Details

analyze15.0ms (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)

sample1.3s (47.9%)

Symmetry

(sort x y)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1186×	`rules-43_binary64`
1182×	`rules-42_binary64`
713×	`fma-neg_binary64`
488×	`fma-def_binary64`
295×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	65	26
2	236	26
3	1142	24
4	3640	24
5	19	24

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

49.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	49.0b	(/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(fma.f64 (.f64 y y) -4 (.f64 x x))
✓	31.1b	(/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series28.0ms (1%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
8.0ms	(fma.f64 (.f64 y y) -4 (.f64 x x))

rewrite70.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

892×	`fma-neg_binary64`
272×	`prod-diff_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
113×	`add-sqr-sqrt_binary64`

Counts

2 → 67

Calls

2 calls:

68.0ms	(fma.f64 (.f64 y y) -4 (.f64 x x))
68.0ms	(/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	278	34
2	3151	34
3	5086	34
0	0	0
1	0	0

simplify51.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
327×	`rules-40_binary64`
327×	`rules-41_binary64`
327×	`rules-42_binary64`
327×	`rules-43_binary64`

Counts

115 → 87

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	807
1	307	789
2	1181	789
3	5048	789

prune56.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Error

0.8b

Counts

88 → 4

Alt Table

Status	Error	Program
	50.8b	(/.f64 (.f64 x (+.f64 x (/.f64 (.f64 (.f64 y y) -4) x))) (fma.f64 x x (.f64 y (*.f64 y 4))))
	49.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))
	32.3b	-1
▶	31.8b	1

Compiler

Compiled 1971 to 1095 computations (44.4% saved)

localize0.0ms (0%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

0.8b

Counts

4 → 4

Alt Table

Status	Error	Program
	50.8b	(/.f64 (.f64 x (+.f64 x (/.f64 (.f64 (.f64 y y) -4) x))) (fma.f64 x x (.f64 y (*.f64 y 4))))
	49.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))
▶	32.3b	-1
✓	31.8b	1

Compiler

Compiled 95 to 65 computations (31.6% saved)

localize0.0ms (0%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.8b

Counts

4 → 4

Alt Table

Status	Error	Program
	50.8b	(/.f64 (.f64 x (+.f64 x (/.f64 (.f64 (.f64 y y) -4) x))) (fma.f64 x x (.f64 y (*.f64 y 4))))
▶	49.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))
✓	32.3b	-1
✓	31.8b	1

Compiler

Compiled 92 to 62 computations (32.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))
✓	0.0b	(pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3)
	2.6b	(fma.f64 (.f64 y y) -4 (.f64 x x))
✓	31.1b	(/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2))

series96.0ms (3.6%)

Counts

3 → 72

Calls

3 calls:

40.0ms

(pow.f64 (/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3)

29.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))

26.0ms

(/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2))

rewrite126.0ms (4.7%)

Algorithm

2×	batch-egg-rewrite

Rules

885×	`fma-neg_binary64`
256×	`prod-diff_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
157×	`egg-rr`

Counts

3 → 157

Calls

3 calls:

121.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))

121.0ms

(pow.f64 (/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3)

121.0ms

(/.f64 (fma.f64 (*.f64 y y) -4 (*.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	330	72
2	3490	72
3	5387	72
0	0	0
1	0	0

simplify121.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

562×	`rules-40_binary64`
562×	`rules-41_binary64`
562×	`rules-42_binary64`
562×	`rules-43_binary64`
561×	`fma-def_binary64`

Counts

229 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	1620
1	462	1566
2	1965	1566
3	4993	1566
4	4838	1566

prune142.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	181	4	185

Error

0.8b

Counts

185 → 4

Alt Table

Status	Error	Program
	50.8b	(/.f64 (.f64 x (+.f64 x (/.f64 (.f64 (.f64 y y) -4) x))) (fma.f64 x x (.f64 y (*.f64 y 4))))
✓	49.0b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (.f64 y y) -4 (.f64 x x)) (pow.f64 (hypot.f64 x (*.f64 2 y)) 2)) 3))
✓	32.3b	-1
✓	31.8b	1

Compiler

Compiled 6285 to 3840 computations (38.9% saved)

regimes273.0ms (10.2%)

Accuracy

Total 30.9b remaining (98.4%)

Threshold costs 0b (0%)

Counts

16 → 8

Compiler

Compiled 1683 to 1113 computations (33.9% saved)

bsearch112.0ms (4.2%)

Steps

Iters	Range		Point
6	6.271235905490264e+261	2.959728493177278e+262	6.341550649972557e+261
6	1.7350149815501675e+198	8.612222184677051e+198	8.524407389953581e+198
8	7.914931333073585e+106	1.1475083507627316e+110	2.541450281263339e+107
7	7.52717689220107e-15	6.264883018649407e-13	8.46966307063159e-14
0	4.7462345658373243e-26	4.767753401631108e-26	4.756993983734216e-26
8	3.202268729379295e-151	3.693976097514281e-147	3.2823881671957526e-151
7	-1.3238230059344828e-173	-2.597607959301908e-175	-2.652976160851104e-175

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	50
1	28	50
2	27	50

end214.0ms (8%)

Compiler: Compiled 201 to 158 computations (21.4% saved)

Details

analyze15.0ms (0.6%)

sample1.3s (47.9%)

simplify58.0ms (2.1%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series28.0ms (1%)

rewrite70.0ms (2.6%)

simplify51.0ms (1.9%)

prune56.0ms (2.1%)

localize0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

prune4.0ms (0.1%)

localize12.0ms (0.4%)

series96.0ms (3.6%)

rewrite126.0ms (4.7%)

simplify121.0ms (4.5%)

prune142.0ms (5.3%)

regimes273.0ms (10.2%)

bsearch112.0ms (4.2%)

simplify2.0ms (0.1%)

end214.0ms (8%)

Profiling