplify77.0ms (2.4%)

prune84.0ms (2.7%)

localize8.0ms (0.3%)

series21.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify73.0ms (2.3%)

prune52.0ms (1.6%)

localize12.0ms (0.4%)

series59.0ms (1.9%)

rewrite9.0ms (0.3%)

simplify85.0ms (2.7%)

prune142.0ms (4.5%)

regimes498.0ms (15.7%)

bsearch32.0ms (1%)

simplify31.0ms (1%)

end1.0ms (0%)

sample926.0ms (29.1%)

Profiling

Iter	Nodes	Cost
0	28	60
1	52	60
2	78	60
3	94	60
4	107	60
5	120	60
6	130	60
7	148	60
8	173	60
9	195	60
10	223	60
11	239	60
12	253	60
13	259	60
14	258	60
15	250	60