Details

analyze1.0s (10%)

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)

sample73.0ms (0.7%)

Algorithm

1×

intervals

Results

50.0ms	256×	body	128	valid
5.0ms	55×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify83.0ms (0.8%)

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

prune6.0ms (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
▶	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize16.0ms (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))
✓	1.8b	(*.f64 (/.f64 x y) z)

rewrite45.0ms (0.4%)

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:

15.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
9.0ms	(*.f64 (/.f64 x y) z)
7.0ms	(/.f64 (+.f64 x 4) y)

series308.0ms (3%)

Counts

3 → 96

Calls

3 calls:

139.0ms	(*.f64 (/.f64 x y) z)
136.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
32.0ms	(/.f64 (+.f64 x 4) y)

simplify234.0ms (2.3%)

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 → 353

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

prune306.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	347	6	353
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	348	7	355

Error

0.0b

Counts

355 → 7

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.4b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	32.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
	29.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
▶	1.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	31.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))

Compiler

Compiled 3763 to 1790 computations (52.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 z)
✓	1.8b	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 50

Calls

2 calls:

14.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
1.0ms	(cbrt.f64 z)

series2.3s (22.9%)

Counts

2 → 48

Calls

2 calls:

1.8s	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
469.0ms	(cbrt.f64 z)

simplify198.0ms (2%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-r_binary64`
726×	`associate-l_binary64`
590×	`unswap-sqr_binary64`
446×	`fma-def_binary64`
293×	`associate-*l/_binary64`

Counts

98 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1283
1	232	1071
2	670	989
3	2951	989
4	4315	989
5	4840	989
6	4932	989

prune216.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	306	7	313

Error

Counts

313 → 7

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.4b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	32.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
▶	1.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (*.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z)) (cbrt.f64 z))))
	29.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	31.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))

Compiler

Compiled 2999 to 1296 computations (56.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 z)
	0.6b	(cbrt.f64 z)
✓	0.9b	(.f64 (.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z))
✓	1.2b	(*.f64 (/.f64 x y) (cbrt.f64 z))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
14×	`associate-l_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

14.0ms	(*.f64 (/.f64 x y) (cbrt.f64 z))
13.0ms	(.f64 (.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z))

series2.5s (24.3%)

Counts

2 → 72

Calls

2 calls:

1.5s	(*.f64 (/.f64 x y) (cbrt.f64 z))
919.0ms	(.f64 (.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z))

simplify153.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

394×	`times-frac_binary64`
386×	`associate-/r/_binary64`
365×	`fma-def_binary64`
350×	`associate-*l/_binary64`
309×	`associate-/r*_binary64`

Counts

137 → 255

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	1883
1	274	1627
2	858	1613
3	2201	1613
4	4373	1533
5	4775	1533
6	4995	1533
7	4933	1533

prune139.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	747	0	747
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	747	7	754

Error

Counts

754 → 7

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.4b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	32.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
▶	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
✓	1.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (*.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z)) (cbrt.f64 z))))
	29.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	31.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))

Compiler

Compiled 3477 to 1475 computations (57.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 x)
✓	0.6b	(*.f64 (/.f64 (cbrt.f64 x) y) z)
✓	4.9b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
33×	`prod-exp_binary64`
29×	`associate-l_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

3 → 104

Calls

3 calls:

10.0ms	(*.f64 (/.f64 (cbrt.f64 x) y) z)
9.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))
1.0ms	(cbrt.f64 x)

series1.1s (10.7%)

Counts

3 → 84

Calls

3 calls:

804.0ms	(*.f64 (/.f64 (cbrt.f64 x) y) z)
213.0ms	(cbrt.f64 x)
69.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))

simplify126.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

757×	`times-frac_binary64`
403×	`*-commutative_binary64`
370×	`associate-/r*_binary64`
289×	`log-prod_binary64`
279×	`cube-prod_binary64`

Counts

188 → 326

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1966
1	338	1728
2	1285	1691
3	3610	1691
4	4892	1691
5	4954	1691

prune148.0ms (1.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	367	7	374

Error

Counts

374 → 7

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.4b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	32.4b	(fabs.f64 (/.f64 (-.f64 (.f64 (+.f64 x 4) y) (.f64 y (.f64 x z))) (.f64 y y)))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
✓	1.7b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (*.f64 (/.f64 x y) (cbrt.f64 z)) (cbrt.f64 z)) (cbrt.f64 z))))
	29.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	31.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) 1) (.f64 (/.f64 (sqrt.f64 x) y) z))))

Compiler

Compiled 4964 to 2057 computations (58.6% saved)

regimes197.0ms (1.9%)

Accuracy

Total 0.7b remaining (98%)

Threshold costs 0.7b (98%)

Compiler

Compiled 3472 to 2206 computations (36.5% 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	17	42
1	27	42
2	41	42
3	63	42
4	85	42
5	99	42
6	105	42
7	106	42
8	105	42

end1.0ms (0%)

Compiler: Compiled 29 to 16 computations (44.8% saved)

sample810.0ms (8%)

Algorithm

1×

intervals

Results

370.0ms	8000×	body	128	valid
56.0ms	1232×	body	128	invalid

Compiler

Compiled 181 to 116 computations (35.9% saved)

Details

analyze1.0s (10%)

sample73.0ms (0.7%)

simplify83.0ms (0.8%)

prune6.0ms (0.1%)

localize16.0ms (0.2%)

rewrite45.0ms (0.4%)

series308.0ms (3%)

simplify234.0ms (2.3%)

prune306.0ms (3%)

localize23.0ms (0.2%)

rewrite56.0ms (0.6%)

series2.3s (22.9%)

simplify198.0ms (2%)

prune216.0ms (2.1%)

localize23.0ms (0.2%)

rewrite34.0ms (0.3%)

series2.5s (24.3%)

simplify153.0ms (1.5%)

prune139.0ms (1.4%)

localize13.0ms (0.1%)

rewrite25.0ms (0.3%)

series1.1s (10.7%)

simplify126.0ms (1.3%)

prune148.0ms (1.5%)

regimes197.0ms (1.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample810.0ms (8%)

Profiling