Details

analyze751.0ms (21.6%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (29.3%)

Results

940.0ms	8256×	body	128	valid
63.0ms	595×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess31.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

764×	`fma-def_binary64`
668×	`div-sub_binary64`
341×	`distribute-rgt-in_binary64`
251×	`sub-neg_binary64`
228×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	91
1	82	91
2	142	91
3	350	91
4	902	91
5	2211	91
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

609×	`times-frac_binary64`
569×	`div-sub_binary64`
535×	`fma-def_binary64`
336×	`fma-neg_binary64`
186×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	30	13
3	68	13
4	167	13
5	324	13
6	712	13
7	2100	13

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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
▶	2.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	9.9b	(*.f64 (-.f64 y x) (/.f64 t (-.f64 y z)))

Compiler

Compiled 74 to 44 computations (40.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.2b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series61.0ms (1.8%)

Counts

2 → 84

Calls

21 calls:

21.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)	t	-inf
3.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)	z	-inf
3.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)	y	inf
3.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)	z	inf
2.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)	z	0

rewrite139.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
258×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	23
2	3214	23

Stop Event

1×	node limit

Counts

2 → 258

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
665×	`times-frac_binary64`
419×	`cancel-sign-sub-inv_binary64`
327×	`sub-neg_binary64`
161×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2783
1	469	2777
2	1799	2157

Stop Event

1×	node limit

Counts

342 → 328

prune225.0ms (6.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	323	5	328
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	324	6	330

Error

Counts

330 → 6

Alt Table

Status	Error	Program
	33.9b	(/.f64 t (/.f64 (-.f64 z y) x))
▶	9.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	34.5b	(-.f64 (fma.f64 (/.f64 t y) z t) (.f64 (/.f64 t y) (+.f64 x (/.f64 (.f64 z x) y))))
	10.7b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
	32.9b	(-.f64 (+.f64 t (/.f64 (.f64 t z) y)) (/.f64 (.f64 t x) y))

Compiler

Compiled 14455 to 4151 computations (71.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

series27.0ms (0.8%)

Counts

1 → 36

Calls

12 calls:

4.0ms	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))	z	0
3.0ms	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))	z	-inf
2.0ms	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))	z	inf
2.0ms	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))	t	-inf
2.0ms	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))	y	0

rewrite52.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	205	13
2	3125	13

Stop Event

1×	node limit

Counts

1 → 45

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Rules

554×	`times-frac_binary64`
470×	`associate-/l*_binary64`
450×	`associate--l+_binary64`
445×	`fma-def_binary64`
246×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1438
1	289	1438
2	1108	1174

Stop Event

1×	node limit

Counts

81 → 82

prune51.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Error

Counts

88 → 6

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	34.5b	(-.f64 (fma.f64 (/.f64 t y) z t) (.f64 (/.f64 t y) (+.f64 x (/.f64 (.f64 z x) y))))
	10.7b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
	32.9b	(-.f64 (+.f64 t (/.f64 (.f64 t z) y)) (/.f64 (.f64 t x) y))
▶	10.0b	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))

Compiler

Compiled 1874 to 660 computations (64.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 t (/.f64 1 (-.f64 z y)))
✓	9.9b	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))

series49.0ms (1.4%)

Counts

3 → 108

Calls

27 calls:

3.0ms	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))	t	-inf
3.0ms	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))	z	-inf
3.0ms	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))	x	0
3.0ms	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))	z	inf
2.0ms	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))	z	0

rewrite54.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
116×	`add-cbrt-cube_binary64`
116×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	241	27
2	3364	27

Stop Event

1×	node limit

Counts

3 → 79

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
638×	`fma-def_binary64`
575×	`associate-/l*_binary64`
277×	`cancel-sign-sub-inv_binary64`
187×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2884
1	405	2866
2	1529	2263

Stop Event

1×	node limit

Counts

187 → 146

prune85.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

Counts

152 → 6

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	34.5b	(-.f64 (fma.f64 (/.f64 t y) z t) (.f64 (/.f64 t y) (+.f64 x (/.f64 (.f64 z x) y))))
▶	10.7b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
	32.9b	(-.f64 (+.f64 t (/.f64 (.f64 t z) y)) (/.f64 (.f64 t x) y))
✓	10.0b	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))

Compiler

Compiled 2890 to 1142 computations (60.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) t)
✓	10.7b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))

series37.0ms (1.1%)

Counts

2 → 76

Calls

21 calls:

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

rewrite57.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

359×	`fma-def_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
210×	`fma-neg_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	217	20
2	3613	20

Stop Event

1×	node limit

Counts

2 → 110

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

554×	`times-frac_binary64`
477×	`associate-/l*_binary64`
455×	`fma-def_binary64`
450×	`associate--l+_binary64`
248×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1952
1	310	1886
2	1151	1433

Stop Event

1×	node limit

Counts

186 → 152

prune77.0ms (2.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	152	6	158

Error

Counts

158 → 6

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))
✓	2.3b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	34.5b	(-.f64 (fma.f64 (/.f64 t y) z t) (.f64 (/.f64 t y) (+.f64 x (/.f64 (.f64 z x) y))))
✓	10.7b	(/.f64 (-.f64 x y) (/.f64 (-.f64 z y) t))
	32.9b	(-.f64 (+.f64 t (/.f64 (.f64 t z) y)) (/.f64 (.f64 t x) y))
✓	10.0b	(.f64 (-.f64 x y) (.f64 t (/.f64 1 (-.f64 z y))))

Compiler

Compiled 2955 to 901 computations (69.5% saved)

regimes438.0ms (12.6%)

Accuracy

Total 1.4b remaining (98.5%)

Threshold costs 0b (0%)

Counts

60 → 3

Compiler

Compiled 5578 to 3522 computations (36.9% saved)

bsearch2.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (-.f64 x y) (-.f64 z y))
0.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

Steps

Iters	Point		Range
1.418303538573969e-267	∈ [	1.418303538573969e-267	,	6.852733770715456e-265	]
-8.451637872316771e-106	∈ [	-8.451637872316771e-106	,	-3.558192898402971e-114	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
1	23	69
2	29	69
3	31	69
4	32	69

Stop Event

1×

saturated

end74.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 195 to 87 computations (55.4% saved)

Details

analyze751.0ms (21.6%)

sample1.0s (29.3%)

preprocess31.0ms (0.9%)

simplify20.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series61.0ms (1.8%)

rewrite139.0ms (4%)

simplify58.0ms (1.7%)

prune225.0ms (6.5%)

localize7.0ms (0.2%)

series27.0ms (0.8%)

rewrite52.0ms (1.5%)

simplify34.0ms (1%)

prune51.0ms (1.5%)

localize7.0ms (0.2%)

series49.0ms (1.4%)

rewrite54.0ms (1.6%)

simplify63.0ms (1.8%)

prune85.0ms (2.4%)

localize6.0ms (0.2%)

series37.0ms (1.1%)

rewrite57.0ms (1.6%)

simplify41.0ms (1.2%)

prune77.0ms (2.2%)

regimes438.0ms (12.6%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end74.0ms (2.1%)

Profiling