Details

analyze651.0ms (13.7%)

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)

sample135.0ms (2.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	24×	body	128	invalid

Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify65.0ms (1.4%)

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 (0.1%)

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

27.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 b c) (.f64 a d))
✓	27.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series94.0ms (2%)

Counts

2 → 96

Calls

2 calls:

85.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
9.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite18.0ms (0.4%)

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 → 48

Calls

2 calls:

11.0ms	(-.f64 (.f64 b c) (.f64 a d))
4.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary64`
380×	`associate-l_binary64`
348×	`fma-def_binary64`
315×	`associate-r_binary64`
247×	`associate-/l*_binary64`

Counts

144 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2762
1	323	2614
2	1084	2567
3	4430	2567
4	4952	2567

prune72.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	8	110

Error

0.7b

Counts

110 → 8

Alt Table

Status	Error	Program
▶	19.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	37.8b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	34.5b	(neg.f64 (/.f64 a d))
	20.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	27.7b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (*.f64 d d))))
✓	27.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	38.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	36.8b	(/.f64 b c)

Compiler

Compiled 2793 to 597 computations (78.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	18.5b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series236.0ms (5%)

Counts

4 → 132

Calls

4 calls:

111.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
98.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
18.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite31.0ms (0.6%)

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 → 139

Calls

4 calls:

11.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
4.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify130.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
537×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`
181×	`sub-neg_binary64`

Counts

271 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6415
1	744	5877
2	2552	5818
3	5061	5818

prune183.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	4	271
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	270	9	279

Error

0.7b

Counts

279 → 9

Alt Table

Status	Error	Program
	38.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	41.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	34.5b	(neg.f64 (/.f64 a d))
	43.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	19.6b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
▶	19.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
✓	27.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	36.8b	(/.f64 b c)
	37.8b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))

Compiler

Compiled 7367 to 2188 computations (70.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	18.5b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series106.0ms (2.2%)

Counts

1 → 48

Calls

1 calls:

106.0ms

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

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 73

Calls

1 calls:

6.0ms

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

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

562×	`times-frac_binary64`
475×	`associate-/l/_binary64`
466×	`associate-/l*_binary64`
465×	`fma-neg_binary64`
359×	`div-sub_binary64`

Counts

121 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	4368
1	439	4066
2	1089	3872
3	4050	3805
4	5223	3805

prune132.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	231	9	240

Error

0.7b

Counts

240 → 9

Alt Table

Status	Error	Program
	38.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	41.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	34.5b	(neg.f64 (/.f64 a d))
	43.0b	(/.f64 (neg.f64 a) (hypot.f64 d c))
▶	19.6b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
✓	19.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
✓	27.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	36.8b	(/.f64 b c)
	37.8b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))

Compiler

Compiled 6224 to 1290 computations (79.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.1b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	18.5b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

series205.0ms (4.3%)

Counts

2 → 96

Calls

2 calls:

106.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
99.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

rewrite23.0ms (0.5%)

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 → 79

Calls

2 calls:

9.0ms	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
7.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d)))

simplify120.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-def_binary64`
441×	`associate-/l/_binary64`
315×	`fma-neg_binary64`
248×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-in_binary64`

Counts

175 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	4543
1	569	4060
2	2124	3990
3	4767	3988
4	4988	3988

prune178.0ms (3.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	271	9	280

Error

0.7b

Counts

280 → 9

Alt Table

Status	Error	Program
✓	19.6b	(/.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (.f64 c b) (*.f64 a d))) (hypot.f64 d c))
	32.8b	(-.f64 (/.f64 (.f64 b c) (.f64 d d)) (/.f64 a d))
	38.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	41.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) a)
	43.0b	(/.f64 (neg.f64 a) (hypot.f64 d c))
✓	19.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
✓	27.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
	36.8b	(/.f64 b c)
	37.8b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))

Compiler

Compiled 6903 to 2228 computations (67.7% saved)

regimes1.1s (24.1%)

Accuracy

Total 10.9b remaining (86.9%)

Threshold costs 0b (0%)

Counts

111 → 5

Compiler

Compiled 11863 to 6679 computations (43.7% saved)

bsearch67.0ms (1.4%)

Steps

Iters	Range		Point
7	7.850259288952477e+167	5.230627704986425e+169	1.096228133156405e+168
5	1.0210531305001881e-171	3.907793493220797e-171	1.2857576694400817e-171
9	-3.8166329834924135e-75	-1.137985837928312e-103	-1.757389697762391e-103
9	-8.945697190249736e+145	-2.8122679138516764e+138	-2.9458923187888928e+141

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	103
1	49	103
2	63	103
3	72	103
4	77	103
5	78	103
6	77	103

end1.0ms (0%)

Compiler: Compiled 74 to 31 computations (58.1% saved)

sample895.0ms (18.9%)

Algorithm

1×

intervals

Results

438.0ms	8000×	body	128	valid
29.0ms	473×	body	128	invalid

Compiler

Compiled 247 to 136 computations (44.9% saved)

Details

analyze651.0ms (13.7%)

sample135.0ms (2.8%)

simplify65.0ms (1.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series94.0ms (2%)

rewrite18.0ms (0.4%)

simplify88.0ms (1.8%)

prune72.0ms (1.5%)

localize9.0ms (0.2%)

series236.0ms (5%)

rewrite31.0ms (0.6%)

simplify130.0ms (2.7%)

prune183.0ms (3.9%)

localize10.0ms (0.2%)

series106.0ms (2.2%)

rewrite16.0ms (0.3%)

simplify114.0ms (2.4%)

prune132.0ms (2.8%)

localize9.0ms (0.2%)

series205.0ms (4.3%)

rewrite23.0ms (0.5%)

simplify120.0ms (2.5%)

prune178.0ms (3.7%)

regimes1.1s (24.1%)

bsearch67.0ms (1.4%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample895.0ms (18.9%)

Profiling