Details

analyze14.0ms (0.6%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample905.0ms (38.1%)

Results

888.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 26 computations (40.9% saved)

preprocess44.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

968×	`fma-def_binary64`
834×	`fma-neg_binary64`
302×	`cancel-sign-sub-inv_binary64`
287×	`div-sub_binary64`
232×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
1	44	48
2	102	48
3	217	48
4	462	48
5	889	48
6	1477	48
7	2476	48
8	4351	48
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 12 computations (42.9% saved)

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
456×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`
358×	`div-sub_binary64`
252×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	24	24
2	56	24
3	114	24
4	240	24
5	457	24
6	723	24
7	987	24
8	1607	24
9	3745	24

Stop Event

1×	node limit

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

29.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.7b	(/.f64 (fma.f64 x x (.f64 -4 (.f64 y y))) (fma.f64 x x (.f64 y (.f64 y 4))))
▶	29.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 118 to 67 computations (43.2% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	3.8b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	29.0b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series36.0ms (1.5%)

Counts

3 → 72

Calls

18 calls:

6.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	y	-inf
3.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	x	0
3.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))	y	inf
2.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	y	0
2.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))	x	inf

rewrite85.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`fma-def_binary64`
279×	`egg-rr`
230×	`fma-neg_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	237	46
2	3393	46

Stop Event

1×	node limit

Counts

3 → 279

simplify40.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
439×	`associate-*r/_binary64`
378×	`fma-def_binary64`
318×	`associate-/r/_binary64`
311×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1038
1	124	984
2	352	972
3	1389	954

Stop Event

1×	node limit

Counts

351 → 301

prune224.0ms (9.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	299	4	303

Error

Counts

303 → 4

Alt Table

Status	Error	Program
▶	29.5b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
	31.4b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	31.6b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
✓	29.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 9345 to 5336 computations (42.9% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	2.0b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	29.0b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))

series21.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))	y	inf
3.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))	x	0
3.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))	y	0
2.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))	x	inf
2.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))	x	-inf

rewrite58.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`prod-diff_binary64`
125×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`
120×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	259	35
2	3509	35

Stop Event

1×	node limit

Counts

2 → 66

simplify32.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-*l/_binary64`
450×	`associate-*r/_binary64`
368×	`fma-def_binary64`
321×	`associate-/r/_binary64`
311×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	807
1	121	753
2	346	741
3	1379	723

Stop Event

1×	node limit

Counts

114 → 86

prune97.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	29.5b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
▶	31.4b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
	31.6b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
✓	29.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 3901 to 2111 computations (45.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 y x))

series72.0ms (3%)

Counts

2 → 48

Calls

12 calls:

32.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)	y	-inf
9.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	inf
6.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	-inf
6.0ms	(*.f64 (/.f64 y x) (/.f64 y x))	y	0
5.0ms	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)	y	inf

rewrite44.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`log1p-expm1-u_binary64`
739×	`expm1-log1p-u_binary64`
136×	`log1p-udef_binary64`
79×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	164	18
2	2054	18

Stop Event

1×	node limit

Counts

2 → 59

simplify30.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
623×	`associate-*l/_binary64`
535×	`associate-/l/_binary64`
377×	`associate-/r/_binary64`
156×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	570
1	32	570
2	74	534
3	242	534
4	1326	534

Stop Event

1×	node limit

Counts

107 → 65

prune35.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	65	4	69

Error

Counts

69 → 4

Alt Table

Status	Error	Program
✓	29.5b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
✓	31.4b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
▶	31.6b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
✓	29.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 852 to 530 computations (37.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series54.0ms (2.3%)

Counts

2 → 48

Calls

12 calls:

11.0ms	(*.f64 (/.f64 x y) (/.f64 x y))	x	0
8.0ms	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)	x	0
7.0ms	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)	x	-inf
6.0ms	(*.f64 (/.f64 x y) (/.f64 x y))	x	-inf
6.0ms	(*.f64 (/.f64 x y) (/.f64 x y))	x	inf

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
140×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	166	18
2	2096	18

Stop Event

1×	node limit

Counts

2 → 59

simplify46.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-/l*_binary64`
388×	`associate-/r*_binary64`
329×	`associate-/l/_binary64`
301×	`unswap-sqr_binary64`
292×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	534
1	27	534
2	51	534
3	139	534
4	675	534
5	4156	534
6	4835	534

Stop Event

1×	node limit

Counts

107 → 66

prune34.0ms (1.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	66	4	70

Error

Counts

70 → 4

Alt Table

Status	Error	Program
✓	29.5b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (+.f64 (.f64 x x) (.f64 (*.f64 y 4) y)))
✓	31.4b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -8 1)
✓	31.6b	(fma.f64 1/2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)
✓	29.5b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 852 to 531 computations (37.7% saved)

regimes307.0ms (12.9%)

Accuracy

Total 12.5b remaining (98.5%)

Threshold costs 0b (0%)

Counts

29 → 6

Compiler

Compiled 2541 to 1607 computations (36.8% saved)

bsearch1.0ms (0%)

Algorithm

5×	left-value

Calls

5 calls:

0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)
0.0ms	(*.f64 x x)

Steps

Iters	Point		Range
1.3990540414211703e+302	∈ [	1.3990540414211703e+302	,	#hash((type . real) (value . +inf))	]
1.1080386546582645e+261	∈ [	1.1080386546582645e+261	,	2.2095867222542145e+266	]
1.0681176063038099e-101	∈ [	1.0681176063038099e-101	,	1.0461272827066565e-99	]
3.467948661196628e-114	∈ [	3.467948661196628e-114	,	2.731830861642487e-111	]
3.274786957776617e-268	∈ [	3.274786957776617e-268	,	4.935181971392658e-265	]

Compiler

Compiled 5 to 3 computations (40% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	147
1	60	147
2	74	147
3	80	147
4	84	147
5	85	147

Stop Event

1×

saturated

end90.0ms (3.8%)

Stop Event

1×

done

Compiler

Compiled 271 to 157 computations (42.1% saved)

Details

analyze14.0ms (0.6%)

sample905.0ms (38.1%)

preprocess44.0ms (1.9%)

simplify33.0ms (1.4%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series36.0ms (1.5%)

rewrite85.0ms (3.6%)

simplify40.0ms (1.7%)

prune224.0ms (9.4%)

localize9.0ms (0.4%)

series21.0ms (0.9%)

rewrite58.0ms (2.4%)

simplify32.0ms (1.3%)

prune97.0ms (4.1%)

localize5.0ms (0.2%)

series72.0ms (3%)

rewrite44.0ms (1.8%)

simplify30.0ms (1.3%)

prune35.0ms (1.5%)

localize5.0ms (0.2%)

series54.0ms (2.3%)

rewrite40.0ms (1.7%)

simplify46.0ms (1.9%)

prune34.0ms (1.4%)

regimes307.0ms (12.9%)

bsearch1.0ms (0%)

simplify7.0ms (0.3%)

end90.0ms (3.8%)

Profiling