Details

analyze676.0ms (9.1%)

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)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

prune10.0ms (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

25.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.1b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.0b	(fma.f64 a c (*.f64 b d))
✓	24.6b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
0.0ms	(fma.f64 a c (*.f64 b d))
0.0ms	(fma.f64 c c (*.f64 d d))

series139.0ms (1.9%)

Counts

3 → 120

Calls

3 calls:

85.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
33.0ms	(fma.f64 a c (*.f64 b d))
21.0ms	(fma.f64 c c (*.f64 d d))

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
410×	`associate-/l/_binary64`
377×	`fma-neg_binary64`
252×	`distribute-rgt-neg-in_binary64`
251×	`distribute-lft-neg-in_binary64`

Counts

169 → 313

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2836
1	205	2674
2	611	2590
3	2163	2542
4	5054	2542

prune92.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	307	6	313
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	308	6	314

Error

1.2b

Counts

314 → 6

Alt Table

Status	Error	Program
	41.0b	(.f64 (/.f64 (sqrt.f64 (fma.f64 d b (.f64 c a))) (hypot.f64 d c)) (/.f64 (sqrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	23.1b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	18.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	37.6b	(/.f64 a c)
	34.1b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
▶	17.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))

Compiler

Compiled 2586 to 516 computations (80% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	16.7b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))
0.0ms	(hypot.f64 d c)

series255.0ms (3.4%)

Counts

4 → 168

Calls

4 calls:

106.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
100.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
35.0ms	(fma.f64 d b (*.f64 c a))
13.0ms	(hypot.f64 d c)

simplify190.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
425×	`fma-neg_binary64`
389×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
283×	`distribute-rgt-in_binary64`

Counts

275 → 513

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	5683
1	623	5331
2	2083	5152
3	4804	5152
4	5030	5152

prune175.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	509	4	513
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	513	6	519

Error

0.0b

Counts

519 → 6

Alt Table

Status	Error	Program
	23.1b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	17.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
	21.1b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	34.1b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	32.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 6728 to 1946 computations (71.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 d c)
	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.1b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
✓	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
14×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

2 → 67

Calls

2 calls:

5.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))
5.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))

series206.0ms (2.8%)

Counts

2 → 96

Calls

2 calls:

104.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a)))
102.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))

simplify152.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

414×	`associate-/l/_binary64`
407×	`associate-/r*_binary64`
377×	`fma-neg_binary64`
358×	`associate-*l/_binary64`
266×	`fma-def_binary64`

Counts

163 → 309

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	4007
1	449	3558
2	1571	3392
3	4207	3392
4	4792	3380
5	4987	3380

prune143.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	471	1	472
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	471	7	478

Error

0.0b

Counts

478 → 7

Alt Table

Status	Error	Program
	23.1b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
✓	17.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
▶	17.9b	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
	21.1b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	34.1b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	32.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 5375 to 1813 computations (66.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 d c)
	0.0b	(fma.f64 d b (*.f64 c a))
✓	0.3b	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
✓	16.7b	(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

430×	`times-frac_binary64`
206×	`*-un-lft-identity_binary64`
206×	`add-sqr-sqrt_binary64`
206×	`add-cube-cbrt_binary64`
30×	`div-inv_binary64`

Counts

2 → 250

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
2.0ms	(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

series164.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

105.0ms	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
58.0ms	(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

simplify372.0ms (5%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-def_binary64`
291×	`associate-/l/_binary64`
269×	`associate-/r*_binary64`
264×	`associate-*l/_binary64`
260×	`associate-/l*_binary64`

Counts

346 → 676

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	15338
1	1060	13814
2	4004	13178
3	5018	13178

prune315.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1002	0	1002
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	1002	7	1009

Error

0.0b

Counts

1009 → 7

Alt Table

Status	Error	Program
	23.1b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
✓	17.9b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 d b (.f64 c a))) (hypot.f64 d c))
✓	17.9b	(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
	21.1b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
	34.1b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	32.1b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	32.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 15706 to 4714 computations (70% saved)

regimes3.3s (44.7%)

Accuracy

Total 10.1b remaining (98.4%)

Threshold costs 0b (0%)

Compiler

Compiled 22503 to 12519 computations (44.4% saved)

bsearch72.0ms (1%)

Steps

Iters	Range		Point
7	3.795620259115813e+95	6.184873560754579e+96	3.5151647360045185e+96
7	3.612890888125792e-221	8.568033066115074e-219	2.7560140316565585e-220
6	-5.362525072029779e-174	-3.87085550367725e-175	-3.44433832248687e-174
8	-8.375429638413106e+81	-1.6434197147451538e+78	-9.06783613733096e+79

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	118
1	54	118
2	58	118
3	61	118
4	62	118
5	61	118

end1.0ms (0%)

Compiler: Compiled 85 to 38 computations (55.3% saved)

sample892.0ms (12.1%)

Algorithm

1×

intervals

Results

439.0ms	8000×	body	128	valid
33.0ms	483×	body	128	invalid

Compiler

Compiled 241 to 123 computations (49% saved)

Details

analyze676.0ms (9.1%)

sample25.0ms (0.3%)

simplify9.0ms (0.1%)

prune10.0ms (0.1%)

localize9.0ms (0.1%)

rewrite5.0ms (0.1%)

series139.0ms (1.9%)

simplify93.0ms (1.3%)

prune92.0ms (1.2%)

localize9.0ms (0.1%)

rewrite19.0ms (0.3%)

series255.0ms (3.4%)

simplify190.0ms (2.6%)

prune175.0ms (2.4%)

localize11.0ms (0.1%)

rewrite14.0ms (0.2%)

series206.0ms (2.8%)

simplify152.0ms (2.1%)

prune143.0ms (1.9%)

localize9.0ms (0.1%)

rewrite31.0ms (0.4%)

series164.0ms (2.2%)

simplify372.0ms (5%)

prune315.0ms (4.3%)

regimes3.3s (44.7%)

bsearch72.0ms (1%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample892.0ms (12.1%)

Profiling