Details

analyze107.0ms (3.1%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample959.0ms (27.5%)

Results

947.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess31.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

931×	`fma-def_binary64`
495×	`fma-neg_binary64`
420×	`associate-+l+_binary64`
334×	`associate-+r+_binary64`
241×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	48	42
2	99	42
3	288	42
4	1136	34
5	3734	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
603×	`associate-l_binary64`
311×	`fma-neg_binary64`
233×	`associate-+l+_binary64`
216×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	64	21
3	193	21
4	779	17
5	2634	17

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series69.0ms (2%)

Counts

3 → 72

Calls

18 calls:

8.0ms	(pow.f64 (hypot.f64 a b) 4)	a	0
6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	0
6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	b	inf
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	-inf
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	inf

rewrite54.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
243×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	212	28
2	2603	28

Stop Event

1×	node limit

Counts

3 → 93

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
306×	`fma-def_binary64`
224×	`distribute-neg-frac_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	1453
1	219	1409
2	691	1303
3	3004	1303

Stop Event

1×	node limit

Counts

165 → 143

prune159.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 2928 to 1918 computations (34.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1))
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
✓	0.0b	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)
✓	0.1b	(.f64 b (fma.f64 2 (.f64 a a) 4))

series71.0ms (2%)

Counts

4 → 96

Calls

24 calls:

7.0ms	(+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1))	b	-inf
5.0ms	(.f64 b (fma.f64 2 (.f64 a a) 4))	b	-inf
4.0ms	(+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1))	b	inf
4.0ms	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))	a	inf
4.0ms	(fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)	b	-inf

rewrite85.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`fma-def_binary64`
273×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
163×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	74
1	303	74
2	3874	74

Stop Event

1×	node limit

Counts

4 → 163

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-neg_binary64`
400×	`unswap-sqr_binary64`
399×	`associate-l_binary64`
342×	`distribute-rgt-neg-in_binary64`
316×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	1854
1	89	1576
2	232	1474
3	840	1474
4	2359	1474

Stop Event

1×	node limit

Counts

259 → 194

prune197.0ms (5.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	194	3	197

Error

Counts

197 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 5302 to 3480 computations (34.4% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 a a))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

series38.0ms (1.1%)

Counts

3 → 60

Calls

15 calls:

6.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))	a	0
6.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))	b	0
3.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))	b	-inf
3.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))	b	0
3.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))	b	inf

rewrite71.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

943×	`prod-diff_binary64`
144×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`
139×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	309	59
2	3678	59

Stop Event

1×	node limit

Counts

3 → 71

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

965×	`fma-def_binary64`
744×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
347×	`associate-l_binary64`
319×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	1067
1	73	1023
2	213	933
3	837	907
4	3016	907

Stop Event

1×	node limit

Counts

131 → 93

prune92.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 2869 to 1642 computations (42.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(.f64 4 (.f64 b b))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series40.0ms (1.1%)

Counts

4 → 84

Calls

21 calls:

5.0ms	(+.f64 (.f64 a a) (.f64 b b))	b	inf
3.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)	a	0
3.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)	a	inf
3.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)	a	-inf
3.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)	b	0

rewrite85.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

647×	`fma-def_binary64`
362×	`fma-neg_binary64`
226×	`log1p-udef_binary64`
225×	`expm1-udef_binary64`
177×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	289	43
2	3780	43

Stop Event

1×	node limit

Counts

4 → 177

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
730×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
326×	`associate-l_binary64`
306×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	1271
1	74	1191
2	217	1101
3	821	1075
4	2988	1075

Stop Event

1×	node limit

Counts

261 → 204

prune189.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Error

Counts

207 → 3

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (fma.f64 b (.f64 b (fma.f64 2 (.f64 a a) 4)) -1)))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 4499 to 2813 computations (37.5% saved)

regimes866.0ms (24.8%)

Accuracy

Total 0.0b remaining (62.7%)

Threshold costs 0.0b (62.7%)

Counts

157 → 1

Compiler

Compiled 16353 to 12133 computations (25.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	17	27

Stop Event

1×

saturated

end107.0ms (3.1%)

Stop Event

1×

done

Compiler

Compiled 106 to 72 computations (32.1% saved)

Details

analyze107.0ms (3.1%)

sample959.0ms (27.5%)

preprocess31.0ms (0.9%)

simplify22.0ms (0.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series69.0ms (2%)

rewrite54.0ms (1.5%)

simplify48.0ms (1.4%)

prune159.0ms (4.6%)

localize11.0ms (0.3%)

series71.0ms (2%)

rewrite85.0ms (2.4%)

simplify58.0ms (1.7%)

prune197.0ms (5.6%)

localize12.0ms (0.3%)

series38.0ms (1.1%)

rewrite71.0ms (2%)

simplify45.0ms (1.3%)

prune92.0ms (2.6%)

localize8.0ms (0.2%)

series40.0ms (1.1%)

rewrite85.0ms (2.4%)

simplify53.0ms (1.5%)

prune189.0ms (5.4%)

regimes866.0ms (24.8%)

simplify2.0ms (0.1%)

end107.0ms (3.1%)

Profiling