Details

analyze668.0ms (7.2%)

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
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)

sample2.7s (28.5%)

Results

749.0ms	5383×	body	128	valid
541.0ms	1178×	body	2048	valid
284.0ms	757×	body	1024	valid
210.0ms	381×	body	4096	valid
120.0ms	1047×	body	128	invalid
118.0ms	390×	body	512	valid
33.0ms	167×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify82.0ms (0.9%)

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

34.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.3b	(/.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
✓	0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series160.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

85.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
37.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
29.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite106.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
317×	`egg-rr`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Counts

4 → 317

Calls

4 calls:

97.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
97.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
97.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
97.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	234	55
2	3299	55
3	4945	55
0	0	0
1	0	0

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
493×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
361×	`fma-def_binary64`
191×	`associate-*l/_binary64`

Counts

413 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	388	2175
2	1292	2133
3	4966	2133

prune341.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	376	9	385
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	377	9	386

Error

7.2b

Counts

386 → 9

Alt Table

Status	Error	Program
	40.6b	(*.f64 -1/2 (/.f64 c b_2))
	34.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	47.3b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	44.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	46.5b	(*.f64 -2 (/.f64 b_2 a))
▶	34.3b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	35.3b	(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2) a)
	46.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	57.4b	(/.f64 (-.f64 b_2 b_2) a)

Compiler

Compiled 9490 to 2842 computations (70.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
✓	1.2b	(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
✓	23.1b	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
✓	52.7b	(fma.f64 a (neg.f64 c) (*.f64 a c))

series146.0ms (1.6%)

Counts

4 → 100

Calls

4 calls:

69.0ms	(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
37.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
33.0ms	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
8.0ms	(fma.f64 a (neg.f64 c) (*.f64 a c))

rewrite103.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
367×	`fma-def_binary64`
217×	`fma-neg_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`

Counts

4 → 193

Calls

4 calls:

98.0ms	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
98.0ms	(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
98.0ms	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
98.0ms	(fma.f64 a (neg.f64 c) (*.f64 a c))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	77
1	232	57
2	2634	57
3	5002	57
0	0	0
1	0	0

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

447×	`unswap-sqr_binary64`
416×	`times-frac_binary64`
278×	`associate-/l*_binary64`
268×	`associate-r_binary64`
235×	`associate-/r*_binary64`

Counts

293 → 242

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	1573
1	269	1557
2	817	1533
3	4011	1533
4	4916	1500
5	4956	1500

prune119.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	241	10	251

Error

7.2b

Counts

251 → 10

Alt Table

Status	Error	Program
	40.6b	(*.f64 -1/2 (/.f64 c b_2))
▶	34.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	47.3b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	50.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (*.f64 a (+.f64 c c))))) b_2))) a)
	44.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	46.5b	(*.f64 -2 (/.f64 b_2 a))
✓	34.3b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	35.3b	(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2) a)
	46.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	57.4b	(/.f64 (-.f64 b_2 b_2) a)

Compiler

Compiled 6374 to 1816 computations (71.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series52.0ms (0.6%)

Counts

1 → 20

Calls

1 calls:

52.0ms

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

rewrite57.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

699×	`fma-def_binary64`
320×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`

Counts

1 → 43

Calls

1 calls:

55.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	267	18
2	3403	18
3	5037	18
0	0	0
1	0	0

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
217×	`associate-r_binary64`

Counts

63 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	204	642
2	668	624
3	3419	624
4	4941	624

prune254.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	381	10	391

Error

7.2b

Counts

391 → 10

Alt Table

Status	Error	Program
	40.6b	(*.f64 -1/2 (/.f64 c b_2))
✓	34.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	47.3b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	50.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (*.f64 a (+.f64 c c))))) b_2))) a)
	44.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	46.5b	(*.f64 -2 (/.f64 b_2 a))
✓	34.3b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
▶	35.3b	(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2) a)
	46.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	57.4b	(/.f64 (-.f64 b_2 b_2) a)

Compiler

Compiled 10017 to 3495 computations (65.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	11.9b	(-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2)
✓	23.8b	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)

series189.0ms (2%)

Counts

3 → 92

Calls

3 calls:

85.0ms	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)
65.0ms	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
39.0ms	(-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2)

rewrite101.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

642×	`fma-def_binary64`
278×	`fma-neg_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
143×	`egg-rr`

Counts

3 → 143

Calls

3 calls:

97.0ms	(pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)
97.0ms	(-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2)
97.0ms	(pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	278	40
2	3203	38
3	4997	38
4	4889	38
0	0	0
1	0	0

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

286×	`times-frac_binary64`
268×	`associate-/r*_binary64`
262×	`sub-neg_binary64`
261×	`fma-neg_binary64`
237×	`associate-r_binary64`

Counts

235 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	329	4384
1	1073	4294
2	4324	4282
3	4980	4282

prune445.0ms (4.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	431	2	433
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	434	9	443

Error

0.8b

Counts

443 → 9

Alt Table

Status	Error	Program
	40.6b	(*.f64 -1/2 (/.f64 c b_2))
✓	34.4b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	47.3b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
	44.0b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) a)
	51.3b	(/.f64 (-.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 a) (log.f64 (/.f64 -1 c))))) 2) b_2) a)
✓	34.3b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
✓	35.3b	(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2) a)
	52.3b	(/.f64 (-.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 c) (log.f64 (/.f64 -1 a))))) 2) b_2) a)
	46.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))

Compiler

Compiled 13222 to 5789 computations (56.2% saved)

regimes3.2s (34.9%)

Accuracy

Total 9.3b remaining (91.9%)

Threshold costs 0b (0%)

Counts

196 → 3

Compiler

Compiled 14628 to 9314 computations (36.3% saved)

bsearch91.0ms (1%)

Steps

Iters	Range		Point
10	2.2479505088929644e-82	9.94413970509067e-64	1.5940605920453892e-74
9	-4.700315450940392e+155	-1.5253663957040454e+147	-2.9158395222175973e+150

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	61
1	36	61
2	41	61
3	44	61
4	45	61
5	45	61

end125.0ms (1.3%)

Compiler: Compiled 244 to 149 computations (38.9% saved)

Details

analyze668.0ms (7.2%)

sample2.7s (28.5%)

simplify82.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series160.0ms (1.7%)

rewrite106.0ms (1.1%)

simplify69.0ms (0.7%)

prune341.0ms (3.7%)

localize13.0ms (0.1%)

series146.0ms (1.6%)

rewrite103.0ms (1.1%)

simplify88.0ms (0.9%)

prune119.0ms (1.3%)

localize8.0ms (0.1%)

series52.0ms (0.6%)

rewrite57.0ms (0.6%)

simplify44.0ms (0.5%)

prune254.0ms (2.7%)

localize24.0ms (0.3%)

series189.0ms (2%)

rewrite101.0ms (1.1%)

simplify106.0ms (1.1%)

prune445.0ms (4.8%)

regimes3.2s (34.9%)

bsearch91.0ms (1%)

simplify3.0ms (0%)

end125.0ms (1.3%)

Profiling