Details

analyze112.0ms (4.8%)

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
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)

sample957.0ms (41.1%)

Results

910.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify20.0ms (0.8%)

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

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 59 to 40 computations (32.2% saved)

localize7.0ms (0.3%)

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)

series62.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
24.0ms	(pow.f64 (hypot.f64 a b) 4)
8.0ms	(hypot.f64 a b)

rewrite67.0ms (2.9%)

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

Calls

3 calls:

65.0ms	(hypot.f64 a b)
65.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
65.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify44.0ms (1.9%)

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

prune115.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
	13.8b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1)))
▶	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2894 to 1898 computations (34.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (fma.f64 b b 4))
✓	0.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
3.0ms	(*.f64 b (fma.f64 b b 4))

rewrite37.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
280×	`log-prod_binary64`
167×	`pow2_binary64`
118×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	137	20
2	1516	20

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

36.0ms	(*.f64 b (fma.f64 b b 4))
36.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

484×	`distribute-rgt-neg-in_binary64`
457×	`associate-l_binary64`
448×	`distribute-lft-neg-in_binary64`
340×	`associate-r_binary64`
272×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	207
1	43	207
2	83	195
3	171	195
4	500	195
5	2376	195

Stop Event

1×	node limit

Counts

90 → 78

prune56.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
▶	13.8b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1)))
✓	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1099 to 708 computations (35.6% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(pow.f64 (hypot.f64 a b) 8)
✓	0.1b	(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)
✓	12.9b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1)))

series147.0ms (6.3%)

Counts

3 → 60

Calls

3 calls:

125.0ms

(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

20.0ms

(pow.f64 (hypot.f64 a b) 8)

3.0ms

(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)

rewrite67.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
161×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	57
1	354	35
2	4546	35

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

65.0ms

(pow.f64 (hypot.f64 a b) 8)

65.0ms

(pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)

65.0ms

(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (*.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

simplify67.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

549×	`associate-+r+_binary64`
446×	`fma-def_binary64`
319×	`associate-+l+_binary64`
318×	`times-frac_binary64`
292×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	347	4382
1	1185	4310

Stop Event

1×	node limit

Counts

144 → 130

prune222.0ms (9.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	154	3	157

Error

Counts

157 → 3

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (pow.f64 (fma.f64 b (.f64 b 4) -1) 2)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1)))
✓	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 8774 to 6387 computations (27.2% saved)

regimes230.0ms (9.9%)

Accuracy

Total 0.0b remaining (47%)

Threshold costs 0.0b (47%)

Counts

38 → 1

Compiler

Compiled 4172 to 3038 computations (27.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17

Stop Event

1×

saturated

end68.0ms (2.9%)

Compiler: Compiled 82 to 57 computations (30.5% saved)

Details

analyze112.0ms (4.8%)

sample957.0ms (41.1%)

simplify20.0ms (0.8%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series62.0ms (2.7%)

rewrite67.0ms (2.9%)

simplify44.0ms (1.9%)

prune115.0ms (4.9%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite37.0ms (1.6%)

simplify24.0ms (1%)

prune56.0ms (2.4%)

localize13.0ms (0.6%)

series147.0ms (6.3%)

rewrite67.0ms (2.9%)

simplify67.0ms (2.9%)

prune222.0ms (9.5%)

regimes230.0ms (9.9%)

simplify2.0ms (0.1%)

end68.0ms (2.9%)

Profiling