Details

analyze852.0ms (12%)

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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify7.0ms (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

prune6.0ms (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

23.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	23.8b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
	23.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 104 to 54 computations (48.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a c (*.f64 b d))
✓	23.3b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series107.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

94.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
12.0ms	(fma.f64 a c (*.f64 b d))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
0.0ms	(fma.f64 a c (*.f64 b d))

simplify113.0ms (1.6%)

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

135 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	2544
1	202	2411
2	604	2327
3	2154	2279
4	5032	2279

prune112.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	9	96

Error

2.1b

Counts

96 → 9

Alt Table

Status	Error	Program
	37.6b	(.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)))
	21.0b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	16.3b	(.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)))
	37.4b	(/.f64 a c)
	36.8b	(/.f64 (.f64 d b) (fma.f64 d d (.f64 c c)))
▶	15.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	34.4b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	37.5b	(/.f64 b d)
	23.7b	(/.f64 (/.f64 (fma.f64 a c (.f64 b d)) (sqrt.f64 (fma.f64 c c (.f64 d d)))) (sqrt.f64 (fma.f64 c c (*.f64 d d))))

Compiler

Compiled 2322 to 504 computations (78.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	0.5b	(fma.f64 d b (*.f64 c a))
✓	14.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series302.0ms (4.3%)

Counts

4 → 168

Calls

4 calls:

137.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
125.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
27.0ms	(/.f64 1 (hypot.f64 d c))
12.0ms	(fma.f64 d b (*.f64 c a))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 130

Calls

4 calls:

11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
3.0ms	(/.f64 1 (hypot.f64 d c))
3.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

simplify219.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
428×	`fma-neg_binary64`
410×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
274×	`distribute-rgt-in_binary64`

Counts

298 → 286

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	6205
1	631	5720
2	2125	5547
3	4841	5539
4	5079	5539

prune229.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	280	6	286
Fresh	8	0	8
Picked	0	1	1
Done	0	0	0
Total	288	7	295

Error

0.1b

Counts

295 → 7

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
▶	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	22.5b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	43.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))

Compiler

Compiled 7311 to 2176 computations (70.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
✓	14.8b	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

series539.0ms (7.6%)

Counts

4 → 136

Calls

4 calls:

277.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
121.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
110.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))
30.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))

rewrite146.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

368×	`times-frac_binary64`
276×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`
186×	`add-cube-cbrt_binary64`
122×	`sqrt-prod_binary64`

Counts

4 → 351

Calls

4 calls:

70.0ms	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
8.0ms	(/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
6.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 d c)))
4.0ms	(/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c))

simplify431.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
308×	`associate-/l*_binary64`
301×	`associate-*l/_binary64`
290×	`associate-/l/_binary64`
284×	`associate-r_binary64`

Counts

487 → 575

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	459	16925
1	1261	15048
2	4049	14855
3	4942	14855
4	4996	14855
5	4957	14855

prune355.0ms (5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	575	0	575
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	575	7	582

Error

0.1b

Counts

582 → 7

Alt Table

Status	Error	Program
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	42.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
▶	22.5b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	43.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))

Compiler

Compiled 20803 to 4422 computations (78.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 d d (*.f64 c c))
✓	1.8b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
✓	15.2b	(/.f64 (.f64 d b) (fma.f64 d d (.f64 c c)))
✓	18.7b	(/.f64 c (fma.f64 d d (*.f64 c c)))

series274.0ms (3.9%)

Counts

4 → 132

Calls

4 calls:

153.0ms	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
91.0ms	(/.f64 (.f64 d b) (fma.f64 d d (.f64 c c)))
21.0ms	(/.f64 c (fma.f64 d d (*.f64 c c)))
8.0ms	(fma.f64 d d (*.f64 c c))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

4.0ms	(/.f64 (.f64 d b) (fma.f64 d d (.f64 c c)))
2.0ms	(/.f64 c (fma.f64 d d (*.f64 c c)))
0.0ms	(fma.f64 d d (*.f64 c c))
0.0ms	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))

simplify217.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

781×	`associate-/l*_binary64`
775×	`times-frac_binary64`
354×	`fma-neg_binary64`
284×	`associate-/l/_binary64`
240×	`cancel-sign-sub-inv_binary64`

Counts

204 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	4352
1	420	4073
2	1353	3959
3	4667	3959
4	4975	3959

prune144.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	205	7	212

Error

Counts

212 → 7

Alt Table

Status	Error	Program
	21.4b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 d (/.f64 (fma.f64 c c (.f64 d d)) b)))
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
✓	15.9b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
	14.2b	(fma.f64 (.f64 (/.f64 1 (hypot.f64 c d)) (/.f64 c (hypot.f64 c d))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
✓	15.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	43.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 c d) a b))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))

Compiler

Compiled 5562 to 1101 computations (80.2% saved)

regimes1.7s (23.7%)

Accuracy

Total 7.1b remaining (98.9%)

Threshold costs 0b (0%)

Counts

134 → 3

Compiler

Compiled 14193 to 7824 computations (44.9% saved)

bsearch68.0ms (1%)

Steps

Iters	Range		Point
8	1.9798221448362845e+146	9.863307307441638e+148	2.6948582591098956e+146
9	-4.5170616791184643e+123	-5.687748492731527e+117	-1.3391945132269083e+119

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	78
1	41	78
2	48	76
3	56	76
4	59	76
5	60	76
6	58	76

end1.0ms (0%)

Compiler: Compiled 57 to 29 computations (49.1% saved)

sample1.1s (16.1%)

Algorithm

1×

intervals

Results

527.0ms	8000×	body	128	valid
31.0ms	477×	body	128	invalid

Compiler

Compiled 222 to 121 computations (45.5% saved)

Details

analyze852.0ms (12%)

sample31.0ms (0.4%)

simplify7.0ms (0.1%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series107.0ms (1.5%)

rewrite6.0ms (0.1%)

simplify113.0ms (1.6%)

prune112.0ms (1.6%)

localize17.0ms (0.2%)

series302.0ms (4.3%)

rewrite32.0ms (0.4%)

simplify219.0ms (3.1%)

prune229.0ms (3.2%)

localize13.0ms (0.2%)

series539.0ms (7.6%)

rewrite146.0ms (2.1%)

simplify431.0ms (6.1%)

prune355.0ms (5%)

localize12.0ms (0.2%)

series274.0ms (3.9%)

rewrite11.0ms (0.2%)

simplify217.0ms (3.1%)

prune144.0ms (2%)

regimes1.7s (23.7%)

bsearch68.0ms (1%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.1s (16.1%)

Profiling