Details

analyze238.0ms (3.9%)

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 (17.5%)

Results

1.0s	8256×	body	128	valid
47.0ms	374×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

preprocess43.0ms (0.7%)

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 (0.6%)

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%)

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)

localize8.0ms (0.1%)

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)))

series255.0ms (4.2%)

Counts

3 → 72

Calls

18 calls:

66.0ms	(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))	y	0
59.0ms	(*.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

rewrite71.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`fma-def_binary64`
313×	`fma-neg_binary64`
239×	`expm1-udef_binary64`
238×	`log1p-udef_binary64`
168×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	269	37
2	3847	37

Stop Event

1×	node limit

Counts

3 → 168

simplify57.0ms (0.9%)

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

prune253.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (.f64 (-.f64 1 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (fma.f64 y (log.f64 z) (.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))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
	0.4b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))
	0.5b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.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))
	15.4b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)) y) (-.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 3889 to 2324 computations (40.2% saved)

localize8.0ms (0.1%)

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))

series88.0ms (1.4%)

Counts

1 → 36

Calls

9 calls:

28.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	x	0
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))	y	0
11.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	y	inf
8.0ms	(fma.f64 y (+.f64 (-.f64 1 z) (log.f64 z)) (*.f64 x 1/2))	x	inf

rewrite49.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`prod-diff_binary64`
206×	`log1p-udef_binary64`
116×	`add-sqr-sqrt_binary64`
110×	`add-cbrt-cube_binary64`
110×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	233	16
2	2999	16

Stop Event

1×	node limit

Counts

1 → 23

simplify43.0ms (0.7%)

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

prune101.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Error

0.0b

Counts

95 → 7

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (.f64 (-.f64 1 z) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (fma.f64 y (log.f64 z) (.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))
	0.8b	(+.f64 (.f64 x 1/2) (pow.f64 (cbrt.f64 (.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))) 3))
▶	0.4b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))
	0.5b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.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))
	15.4b	(+.f64 (.f64 x 1/2) (/.f64 (.f64 (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)) y) (-.f64 (-.f64 1 z) (log.f64 z))))

Compiler

Compiled 1727 to 1071 computations (38% saved)

localize37.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (.f64 y (-.f64 1 z)))
✓	0.3b	(*.f64 (cbrt.f64 (log.f64 z)) y)
✓	0.5b	(pow.f64 (cbrt.f64 (log.f64 z)) 2)
✓	0.5b	(cbrt.f64 (log.f64 z))

series1.3s (20.5%)

Counts

4 → 72

Calls

18 calls:

166.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (.f64 y (-.f64 1 z)))	y	0
144.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (.f64 y (-.f64 1 z)))	y	inf
135.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (.f64 y (-.f64 1 z)))	y	-inf
93.0ms	(fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (.f64 y (-.f64 1 z)))	z	inf
92.0ms	(*.f64 (cbrt.f64 (log.f64 z)) y)	z	inf

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
338×	`prod-diff_binary64`
196×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
176×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	242	36
2	2806	34

Stop Event

1×	node limit

Counts

4 → 94

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

847×	`fma-neg_binary64`
440×	`associate-l_binary64`
391×	`associate-r_binary64`
330×	`fma-def_binary64`
196×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	736
1	149	707
2	365	665
3	1111	665
4	3964	665

Stop Event

1×	node limit

Counts

166 → 117

prune167.0ms (2.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
	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))
▶	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 1 z)) (*.f64 (log.f64 z) y)))
✓	0.4b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))
	0.5b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.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))
	0.3b	(+.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))))

Compiler

Compiled 3555 to 1908 computations (46.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 1 z))
✓	0.0b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 1 z)) (*.f64 (log.f64 z) y)))
✓	0.2b	(+.f64 (.f64 y (-.f64 1 z)) (.f64 (log.f64 z) y))
✓	0.3b	(*.f64 (log.f64 z) y)

series429.0ms (7%)

Counts

4 → 80

Calls

27 calls:

62.0ms	(+.f64 (.f64 y (-.f64 1 z)) (.f64 (log.f64 z) y))	y	0
61.0ms	(*.f64 (log.f64 z) y)	y	0
52.0ms	(*.f64 (log.f64 z) y)	y	inf
48.0ms	(+.f64 (.f64 y (-.f64 1 z)) (.f64 (log.f64 z) y))	y	-inf
48.0ms	(+.f64 (.f64 y (-.f64 1 z)) (.f64 (log.f64 z) y))	y	inf

rewrite65.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

361×	`fma-neg_binary64`
253×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
135×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	284	41
2	3875	41

Stop Event

1×	node limit

Counts

4 → 112

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

498×	`sub-neg_binary64`
483×	`fma-def_binary64`
345×	`unsub-neg_binary64`
335×	`distribute-neg-in_binary64`
217×	`associate--l-_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	1013
1	137	957
2	366	796
3	997	796
4	2858	796
5	4199	796

Stop Event

1×	node limit

Counts

192 → 136

prune142.0ms (2.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
	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))
✓	0.1b	(+.f64 (.f64 x 1/2) (+.f64 (.f64 y (-.f64 1 z)) (*.f64 (log.f64 z) y)))
✓	0.4b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 (log.f64 z)) 2) (.f64 (cbrt.f64 (log.f64 z)) y) (*.f64 y (-.f64 1 z))))
	0.5b	(+.f64 (.f64 x 1/2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.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))
	0.3b	(+.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))))

Compiler

Compiled 2799 to 1663 computations (40.6% saved)

regimes1.4s (23.2%)

Accuracy

Total 0.1b remaining (64.3%)

Threshold costs 0.1b (64.3%)

Counts

169 → 1

Compiler

Compiled 21354 to 15494 computations (27.4% saved)

simplify2.0ms (0%)

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

end108.0ms (1.8%)

Stop Event

1×

fuel

Compiler

Compiled 148 to 103 computations (30.4% saved)

Details

analyze238.0ms (3.9%)

sample1.1s (17.5%)

preprocess43.0ms (0.7%)

simplify39.0ms (0.6%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series255.0ms (4.2%)

rewrite71.0ms (1.2%)

simplify57.0ms (0.9%)

prune253.0ms (4.1%)

localize8.0ms (0.1%)

series88.0ms (1.4%)

rewrite49.0ms (0.8%)

simplify43.0ms (0.7%)

prune101.0ms (1.6%)

localize37.0ms (0.6%)

series1.3s (20.5%)

rewrite55.0ms (0.9%)

simplify48.0ms (0.8%)

prune167.0ms (2.7%)

localize9.0ms (0.2%)

series429.0ms (7%)

rewrite65.0ms (1.1%)

simplify56.0ms (0.9%)

prune142.0ms (2.3%)

regimes1.4s (23.2%)

simplify2.0ms (0%)

end108.0ms (1.8%)

Profiling