Details

analyze665.0ms (10.4%)

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
34.7%	55.4%	9.9%	9
36.1%	51.1%	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)

sample2.4s (37.8%)

Results

655.0ms	5394×	body	128	valid
629.0ms	1149×	body	2048	valid
296.0ms	775×	body	1024	valid
223.0ms	399×	body	4096	valid
120.0ms	1055×	body	128	invalid
100.0ms	349×	body	512	valid
38.0ms	190×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify84.0ms (1.3%)

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

34.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.6b	(/.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)
✓	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series116.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

49.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
33.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
26.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite284.0ms (4.5%)

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:

262.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify317.0ms (5%)

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 → 237

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

prune160.0ms (2.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	225	12	237
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	225	13	238

Error

6.5b

Counts

238 → 13

Alt Table

Status	Error	Program
	34.4b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	43.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	48.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	48.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	35.1b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	44.5b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
▶	34.3b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	39.4b	(*.f64 -1/2 (/.f64 c b_2))
	43.3b	(/.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)
	48.3b	(/.f64 (*.f64 -2 b_2) a)
	35.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) (cbrt.f64 a)))
✓	34.6b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	48.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))

Compiler

Compiled 6006 to 1749 computations (70.9% saved)

localize11.0ms (0.2%)

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))
✓	0.2b	(/.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)
✓	10.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series560.0ms (8.8%)

Counts

4 → 36

Calls

4 calls:

233.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
186.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
128.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
12.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite36.0ms (0.6%)

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)))
5.0ms	(/.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)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify192.0ms (3%)

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 → 300

Iterations

Useful iterations: 3 (0.0ms)

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

prune184.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	302	11	313

Error

0.2b

Counts

313 → 11

Alt Table

Status	Error	Program
	39.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
▶	35.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) (cbrt.f64 a)))
	48.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	48.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	39.4b	(*.f64 -1/2 (/.f64 c b_2))
	46.5b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	43.3b	(/.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)
	43.9b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
✓	34.6b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	48.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	44.8b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))

Compiler

Compiled 8510 to 2445 computations (71.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 a)
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series34.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

34.0ms

(cbrt.f64 a)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 a)

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l/_binary64`
374×	`log-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`

Counts

25 → 18

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	141
1	38	137
2	86	137
3	208	137
4	626	133
5	1904	133
6	2565	133
7	3552	133
8	4861	133

prune113.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	206	11	217

Error

0.2b

Counts

217 → 11

Alt Table

Status	Error	Program
	39.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
✓	35.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) (cbrt.f64 a)))
	47.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.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)) (cbrt.f64 a)))
	48.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	48.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
▶	39.4b	(*.f64 -1/2 (/.f64 c b_2))
	46.5b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	43.3b	(/.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)
✓	34.6b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	48.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	44.8b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))

Compiler

Compiled 6606 to 2083 computations (68.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (/.f64 c b_2))

series7.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

7.0ms

(*.f64 -1/2 (/.f64 c b_2))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

5.0ms

(*.f64 -1/2 (/.f64 c b_2))

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l/_binary64`
791×	`times-frac_binary64`
407×	`associate-/l*_binary64`
344×	`pow-sqr_binary64`
338×	`associate-*l/_binary64`

Counts

34 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	381
1	156	345
2	390	345
3	850	345
4	1897	345
5	2021	345
6	2193	345
7	2428	345
8	2951	345
9	3248	345
10	4846	345
11	4925	345
12	5000	345
13	4931	345

prune25.0ms (0.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	40	11	51

Error

0.2b

Counts

51 → 11

Alt Table

Status	Error	Program
	39.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
✓	35.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) (cbrt.f64 a)))
	47.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.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)) (cbrt.f64 a)))
	48.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) a)) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
	48.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	43.3b	(/.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)
✓	34.6b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	39.3b	(/.f64 (*.f64 -1/2 c) b_2)
	48.2b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 3))
	46.5b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	44.8b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))

Compiler

Compiled 666 to 359 computations (46.1% saved)

regimes737.0ms (11.6%)

Accuracy

Total 10.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts

88 → 3

Compiler

Compiled 7356 to 4138 computations (43.7% saved)

bsearch78.0ms (1.2%)

Steps

Iters	Range		Point
8	4.711838323479284e-51	5.766566898698519e-48	2.8943632832812116e-49
9	-3.065242740965835e+70	-7.868367830038492e+64	-1.24070021974044e+69

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	51
1	36	51
2	49	51
3	57	51
4	62	51
5	63	51
6	63	51

end143.0ms (2.2%)

Compiler: Compiled 290 to 177 computations (39% saved)

Details

analyze665.0ms (10.4%)

sample2.4s (37.8%)

simplify84.0ms (1.3%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series116.0ms (1.8%)

rewrite284.0ms (4.5%)

simplify317.0ms (5%)

prune160.0ms (2.5%)

localize11.0ms (0.2%)

series560.0ms (8.8%)

rewrite36.0ms (0.6%)

simplify192.0ms (3%)

prune184.0ms (2.9%)

localize12.0ms (0.2%)

series34.0ms (0.5%)

rewrite1.0ms (0%)

simplify62.0ms (1%)

prune113.0ms (1.8%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify114.0ms (1.8%)

prune25.0ms (0.4%)

regimes737.0ms (11.6%)

bsearch78.0ms (1.2%)

simplify4.0ms (0.1%)

end143.0ms (2.2%)

Profiling