Details

analyze632.0ms (5.8%)

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)

sample2.8s (25.3%)

Results

808.0ms	1156×	body	2048	valid
673.0ms	5412×	body	128	valid
295.0ms	754×	body	1024	valid
220.0ms	388×	body	4096	valid
197.0ms	365×	body	512	valid
129.0ms	1051×	body	128	invalid
43.0ms	181×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify85.0ms (0.8%)

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

36.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.6b	(/.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)

localize7.0ms (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))
✓	0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	24.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series174.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

73.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
53.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
39.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite29.0ms (0.3%)

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)
8.0ms	(-.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))

simplify357.0ms (3.3%)

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

prune145.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	13	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	13	238

Error

7.2b

Counts

238 → 13

Alt Table

Status	Error	Program
	36.7b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	43.9b	(/.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)
	37.7b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a))))) b_2) a)
	55.9b	(/.f64 (-.f64 b_2 b_2) a)
▶	34.6b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	49.1b	(/.f64 (*.f64 -2 b_2) a)
	36.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))) a)
	44.8b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	40.3b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	49.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.2b	(/.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)
	39.1b	(*.f64 -1/2 (/.f64 c b_2))
	48.3b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)

Compiler

Compiled 5983 to 1756 computations (70.7% 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)))
✓	0.3b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	16.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series851.0ms (7.8%)

Counts

4 → 36

Calls

4 calls:

428.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
263.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
144.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
16.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite41.0ms (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:

10.0ms	(/.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)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify186.0ms (1.7%)

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

prune158.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	303	10	313

Error

0.3b

Counts

313 → 10

Alt Table

Status	Error	Program
	34.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
	43.9b	(/.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)
	38.7b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
	49.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	48.2b	(/.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)
	44.8b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
▶	34.5b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	39.1b	(*.f64 -1/2 (/.f64 c b_2))
	46.6b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
	46.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))

Compiler

Compiled 8501 to 2450 computations (71.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	0.3b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	16.2b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series208.0ms (1.9%)

Counts

1 → 12

Calls

1 calls:

208.0ms

(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`associate-l_binary64`

Counts

1 → 69

Calls

1 calls:

8.0ms

(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/l*_binary64`
489×	`associate-/r*_binary64`
447×	`fma-def_binary64`
216×	`associate-*l/_binary64`
191×	`distribute-rgt-in_binary64`

Counts

81 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2317
1	469	2032
2	1462	1897
3	4681	1895
4	4962	1895

prune119.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	194	11	205

Error

0.3b

Counts

205 → 11

Alt Table

Status	Error	Program
	46.0b	(.f64 (/.f64 1 a) (/.f64 (.f64 -1/2 (*.f64 c a)) b_2))
	38.7b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
	39.1b	(*.f64 -1/2 (/.f64 c b_2))
	46.0b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
▶	34.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
	43.9b	(/.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)
	49.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.8b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
✓	34.5b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	46.6b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
	46.6b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))

Compiler

Compiled 5509 to 1836 computations (66.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
✓	0.2b	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
✓	0.3b	(-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
✓	17.6b	(cbrt.f64 (neg.f64 (*.f64 c a)))

series2.4s (22%)

Counts

4 → 120

Calls

4 calls:

845.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
680.0ms	(-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
499.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
377.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`add-sqr-sqrt_binary64`
123×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`

Counts

4 → 213

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
10.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
6.0ms	(-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)
1.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))

simplify322.0ms (3%)

Algorithm

1×	egg-herbie

Rules

406×	`fma-neg_binary64`
345×	`cancel-sign-sub-inv_binary64`
269×	`unswap-sqr_binary64`
254×	`associate-r_binary64`
252×	`associate-l_binary64`

Counts

333 → 366

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	468	14849
1	1076	12390
2	3207	10257
3	4632	8526
4	4941	8471
5	4890	8471

prune245.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	399	0	399
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	399	11	410

Error

0.3b

Counts

410 → 11

Alt Table

Status	Error	Program
	46.0b	(.f64 (/.f64 1 a) (/.f64 (.f64 -1/2 (*.f64 c a)) b_2))
	38.7b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
	39.1b	(*.f64 -1/2 (/.f64 c b_2))
	46.0b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
✓	34.7b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2)))
	43.9b	(/.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)
	49.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.8b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
✓	34.5b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	46.6b	(.f64 (/.f64 1 a) (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
	46.6b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))

Compiler

Compiled 14374 to 4623 computations (67.8% saved)

regimes1.6s (15%)

Accuracy

Total 10.3b remaining (98%)

Threshold costs 0b (0%)

Counts

141 → 3

Compiler

Compiled 10948 to 6814 computations (37.8% saved)

bsearch83.0ms (0.8%)

Steps

Iters	Range		Point
6	7.365653933289304e-79	8.326122624814442e-78	9.920277852078554e-79
6	-4.099498894066867e+85	-4.915213818451088e+84	-3.432082904239482e+85

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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	25	44
1	37	44
2	49	44
3	57	44
4	62	44
5	63	44
6	62	44

end271.0ms (2.5%)

Compiler: Compiled 252 to 166 computations (34.1% saved)

Details

analyze632.0ms (5.8%)

sample2.8s (25.3%)

simplify85.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series174.0ms (1.6%)

rewrite29.0ms (0.3%)

simplify357.0ms (3.3%)

prune145.0ms (1.3%)

localize9.0ms (0.1%)

series851.0ms (7.8%)

rewrite41.0ms (0.4%)

simplify186.0ms (1.7%)

prune158.0ms (1.4%)

localize8.0ms (0.1%)

series208.0ms (1.9%)

rewrite16.0ms (0.1%)

simplify86.0ms (0.8%)

prune119.0ms (1.1%)

localize12.0ms (0.1%)

series2.4s (22%)

rewrite56.0ms (0.5%)

simplify322.0ms (3%)

prune245.0ms (2.3%)

regimes1.6s (15%)

bsearch83.0ms (0.8%)

simplify4.0ms (0%)

end271.0ms (2.5%)

Profiling