Details

analyze1.1s (27.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
10.9%	88.9%	0.2%	10
13.3%	85.8%	1%	11
17.9%	79.3%	2.7%	12
25.5%	70.3%	4.1%	13
31.7%	63.9%	4.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (30.7%)

Results

902.0ms	8256×	body	128	valid
264.0ms	2380×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess37.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

505×	`unsub-neg_binary64`
463×	`div-sub_binary64`
427×	`fma-def_binary64`
325×	`sub-neg_binary64`
271×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	77
1	76	77
2	205	77
3	490	77
4	1034	77
5	2211	77
6	4011	77
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify73.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
107×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	38	11
3	84	11
4	178	11
5	316	11
6	542	11
7	1015	11
8	1989	11
9	2988	11
10	3630	11
11	3668	11
12	3698	11
13	3703	11
14	3703	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
	6.3b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
▶	1.8b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.8b	(*.f64 (/.f64 x y) (-.f64 z t))

series18.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

2.0ms	(*.f64 (/.f64 x y) (-.f64 z t))	t	inf
2.0ms	(*.f64 (/.f64 x y) (-.f64 z t))	t	0
2.0ms	(*.f64 (/.f64 x y) (-.f64 z t))	x	-inf
2.0ms	(*.f64 (/.f64 x y) (-.f64 z t))	z	-inf
2.0ms	(*.f64 (/.f64 x y) (-.f64 z t))	x	0

rewrite86.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
377×	`prod-diff_binary64`
186×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	176	10
2	2563	10

Stop Event

1×	node limit

Counts

1 → 48

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-def_binary64`
458×	`fma-neg_binary64`
156×	`cancel-sign-sub-inv_binary64`
123×	`div-sub_binary64`
118×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	468
1	52	468
2	120	468
3	282	468
4	624	468
5	1312	468
6	2519	468
7	3274	468
8	3370	468
9	3402	468
10	3407	468
11	3407	468

Stop Event

1×

saturated

Counts

96 → 57

prune35.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Error

Counts

59 → 4

Alt Table

Status	Error	Program
	6.3b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
	6.7b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
▶	1.8b	(+.f64 (/.f64 (-.f64 z t) (/.f64 y x)) t)
✓	1.8b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 917 to 317 computations (65.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.3b	(/.f64 (-.f64 z t) (/.f64 y x))

series19.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

3.0ms	(/.f64 (-.f64 z t) (/.f64 y x))	x	-inf
2.0ms	(/.f64 (-.f64 z t) (/.f64 y x))	z	0
2.0ms	(/.f64 (-.f64 z t) (/.f64 y x))	z	-inf
2.0ms	(/.f64 (-.f64 z t) (/.f64 y x))	z	inf
1.0ms	(/.f64 (-.f64 z t) (/.f64 y x))	x	0

rewrite141.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`prod-diff_binary64`
369×	`egg-rr`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
99×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	185	10
2	2936	10

Stop Event

1×	node limit

Counts

1 → 369

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-def_binary64`
458×	`fma-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`
123×	`div-sub_binary64`
118×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	468
1	52	468
2	120	468
3	282	468
4	623	468
5	1317	468
6	2531	468
7	3287	468
8	3383	468
9	3415	468
10	3420	468
11	3420	468

Stop Event

1×

saturated

Counts

417 → 377

prune265.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	377	4	381

Error

Counts

381 → 4

Alt Table

Status	Error	Program
▶	6.3b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
	6.7b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
✓	1.8b	(+.f64 (/.f64 (-.f64 z t) (/.f64 y x)) t)
✓	1.8b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 17387 to 5100 computations (70.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) y)
✓	5.9b	(fma.f64 x (/.f64 (-.f64 z t) y) t)

series26.0ms (0.7%)

Counts

2 → 76

Calls

21 calls:

3.0ms	(fma.f64 x (/.f64 (-.f64 z t) y) t)	t	inf
2.0ms	(fma.f64 x (/.f64 (-.f64 z t) y) t)	z	-inf
2.0ms	(fma.f64 x (/.f64 (-.f64 z t) y) t)	z	inf
2.0ms	(fma.f64 x (/.f64 (-.f64 z t) y) t)	t	-inf
1.0ms	(fma.f64 x (/.f64 (-.f64 z t) y) t)	t	0

rewrite81.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
211×	`fma-def_binary64`
195×	`egg-rr`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	178	18
2	2609	18

Stop Event

1×	node limit

Counts

2 → 195

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
664×	`fma-neg_binary64`
180×	`cancel-sign-sub-inv_binary64`
136×	`distribute-rgt-in_binary64`
116×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	811
1	83	811
2	199	780
3	462	664
4	995	664
5	1931	664
6	2953	664
7	3342	664
8	3384	664
9	3429	664
10	3429	664

Stop Event

1×

saturated

Counts

271 → 213

prune133.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	213	4	217

Error

Counts

217 → 4

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
▶	6.7b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
✓	1.8b	(+.f64 (/.f64 (-.f64 z t) (/.f64 y x)) t)
✓	1.8b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 7032 to 2416 computations (65.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) x)
✓	7.3b	(/.f64 (*.f64 (-.f64 z t) x) y)

series24.0ms (0.6%)

Counts

2 → 56

Calls

21 calls:

3.0ms	(/.f64 (*.f64 (-.f64 z t) x) y)	z	0
2.0ms	(/.f64 (*.f64 (-.f64 z t) x) y)	x	-inf
2.0ms	(/.f64 (*.f64 (-.f64 z t) x) y)	z	-inf
2.0ms	(/.f64 (*.f64 (-.f64 z t) x) y)	z	inf
1.0ms	(/.f64 (*.f64 (-.f64 z t) x) y)	x	0

rewrite46.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
386×	`prod-diff_binary64`
181×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	176	17
2	2582	17

Stop Event

1×	node limit

Counts

2 → 73

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1020×	`fma-def_binary64`
451×	`fma-neg_binary64`
161×	`cancel-sign-sub-inv_binary64`
120×	`distribute-rgt-in_binary64`
120×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	464
1	51	464
2	118	464
3	283	464
4	630	464
5	1330	464
6	2539	464
7	3296	464
8	3392	464
9	3424	464
10	3429	464
11	3429	464

Stop Event

1×

saturated

Counts

129 → 87

prune46.0ms (1.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	87	4	91

Error

Counts

91 → 4

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 x (/.f64 (-.f64 z t) y) t)
✓	6.7b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
✓	1.8b	(+.f64 (/.f64 (-.f64 z t) (/.f64 y x)) t)
✓	1.8b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 1242 to 426 computations (65.7% saved)

regimes174.0ms (4.5%)

Accuracy

Total 2.0b remaining (99.3%)

Threshold costs 0b (0%)

Counts

20 → 3

Compiler

Compiled 1486 to 962 computations (35.3% saved)

bsearch74.0ms (1.9%)

Algorithm

2×	binary-search

Calls

2 calls:

48.0ms	y
25.0ms	y

Steps

Iters	Point		Range
-1.446115896866537e-282	∈ [	-2.9447176877036542e-270	,	-9.238499693992928e-284	]
-2.4152352409574924e-67	∈ [	-3.266785888630164e-67	,	-8.883459911884634e-76	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-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	21	49
1	27	49
2	32	49
3	34	49
4	35	49

Stop Event

1×

saturated

end60.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 127 to 69 computations (45.7% saved)

Details

analyze1.1s (27.2%)

sample1.2s (30.7%)

preprocess37.0ms (0.9%)

simplify73.0ms (1.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series18.0ms (0.5%)

rewrite86.0ms (2.2%)

simplify62.0ms (1.6%)

prune35.0ms (0.9%)

localize6.0ms (0.2%)

series19.0ms (0.5%)

rewrite141.0ms (3.6%)

simplify68.0ms (1.8%)

prune265.0ms (6.8%)

localize5.0ms (0.1%)

series26.0ms (0.7%)

rewrite81.0ms (2.1%)

simplify81.0ms (2.1%)

prune133.0ms (3.4%)

localize6.0ms (0.1%)

series24.0ms (0.6%)

rewrite46.0ms (1.2%)

simplify58.0ms (1.5%)

prune46.0ms (1.2%)

regimes174.0ms (4.5%)

bsearch74.0ms (1.9%)

simplify3.0ms (0.1%)

end60.0ms (1.5%)

Profiling