Details

analyze380.0ms (3.2%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
40.6%	54.6%	4.8%	7
48.4%	46%	5.6%	8
53.8%	37.8%	8.3%	9
56.2%	32.6%	11.3%	10
60.8%	26%	13.1%	11
63.8%	21%	15.2%	12
65.1%	17.8%	17%	13
67.7%	13.9%	18.4%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.8s (32%)

Results

1.0s	5645×	body	128	valid
834.0ms	1094×	body	2048	valid
373.0ms	667×	body	1024	valid
320.0ms	365×	body	4096	valid
157.0ms	321×	body	512	valid
138.0ms	801×	body	128	invalid
48.0ms	164×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (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

28.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.8b	(/.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)

localize8.0ms (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 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series200.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
45.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
10.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite31.0ms (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:

9.0ms	(/.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))

simplify385.0ms (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	5568
1	683	4769
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune430.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	11	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	11	238

Error

4.1b

Counts

238 → 11

Alt Table

Status	Error	Program
	28.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.6b	(/.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)
	47.1b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) (sqrt.f64 a)))
	41.4b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	41.4b	(/.f64 (*.f64 -2 b_2) a)
	45.0b	(.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)))
	33.1b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.4b	(*.f64 -1/2 (/.f64 c b_2))
▶	27.9b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	28.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	28.8b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Compiler

Compiled 5959 to 1712 computations (71.3% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
✓	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	12.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series813.0ms (6.9%)

Counts

3 → 24

Calls

3 calls:

479.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
301.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
33.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

3 → 88

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
6.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
3.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify165.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-def_binary64`
428×	`fma-neg_binary64`
291×	`cancel-sign-sub-inv_binary64`
277×	`div-sub_binary64`
219×	`associate-/r/_binary64`

Counts

112 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3125
1	530	2608
2	1783	2484
3	4376	2480
4	5049	2480

prune176.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	143	10	153

Error

0.3b

Counts

153 → 10

Alt Table

Status	Error	Program
	28.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.6b	(/.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)
▶	28.0b	(.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) (/.f64 1 a))
	41.4b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.4b	(*.f64 -1/2 (/.f64 c b_2))
	28.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	47.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	44.8b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	45.0b	(.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)))
	28.0b	(/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)

Compiler

Compiled 3792 to 1131 computations (70.2% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) (/.f64 1 a))
	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	12.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series394.0ms (3.4%)

Counts

1 → 12

Calls

1 calls:

393.0ms

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

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 44

Calls

1 calls:

16.0ms

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

simplify147.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

532×	`times-frac_binary64`
423×	`fma-neg_binary64`
333×	`associate-r_binary64`
326×	`associate-l_binary64`
326×	`associate-/l*_binary64`

Counts

56 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1627
1	367	1456
2	1120	1421
3	4740	1421
4	5036	1421

prune127.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	162	12	174

Error

0.3b

Counts

174 → 12

Alt Table

Status	Error	Program
▶	28.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.6b	(/.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)
✓	28.0b	(.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2) (/.f64 1 a))
	41.4b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	47.4b	(.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (/.f64 1 a))
	42.4b	(*.f64 -1/2 (/.f64 c b_2))
	48.1b	(/.f64 (.f64 (.f64 c a) -1/2) (*.f64 a b_2))
	28.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	47.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	44.8b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	45.0b	(.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)))
	28.0b	(/.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2) b_2) a)

Compiler

Compiled 4510 to 1556 computations (65.5% 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)))
	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
	12.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.1s (9.5%)

Counts

2 → 24

Calls

2 calls:

788.0ms	(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
321.0ms	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 149

Calls

2 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))

simplify240.0ms (2%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-/l*_binary64`
605×	`associate-/r*_binary64`
347×	`fma-def_binary64`
338×	`associate-/r/_binary64`
162×	`associate-/l/_binary64`

Counts

173 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	5993
1	561	5467
2	1768	5322
3	5166	5322

prune237.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	2	8	10
Picked	0	1	1
Done	1	0	1
Total	299	10	309

Error

0.3b

Counts

309 → 10

Alt Table

Status	Error	Program
✓	28.0b	(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.6b	(/.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)
	47.4b	(.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (/.f64 1 a))
	41.4b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.4b	(*.f64 -1/2 (/.f64 c b_2))
	48.1b	(/.f64 (.f64 (.f64 c a) -1/2) (*.f64 a b_2))
	28.1b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	47.4b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a)
	44.8b	(/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a)
	45.0b	(.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)))

Compiler

Compiled 8244 to 2306 computations (72% saved)

regimes2.6s (22.5%)

Accuracy

Total 8.7b remaining (97.1%)

Threshold costs 0b (0%)

Counts

150 → 3

Compiler

Compiled 12580 to 7338 computations (41.7% saved)

bsearch77.0ms (0.7%)

Steps

Iters	Range		Point
5	6.177578211779319e-36	1.2451145877205563e-35	6.272367677451717e-36
6	-2.728471400924003e+154	-2.3529362758860427e+153	-2.4002508252193456e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	51
1	38	51
2	49	51
3	56	51
4	59	51
5	59	51

end150.0ms (1.3%)

Compiler: Compiled 243 to 149 computations (38.7% saved)

Details

analyze380.0ms (3.2%)

sample3.8s (32%)

simplify118.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series200.0ms (1.7%)

rewrite31.0ms (0.3%)

simplify385.0ms (3.3%)

prune430.0ms (3.7%)

localize16.0ms (0.1%)

series813.0ms (6.9%)

rewrite29.0ms (0.2%)

simplify165.0ms (1.4%)

prune176.0ms (1.5%)

localize17.0ms (0.1%)

series394.0ms (3.4%)

rewrite24.0ms (0.2%)

simplify147.0ms (1.3%)

prune127.0ms (1.1%)

localize9.0ms (0.1%)

series1.1s (9.5%)

rewrite46.0ms (0.4%)

simplify240.0ms (2%)

prune237.0ms (2%)

regimes2.6s (22.5%)

bsearch77.0ms (0.7%)

simplify9.0ms (0.1%)

end150.0ms (1.3%)

Profiling