Details

analyze243.0ms (5.4%)

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%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
12.5%	43.7%	43.8%	7
12.5%	43.7%	43.8%	8
25%	28.1%	47%	9
28.1%	20.3%	51.6%	10
28.1%	20.3%	51.6%	11
34.3%	13.3%	52.4%	12
35.9%	9.8%	54.4%	13
35.9%	9.8%	54.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample1.1s (24.2%)

Results

1.0s	8256×	body	128	valid
45.0ms	374×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

preprocess51.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

811×	`fma-def_binary64`
443×	`unsub-neg_binary64`
369×	`distribute-rgt-in_binary64`
336×	`fma-neg_binary64`
248×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	64
1	82	64
2	209	64
3	491	64
4	1161	56
5	2534	56
6	4299	56
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

982×	`fma-def_binary64`
790×	`fma-neg_binary64`
274×	`sub-neg_binary64`
221×	`associate--r+_binary64`
216×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	29	16
2	65	16
3	143	16
4	336	14
5	718	14
6	1240	14
7	1881	14
8	2833	14
9	3323	14
10	4425	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
✓	0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
✓	0.2b	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

series246.0ms (5.5%)

Counts

3 → 72

Calls

18 calls:

67.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))	y	0
49.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))	y	inf
45.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))	y	-inf
13.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))	y	inf
11.0ms	(+.f64 (.f64 x 1/2) (.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))	y	-inf

rewrite70.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`fma-def_binary64`
313×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
140×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	268	37
2	3898	37

Stop Event

1×	node limit

Counts

3 → 168

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
425×	`unsub-neg_binary64`
372×	`sub-neg_binary64`
238×	`fma-neg_binary64`
218×	`associate--r-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	950
1	150	867
2	398	867
3	1182	765
4	3314	765
5	4689	765

Stop Event

1×	node limit

Counts

240 → 193

prune182.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	185	8	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	8	194

Error

0.0b

Counts

194 → 8

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))
	34.4b	(+.f64 (.f64 x 1/2) (pow.f64 (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))) (.f64 x 1/2))
	29.8b	(+.f64 (.f64 x 1/2) (fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (log.f64 z)) (*.f64 y (-.f64 1 z))))
▶	0.1b	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
	15.4b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)) y) (-.f64 1 (+.f64 z (log.f64 z)))))
	0.3b	(+.f64 (.f64 x 1/2) (fma.f64 (cbrt.f64 (pow.f64 (log.f64 z) 2)) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))

Compiler

Compiled 3909 to 2337 computations (40.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (-.f64 1 z) (log.f64 z))
✓	0.1b	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))

series71.0ms (1.6%)

Counts

1 → 36

Calls

9 calls:

12.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	y	inf
12.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	x	0
11.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	y	-inf
11.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	y	0
8.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	x	inf

rewrite47.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`prod-diff_binary64`
206×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
115×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	232	16
2	3022	16

Stop Event

1×	node limit

Counts

1 → 23

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

545×	`sub-neg_binary64`
494×	`fma-neg_binary64`
423×	`fma-def_binary64`
339×	`unsub-neg_binary64`
327×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	108	503
2	296	503
3	812	443
4	2162	443
5	4558	443

Stop Event

1×	node limit

Counts

59 → 36

prune86.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	88	8	96

Error

0.0b

Counts

96 → 8

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))
	34.4b	(+.f64 (.f64 x 1/2) (pow.f64 (sqrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 2))
✓	0.1b	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
	15.4b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)) y) (-.f64 1 (+.f64 z (log.f64 z)))))
	16.2b	(fma.f64 y (cbrt.f64 (pow.f64 (+.f64 (-.f64 1 z) (log.f64 z)) 3)) (*.f64 x 1/2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))) (.f64 x 1/2))
	0.3b	(+.f64 (.f64 x 1/2) (fma.f64 (cbrt.f64 (pow.f64 (log.f64 z) 2)) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))

Compiler

Compiled 1741 to 1087 computations (37.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))
✓	0.1b	(fma.f64 y (log.f64 z) (*.f64 x 1/2))

series157.0ms (3.5%)

Counts

2 → 72

Calls

18 calls:

12.0ms	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))	y	inf
12.0ms	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))	x	0
12.0ms	(fma.f64 y (log.f64 z) (*.f64 x 1/2))	y	-inf
11.0ms	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))	y	-inf
11.0ms	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))	y	0

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
332×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
162×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	221	27
2	2615	27

Stop Event

1×	node limit

Counts

2 → 59

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

615×	`sub-neg_binary64`
584×	`fma-neg_binary64`
475×	`fma-def_binary64`
370×	`unsub-neg_binary64`
360×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	916
1	128	833
2	334	833
3	931	773
4	2408	773
5	4638	773

Stop Event

1×	node limit

Counts

131 → 77

prune79.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	77	8	85

Error

0.0b

Counts

85 → 8

Alt Table

Status	Error	Program
	15.4b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)) y) (-.f64 1 (+.f64 z (log.f64 z)))))
	1.0b	(fma.f64 y (-.f64 1 z) (pow.f64 (cbrt.f64 (fma.f64 y (log.f64 z) (*.f64 x 1/2))) 3))
✓	0.1b	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))
✓	0.1b	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
	16.2b	(fma.f64 y (cbrt.f64 (pow.f64 (+.f64 (-.f64 1 z) (log.f64 z)) 3)) (*.f64 x 1/2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))) (.f64 x 1/2))
▶	0.3b	(+.f64 (.f64 x 1/2) (fma.f64 (cbrt.f64 (pow.f64 (log.f64 z) 2)) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))

Compiler

Compiled 1598 to 952 computations (40.4% saved)

localize45.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (log.f64 z)) y)
✓	0.5b	(cbrt.f64 (log.f64 z))
✓	0.5b	(cbrt.f64 (pow.f64 (log.f64 z) 2))
✓	0.5b	(pow.f64 (log.f64 z) 2)

series718.0ms (16.1%)

Counts

4 → 56

Calls

15 calls:

110.0ms	(*.f64 (cbrt.f64 (log.f64 z)) y)	y	-inf
87.0ms	(*.f64 (cbrt.f64 (log.f64 z)) y)	z	inf
85.0ms	(cbrt.f64 (log.f64 z))	z	inf
82.0ms	(*.f64 (cbrt.f64 (log.f64 z)) y)	y	0
70.0ms	(cbrt.f64 (pow.f64 (log.f64 z) 2))	z	-inf

rewrite48.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`pow1_binary64`
631×	`add-log-exp_binary64`
631×	`log1p-expm1-u_binary64`
631×	`expm1-log1p-u_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	174	27
2	1853	27

Stop Event

1×	node limit

Counts

4 → 78

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
384×	`unswap-sqr_binary64`
269×	`unsub-neg_binary64`
267×	`fma-neg_binary64`
224×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	468
1	74	452
2	137	452
3	372	452
4	1220	452
5	3231	452

Stop Event

1×	node limit

Counts

134 → 93

prune139.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	94	7	101

Error

0.0b

Counts

101 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (pow.f64 (log.f64 z) 2) 1/3) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))
✓	0.1b	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))
✓	0.1b	(fma.f64 y (-.f64 1 z) (fma.f64 y (log.f64 z) (*.f64 x 1/2)))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
	1.0b	(fma.f64 y (-.f64 1 z) (pow.f64 (cbrt.f64 (fma.f64 y (log.f64 z) (*.f64 x 1/2))) 3))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (+.f64 (-.f64 1 z) (log.f64 z))) (.f64 x 1/2))
✓	0.3b	(+.f64 (.f64 x 1/2) (fma.f64 (cbrt.f64 (pow.f64 (log.f64 z) 2)) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))

Compiler

Compiled 2347 to 1315 computations (44% saved)

regimes769.0ms (17.2%)

Accuracy

Total 0.1b remaining (80.8%)

Threshold costs 0.1b (80.8%)

Counts

99 → 1

Compiler

Compiled 11976 to 8630 computations (27.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	21	16
3	23	16
4	24	16

Stop Event

1×

saturated

end116.0ms (2.6%)

Stop Event

1×

fuel

Compiler

Compiled 160 to 114 computations (28.8% saved)

Details

analyze243.0ms (5.4%)

sample1.1s (24.2%)

preprocess51.0ms (1.1%)

simplify39.0ms (0.9%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series246.0ms (5.5%)

rewrite70.0ms (1.6%)

simplify58.0ms (1.3%)

prune182.0ms (4.1%)

localize8.0ms (0.2%)

series71.0ms (1.6%)

rewrite47.0ms (1.1%)

simplify42.0ms (1%)

prune86.0ms (1.9%)

localize10.0ms (0.2%)

series157.0ms (3.5%)

rewrite49.0ms (1.1%)

simplify53.0ms (1.2%)

prune79.0ms (1.8%)

localize45.0ms (1%)

series718.0ms (16.1%)

rewrite48.0ms (1.1%)

simplify39.0ms (0.9%)

prune139.0ms (3.1%)

regimes769.0ms (17.2%)

simplify3.0ms (0.1%)

end116.0ms (2.6%)

Profiling