Details

analyze1.4s (16.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample49.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	39×	body	2048	valid
11.0ms	162×	body	128	valid
5.0ms	21×	body	1024	valid
4.0ms	13×	body	4096	valid
2.0ms	14×	body	512	valid
2.0ms	34×	body	128	nan
1.0ms	7×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 36 to 24 computations (33.3% saved)

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

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

33.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.6b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
19×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series177.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

67.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
48.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
38.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify354.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
364×	`cancel-sign-sub-inv_binary64`
248×	`distribute-rgt-neg-in_binary64`
220×	`distribute-lft-neg-in_binary64`
172×	`distribute-rgt-in_binary64`

Counts

216 → 398

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5492
1	683	4712
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune150.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	386	12	398
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	387	12	399

Error

5.3b

Counts

399 → 12

Alt Table

Status	Error	Program
	33.7b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
	47.5b	(/.f64 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8)) a)
▶	31.8b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	34.8b	(/.f64 (-.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	44.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	38.5b	(*.f64 -1/2 (/.f64 c b_2))
	33.9b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	55.5b	(/.f64 (-.f64 b_2 b_2) a)
	38.2b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	47.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	47.0b	(/.f64 (*.f64 -2 b_2) a)

Compiler

Compiled 5904 to 1714 computations (71% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
✓	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	14.6b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
116×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

4 → 197

Calls

4 calls:

7.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
4.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

series836.0ms (10%)

Counts

4 → 36

Calls

4 calls:

367.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
252.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
202.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
15.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify315.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
384×	`cancel-sign-sub-inv_binary64`
289×	`fma-neg_binary64`
216×	`div-sub_binary64`
164×	`distribute-neg-frac_binary64`

Counts

233 → 406

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	7449
1	719	6508
2	2604	6286
3	4744	6282
4	5014	6282

prune191.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	399	7	406
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	407	11	418

Error

0.0b

Counts

418 → 11

Alt Table

Status	Error	Program
	48.4b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
	38.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
	31.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	44.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	38.5b	(*.f64 -1/2 (/.f64 c b_2))
	31.9b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))) (/.f64 1 (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))))
▶	31.7b	(.f64 1 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a))
	47.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.3b	(fma.f64 (.f64 (neg.f64 c) (/.f64 (neg.f64 (.f64 c a)) (pow.f64 b_2 3))) -1/8 (*.f64 1/2 (/.f64 (neg.f64 c) b_2)))

Compiler

Compiled 8537 to 2472 computations (71% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
✓	0.1b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	14.6b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

series296.0ms (3.5%)

Counts

2 → 26

Calls

2 calls:

191.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
104.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
616×	`associate-/l*_binary64`
532×	`associate-/r*_binary64`
196×	`associate-*l/_binary64`
194×	`fma-neg_binary64`

Counts

76 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2173
1	453	2043
2	1342	1943
3	4606	1941
4	4998	1941

prune118.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Error

0.0b

Counts

213 → 12

Alt Table

Status	Error	Program
	48.4b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
	38.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
▶	31.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	44.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	38.5b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(.f64 1 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a))
	42.3b	(fma.f64 (.f64 (neg.f64 c) (/.f64 (neg.f64 (.f64 c a)) (pow.f64 b_2 3))) -1/8 (*.f64 1/2 (/.f64 (neg.f64 c) b_2)))
	31.9b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))) (/.f64 1 (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))))
✓	31.7b	(.f64 1 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a))
	47.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 4845 to 1826 computations (62.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	0.7b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	14.6b	(sqrt.f64 (neg.f64 (*.f64 c a)))
	14.6b	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune96.0ms (1.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	552	0	552
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	552	12	564

Error

0.0b

Counts

564 → 12

Alt Table

Status	Error	Program
	48.4b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	33.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	46.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
	38.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
✓	31.9b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	44.3b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
	38.5b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(.f64 1 (/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a))
	42.3b	(fma.f64 (.f64 (neg.f64 c) (/.f64 (neg.f64 (.f64 c a)) (pow.f64 b_2 3))) -1/8 (*.f64 1/2 (/.f64 (neg.f64 c) b_2)))
	31.9b	(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))) (/.f64 1 (/.f64 a (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))))
✓	31.7b	(.f64 1 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a))
	47.1b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 5563 to 1284 computations (76.9% saved)

regimes2.4s (28.2%)

Accuracy

Total 10.3b remaining (99.2%)

Threshold costs 0b (0%)

Compiler

Compiled 14124 to 8362 computations (40.8% saved)

bsearch51.0ms (0.6%)

Steps

Iters	Range		Point
9	1.8149281730708693e-48	3.0440656134958992e-43	1.1010667460580007e-45
2	-1.0457284988101661e+157	-1.14576045703764e+152	-2.0131745716447322e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	26	47
1	39	47
2	53	47
3	63	47
4	70	47
5	72	47
6	71	47

end1.0ms (0%)

Compiler: Compiled 35 to 22 computations (37.1% saved)

sample1.7s (19.9%)

Algorithm

1×

intervals

Results

368.0ms	5202×	body	128	valid
305.0ms	1095×	body	2048	valid
160.0ms	714×	body	1024	valid
143.0ms	430×	body	4096	valid
122.0ms	371×	body	512	valid
49.0ms	825×	body	128	nan
21.0ms	188×	body	256	valid
14.0ms	238×	body	128	invalid

Compiler

Compiled 281 to 177 computations (37% saved)

Details

analyze1.4s (16.7%)

sample49.0ms (0.6%)

simplify90.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite29.0ms (0.4%)

series177.0ms (2.1%)

simplify354.0ms (4.2%)

prune150.0ms (1.8%)

localize9.0ms (0.1%)

rewrite31.0ms (0.4%)

series836.0ms (10%)

simplify315.0ms (3.8%)

prune191.0ms (2.3%)

localize9.0ms (0.1%)

rewrite8.0ms (0.1%)

series296.0ms (3.5%)

simplify95.0ms (1.1%)

prune118.0ms (1.4%)

localize11.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify14.0ms (0.2%)

prune96.0ms (1.1%)

regimes2.4s (28.2%)

bsearch51.0ms (0.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (19.9%)

Profiling