Details

analyze1.3s (14.2%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.2s (13.3%)

Results

1.0s	8256×	body	128	valid
55.0ms	467×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

prune3.0ms (0%)

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

25.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (.f64 b c) (.f64 a d))
✓	24.9b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series91.0ms (1%)

Counts

2 → 96

Calls

2 calls:

83.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
8.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite79.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

449×	`fma-def_binary64`
239×	`fma-neg_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
224×	`egg-rr`

Counts

2 → 224

Calls

2 calls:

73.0ms	(-.f64 (.f64 b c) (.f64 a d))
73.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	244	29
2	3323	29
3	5042	29
0	0	0
1	0	0

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

905×	`fma-neg_binary64`
615×	`fma-def_binary64`
483×	`associate-*l/_binary64`
469×	`cancel-sign-sub-inv_binary64`
360×	`associate-/r/_binary64`

Counts

320 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1722
1	131	1638
2	372	1599
3	1558	1554
4	4686	1554
5	5175	1554

prune204.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	241	8	249
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	241	9	250

Error

0.8b

Counts

250 → 9

Alt Table

Status	Error	Program
	41.2b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
	34.2b	(neg.f64 (/.f64 a d))
▶	15.3b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))))
	32.7b	(-.f64 (.f64 (/.f64 c (.f64 d d)) (+.f64 b (/.f64 (*.f64 a c) d))) (/.f64 a d))
	17.5b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 2) (hypot.f64 c d)) (/.f64 (cbrt.f64 (-.f64 (.f64 b c) (*.f64 a d))) (hypot.f64 c d)))
	17.0b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (-.f64 (.f64 b c) (*.f64 a d)) (hypot.f64 c d)))
	41.0b	(-.f64 (/.f64 b c) (.f64 (/.f64 d (.f64 c c)) (+.f64 a (/.f64 (*.f64 d b) c))))
	41.6b	(/.f64 b c)
✓	25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 6322 to 1602 computations (74.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 c (hypot.f64 c d))
✓	0.0b	(pow.f64 (hypot.f64 c d) 2)
✓	0.3b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))))
✓	16.8b	(/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))

series396.0ms (4.4%)

Counts

4 → 132

Calls

4 calls:

234.0ms	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))))
95.0ms	(/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))
47.0ms	(pow.f64 (hypot.f64 c d) 2)
20.0ms	(/.f64 c (hypot.f64 c d))

rewrite213.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

598×	`prod-diff_binary64`
581×	`egg-rr`
254×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`

Counts

4 → 581

Calls

4 calls:

185.0ms	(/.f64 c (hypot.f64 c d))
185.0ms	(pow.f64 (hypot.f64 c d) 2)
185.0ms	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))))
185.0ms	(/.f64 (*.f64 a d) (pow.f64 (hypot.f64 c d) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	303	55
2	3692	55
3	5297	55
0	0	0
1	0	0

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

632×	`times-frac_binary64`
407×	`associate-/l*_binary64`
291×	`associate-/r*_binary64`
280×	`cancel-sign-sub-inv_binary64`
258×	`sub-neg_binary64`

Counts

713 → 654

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	2980
1	319	2826
2	1013	2708
3	4632	2681
4	5015	2681

prune620.0ms (6.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	650	4	654
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	656	7	663

Error

0.0b

Counts

663 → 7

Alt Table

Status	Error	Program
	13.1b	(+.f64 (fma.f64 b (.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 c (hypot.f64 c d))) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
✓	25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	12.5b	(+.f64 (fma.f64 (.f64 (/.f64 b (hypot.f64 c d)) c) (/.f64 1 (hypot.f64 c d)) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
	41.2b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
	17.0b	(.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 (-.f64 (.f64 b c) (*.f64 a d)) (hypot.f64 c d)))
▶	0.6b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))
	15.4b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (.f64 d (.f64 a (pow.f64 (hypot.f64 c d) -2)))))

Compiler

Compiled 34068 to 12307 computations (63.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (hypot.f64 c d))
	0.0b	(/.f64 c (hypot.f64 c d))
✓	0.3b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))
✓	0.4b	(*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))

series405.0ms (4.5%)

Counts

3 → 120

Calls

3 calls:

237.0ms

(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))

92.0ms

(*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))

76.0ms

(/.f64 b (hypot.f64 c d))

rewrite251.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

691×	`prod-diff_binary64`
650×	`egg-rr`
148×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Counts

3 → 650

Calls

3 calls:

217.0ms

(/.f64 b (hypot.f64 c d))

217.0ms

(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))

217.0ms

(*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	289	48
2	3842	48
3	5238	48
0	0	0
1	0	0

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-neg_binary64`
547×	`times-frac_binary64`
474×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
291×	`cancel-sign-sub-inv_binary64`

Counts

770 → 719

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	3142
1	345	2998
2	1106	2880
3	4638	2880
4	5222	2880

prune802.0ms (9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	779	2	781
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	781	7	788

Error

Counts

788 → 7

Alt Table

Status	Error	Program
	13.1b	(+.f64 (fma.f64 b (.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 c (hypot.f64 c d))) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
✓	25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	12.5b	(+.f64 (fma.f64 (.f64 (/.f64 b (hypot.f64 c d)) c) (/.f64 1 (hypot.f64 c d)) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
	41.2b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
▶	0.7b	(fma.f64 (/.f64 b (hypot.f64 c d)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d)))) (neg.f64 (.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))
	15.4b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (.f64 d (.f64 a (pow.f64 (hypot.f64 c d) -2)))))
	9.7b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 d (*.f64 (/.f64 (hypot.f64 c d) a) (hypot.f64 c d)))))

Compiler

Compiled 43412 to 11489 computations (73.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d))))
✓	0.3b	(fma.f64 (/.f64 b (hypot.f64 c d)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d)))) (neg.f64 (.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))
✓	0.4b	(/.f64 c (sqrt.f64 (hypot.f64 c d)))
	0.4b	(*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))

series277.0ms (3.1%)

Counts

3 → 80

Calls

3 calls:

229.0ms

(fma.f64 (/.f64 b (hypot.f64 c d)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d)))) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))

28.0ms

(/.f64 c (sqrt.f64 (hypot.f64 c d)))

19.0ms

(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d))))

rewrite303.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

794×	`prod-diff_binary64`
698×	`egg-rr`
181×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`

Counts

3 → 698

Calls

3 calls:

267.0ms

(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d))))

267.0ms

(fma.f64 (/.f64 b (hypot.f64 c d)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d)))) (neg.f64 (*.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))

267.0ms

(/.f64 c (sqrt.f64 (hypot.f64 c d)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	50
1	369	44
2	4765	44
3	6404	44
0	0	0
1	0	0

simplify139.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
319×	`fma-def_binary64`
314×	`associate-r_binary64`
312×	`cancel-sign-sub-inv_binary64`
289×	`associate-/l*_binary64`

Counts

778 → 762

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	2152
1	381	2054
2	1181	1993
3	4668	1966
4	5040	1966

prune970.0ms (10.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	843	0	843
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	843	7	850

Error

Counts

850 → 7

Alt Table

Status	Error	Program
	13.1b	(+.f64 (fma.f64 b (.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 c (hypot.f64 c d))) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
✓	25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	12.5b	(+.f64 (fma.f64 (.f64 (/.f64 b (hypot.f64 c d)) c) (/.f64 1 (hypot.f64 c d)) (neg.f64 (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a))) (fma.f64 (neg.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2))) a (.f64 (.f64 d (pow.f64 (hypot.f64 c d) -2)) a)))
	41.2b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
✓	0.7b	(fma.f64 (/.f64 b (hypot.f64 c d)) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 c d))) (/.f64 c (sqrt.f64 (hypot.f64 c d)))) (neg.f64 (.f64 (/.f64 a (hypot.f64 c d)) (/.f64 d (hypot.f64 c d)))))
	15.4b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (.f64 d (.f64 a (pow.f64 (hypot.f64 c d) -2)))))
	9.7b	(fma.f64 (/.f64 b (hypot.f64 c d)) (/.f64 c (hypot.f64 c d)) (neg.f64 (/.f64 d (*.f64 (/.f64 (hypot.f64 c d) a) (hypot.f64 c d)))))

Compiler

Compiled 48911 to 12829 computations (73.8% saved)

regimes1.2s (12.9%)

Accuracy

Total 1.4b remaining (91.7%)

Threshold costs 0b (0%)

Counts

163 → 1

Compiler

Compiled 24568 to 12784 computations (48% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	27	38
2	42	38
3	55	38
4	64	38
5	69	38
6	70	38
7	70	38

end125.0ms (1.4%)

Compiler: Compiled 275 to 141 computations (48.7% saved)

Details

analyze1.3s (14.2%)

sample1.2s (13.3%)

simplify67.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series91.0ms (1%)

rewrite79.0ms (0.9%)

simplify76.0ms (0.9%)

prune204.0ms (2.3%)

localize11.0ms (0.1%)

series396.0ms (4.4%)

rewrite213.0ms (2.4%)

simplify120.0ms (1.3%)

prune620.0ms (6.9%)

localize11.0ms (0.1%)

series405.0ms (4.5%)

rewrite251.0ms (2.8%)

simplify126.0ms (1.4%)

prune802.0ms (9%)

localize15.0ms (0.2%)

series277.0ms (3.1%)

rewrite303.0ms (3.4%)

simplify139.0ms (1.6%)

prune970.0ms (10.9%)

regimes1.2s (12.9%)

simplify4.0ms (0%)

end125.0ms (1.4%)

Profiling