Details

analyze440.0ms (18.4%)

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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
40.6%	50.7%	8.7%	10
48.4%	42.1%	9.5%	11
54.2%	35.5%	10.3%	12
59.1%	25.9%	15%	13
63.9%	20.9%	15.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample946.0ms (39.6%)

Results

805.0ms	8256×	body	128	valid
63.0ms	632×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify36.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
515×	`fma-neg_binary64`
141×	`cancel-sign-sub-inv_binary64`
122×	`distribute-rgt-in_binary64`
106×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	11
2	37	11
3	93	11
4	218	11
5	415	11
6	601	11
7	952	11
8	1570	11
9	2157	11
10	2614	11
11	2678	11
12	2680	11
13	2680	11

Stop Event

1×

saturated

Counts

1 → 2

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
	0.2b	(fma.f64 6 (*.f64 (-.f64 y x) z) x)
▶	0.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.2b	(.f64 (.f64 (-.f64 y x) 6) z)

series20.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

9.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
8.0ms	(.f64 (.f64 (-.f64 y x) 6) z)
3.0ms	(*.f64 (-.f64 y x) 6)

rewrite52.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

513×	`log-prod_binary64`
404×	`fma-def_binary64`
190×	`fma-neg_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	201	28
2	2829	28

Stop Event

1×	node limit

Counts

3 → 103

Calls

3 calls:

50.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) z))
50.0ms	(*.f64 (-.f64 y x) 6)
50.0ms	(.f64 (.f64 (-.f64 y x) 6) z)

simplify65.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
516×	`fma-neg_binary64`
103×	`cancel-sign-sub-inv_binary64`
98×	`associate-l_binary64`
95×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	1119
1	98	915
2	236	909
3	524	855
4	1009	855
5	1721	855
6	2131	855
7	2362	855
8	2366	855
9	2366	855

Stop Event

1×

saturated

Counts

199 → 122

prune88.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

Counts

124 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (-.f64 y x) (*.f64 6 z) x)
	0.2b	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
	31.9b	(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (.f64 (-.f64 y x) 6)) x)
▶	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)
	27.1b	(+.f64 x (.f64 (/.f64 (.f64 (fma.f64 y y (neg.f64 (*.f64 x x))) 6) (+.f64 y x)) z))

Compiler

Compiled 1881 to 997 computations (47% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

series10.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(fma.f64 (*.f64 (-.f64 y x) 6) z x)

rewrite43.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

847×	`log1p-expm1-u_binary64`
847×	`expm1-log1p-u_binary64`
433×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	171	11
2	2209	11

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

42.0ms

(fma.f64 (*.f64 (-.f64 y x) 6) z x)

simplify51.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
517×	`fma-neg_binary64`
101×	`cancel-sign-sub-inv_binary64`
99×	`associate-l_binary64`
95×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	531
1	82	423
2	205	417
3	481	363
4	966	363
5	1684	363
6	2229	363
7	2466	363
8	2470	363
9	2470	363

Stop Event

1×

saturated

Counts

59 → 35

prune38.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	63	5	68

Error

Counts

68 → 5

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (-.f64 y x) (*.f64 6 z) x)
	0.2b	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
	27.1b	(fma.f64 (/.f64 (.f64 6 (fma.f64 y y (neg.f64 (.f64 x x)))) (+.f64 y x)) z x)
	31.9b	(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (.f64 (-.f64 y x) 6)) x)
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 886 to 482 computations (45.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (-.f64 y x) (*.f64 6 z) x)

series8.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 (-.f64 y x) (*.f64 6 z) x)

rewrite41.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

841×	`log1p-expm1-u_binary64`
841×	`expm1-log1p-u_binary64`
433×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	171	11
2	2199	11

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

41.0ms

(fma.f64 (-.f64 y x) (*.f64 6 z) x)

simplify48.0ms (2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
517×	`fma-neg_binary64`
101×	`cancel-sign-sub-inv_binary64`
99×	`associate-l_binary64`
95×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	531
1	82	423
2	205	417
3	481	363
4	966	363
5	1684	363
6	2229	363
7	2466	363
8	2470	363
9	2470	363

Stop Event

1×

saturated

Counts

59 → 35

prune18.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	35	5	40

Error

Counts

40 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (-.f64 y x) (*.f64 6 z) x)
▶	0.2b	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
	27.1b	(fma.f64 (/.f64 (.f64 6 (fma.f64 y y (neg.f64 (.f64 x x)))) (+.f64 y x)) z x)
	31.9b	(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (.f64 (-.f64 y x) 6)) x)
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 529 to 294 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 x y))
✓	0.0b	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
✓	0.3b	(.f64 -6 (.f64 z (-.f64 x y)))

series26.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

10.0ms	(.f64 -6 (.f64 z (-.f64 x y)))
10.0ms	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
6.0ms	(*.f64 z (-.f64 x y))

rewrite59.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
400×	`fma-def_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
187×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	201	28
2	2844	28

Stop Event

1×	node limit

Counts

3 → 106

Calls

3 calls:

57.0ms	(*.f64 z (-.f64 x y))
57.0ms	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
57.0ms	(.f64 -6 (.f64 z (-.f64 x y)))

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
561×	`fma-neg_binary64`
144×	`cancel-sign-sub-inv_binary64`
99×	`associate-l_binary64`
93×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	1113
1	108	1005
2	264	999
3	582	945
4	1146	945
5	1981	945
6	2392	945
7	2505	945
8	2506	945
9	2506	945

Stop Event

1×

saturated

Counts

214 → 128

prune77.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	128	5	133

Error

Counts

133 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (-.f64 y x) (*.f64 6 z) x)
✓	0.2b	(+.f64 x (.f64 -6 (.f64 z (-.f64 x y))))
	27.1b	(fma.f64 (/.f64 (.f64 6 (fma.f64 y y (neg.f64 (.f64 x x)))) (+.f64 y x)) z x)
	31.9b	(fma.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (.f64 (-.f64 y x) 6)) x)
✓	0.1b	(fma.f64 (*.f64 (-.f64 y x) 6) z x)

Compiler

Compiled 1871 to 900 computations (51.9% saved)

regimes151.0ms (6.3%)

Accuracy

Total 0.2b remaining (93.9%)

Threshold costs 0.2b (93.9%)

Counts

41 → 1

Compiler

Compiled 1996 to 1366 computations (31.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	8	11
1	11	11
2	16	11
3	18	11
4	19	11

Stop Event

1×

saturated

end65.0ms (2.7%)

Compiler: Compiled 90 to 56 computations (37.8% saved)

Details

analyze440.0ms (18.4%)

sample946.0ms (39.6%)

simplify36.0ms (1.5%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series20.0ms (0.8%)

rewrite52.0ms (2.2%)

simplify65.0ms (2.7%)

prune88.0ms (3.7%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite43.0ms (1.8%)

simplify51.0ms (2.1%)

prune38.0ms (1.6%)

localize6.0ms (0.2%)

series8.0ms (0.4%)

rewrite41.0ms (1.7%)

simplify48.0ms (2%)

prune18.0ms (0.8%)

localize5.0ms (0.2%)

series26.0ms (1.1%)

rewrite59.0ms (2.5%)

simplify74.0ms (3.1%)

prune77.0ms (3.2%)

regimes151.0ms (6.3%)

simplify2.0ms (0.1%)

end65.0ms (2.7%)

Profiling