Details

analyze421.0ms (11.8%)

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
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (30.7%)

Results

832.0ms	8256×	body	128	valid
75.0ms	786×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

3.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize10.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series10.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

1 → 52

Calls

1 calls:

5.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

simplify96.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

412×	`unsub-neg_binary64`
396×	`exp-prod_binary64`
359×	`distribute-rgt-in_binary64`
334×	`distribute-lft-in_binary64`
331×	`fma-def_binary64`

Counts

88 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1249
1	225	1167
2	784	1113
3	2358	1057
4	3941	1057
5	4982	1057
6	4909	1057

prune56.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Alt Table

Status	Error	Program
	17.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	34.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
✓	3.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	32.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
	4.6b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (cbrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
▶	1.4b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 1619 to 773 computations (52.3% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.6b	(.f64 y (.f64 z x))

series27.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

10.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
9.0ms	(.f64 y (.f64 z x))
7.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(.f64 y (.f64 z x))
6.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune58.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Error

Counts

109 → 6

Alt Table

Status	Error	Program
▶	17.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	34.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.8b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	32.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
✓	1.4b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 1883 to 525 computations (72.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.1b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	2.4b	(sqrt.f64 (-.f64 (fma.f64 y z 1) z))

series150.0ms (4.2%)

Counts

3 → 64

Calls

3 calls:

87.0ms	(*.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
53.0ms	(sqrt.f64 (-.f64 (fma.f64 y z 1) z))
10.0ms	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
16×	`sqrt-div_binary64`
15×	`*-un-lft-identity_binary64`

Counts

3 → 80

Calls

3 calls:

9.0ms	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
5.0ms	(*.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
5.0ms	(sqrt.f64 (-.f64 (fma.f64 y z 1) z))

simplify106.0ms (3%)

Algorithm

1×	egg-herbie

Rules

474×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
382×	`cancel-sign-sub-inv_binary64`
324×	`associate-l_binary64`
306×	`fma-neg_binary64`

Counts

144 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2879
1	636	2716
2	2191	2674
3	4858	2664
4	5032	2664

prune158.0ms (4.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	204	6	210

Error

Counts

210 → 6

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	34.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.8b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
▶	32.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
✓	1.4b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 5998 to 3748 computations (37.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))
✓	0.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
	3.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series436.0ms (12.2%)

Counts

2 → 40

Calls

2 calls:

270.0ms	(sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))
165.0ms	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
16×	`associate-*r/_binary64`
14×	`sqrt-div_binary64`

Counts

2 → 74

Calls

2 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
6.0ms	(sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
583×	`fma-neg_binary64`
392×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`
227×	`cancel-sign-sub-inv_binary64`

Counts

114 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2161
1	413	1985
2	1487	1844
3	4652	1842
4	5118	1842

prune196.0ms (5.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	307	6	313

Error

Counts

313 → 6

Alt Table

Status	Error	Program
✓	17.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	34.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (fma.f64 y z 1) z)))
	32.8b	(.f64 (-.f64 (.f64 y x) x) z)
✓	3.3b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
✓	32.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))))
✓	1.4b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))

Compiler

Compiled 9112 to 5066 computations (44.4% saved)

regimes323.0ms (9.1%)

Accuracy

Total 0.3b remaining (96.6%)

Threshold costs 0.3b (96.6%)

Counts

37 → 3

Compiler

Compiled 4293 to 2819 computations (34.3% saved)

bsearch29.0ms (0.8%)

Steps

Iters	Range		Point
3	1.0381680177371557e-75	3.300973252377263e-73	1.599520831582608e-73
8	-3.829701417174297e+87	-8.680008759409105e+83	-8.795145312110055e+83

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	28	51
2	38	51
3	44	51
4	48	51
5	49	51
6	48	51

end90.0ms (2.5%)

Compiler: Compiled 170 to 88 computations (48.2% saved)

Details

analyze421.0ms (11.8%)

sample1.1s (30.7%)

simplify40.0ms (1.1%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series10.0ms (0.3%)

rewrite10.0ms (0.3%)

simplify96.0ms (2.7%)

prune56.0ms (1.6%)

localize5.0ms (0.1%)

series27.0ms (0.7%)

rewrite18.0ms (0.5%)

simplify81.0ms (2.3%)

prune58.0ms (1.6%)

localize7.0ms (0.2%)

series150.0ms (4.2%)

rewrite25.0ms (0.7%)

simplify106.0ms (3%)

prune158.0ms (4.4%)

localize7.0ms (0.2%)

series436.0ms (12.2%)

rewrite25.0ms (0.7%)

simplify84.0ms (2.3%)

prune196.0ms (5.5%)

regimes323.0ms (9.1%)

bsearch29.0ms (0.8%)

simplify3.0ms (0.1%)

end90.0ms (2.5%)

Profiling