Details

analyze113.0ms (6.4%)

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%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample774.0ms (43.8%)

Results

762.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess18.0ms (1%)

Algorithm

2×	egg-herbie

Rules

26×	`fma-def_binary64`
10×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	22
2	62	22
3	76	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	34	11
3	42	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.2%)

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
	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 67 to 39 computations (41.8% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 x (+.f64 x 2) (*.f64 y y))	y	-inf
1.0ms	(fma.f64 x (+.f64 x 2) (*.f64 y y))	y	inf
1.0ms	(fma.f64 x (+.f64 x 2) (*.f64 y y))	y	0
1.0ms	(fma.f64 x (+.f64 x 2) (*.f64 y y))	x	-inf
1.0ms	(fma.f64 x (+.f64 x 2) (*.f64 y y))	x	0

rewrite34.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
176×	`prod-diff_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1849	11

Stop Event

1×	node limit

Counts

1 → 23

simplify58.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
502×	`fma-def_binary64`
422×	`associate-l_binary64`
288×	`cube-prod_binary64`
285×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	300
1	24	214
2	54	214
3	89	214
4	190	214
5	472	214
6	1645	214
7	2318	214
8	2638	214
9	2898	214
10	3237	214
11	3719	214
12	4378	214

Stop Event

1×	node limit

Counts

47 → 33

prune22.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Error

Counts

35 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
	27.7b	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 x 2)) (.f64 x (+.f64 x 2))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (*.f64 y y)))
	16.6b	(fma.f64 y y (*.f64 2 x))
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 480 to 274 computations (42.9% saved)

localize10.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x 2) (.f64 x x))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

series9.0ms (0.5%)

Counts

2 → 36

Calls

9 calls:

1.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))	y	-inf
1.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))	y	inf
1.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))	y	0
1.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))	x	-inf
1.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))	x	0

rewrite61.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`fma-def_binary64`
467×	`log-prod_binary64`
280×	`fma-neg_binary64`
177×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	18
2	2846	18

Stop Event

1×	node limit

Counts

2 → 157

simplify97.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
502×	`fma-def_binary64`
422×	`associate-l_binary64`
288×	`cube-prod_binary64`
285×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	402
1	24	289
2	54	289
3	89	289
4	190	289
5	472	289
6	1645	289
7	2318	289
8	2638	289
9	2898	289
10	3237	289
11	3719	289
12	4378	289

Stop Event

1×	node limit

Counts

193 → 168

prune138.0ms (7.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	169	3	172

Error

Counts

172 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 2581 to 1173 computations (54.6% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))
✓	0.0b	(*.f64 x (+.f64 x 2))

series8.0ms (0.5%)

Counts

2 → 36

Calls

9 calls:

1.0ms	(fma.f64 y y (*.f64 x (+.f64 x 2)))	y	inf
1.0ms	(fma.f64 y y (*.f64 x (+.f64 x 2)))	y	-inf
1.0ms	(fma.f64 y y (*.f64 x (+.f64 x 2)))	y	0
1.0ms	(fma.f64 y y (*.f64 x (+.f64 x 2)))	x	-inf
1.0ms	(fma.f64 y y (*.f64 x (+.f64 x 2)))	x	inf

rewrite45.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`log1p-expm1-u_binary64`
728×	`expm1-log1p-u_binary64`
219×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	153	18
2	1939	18

Stop Event

1×	node limit

Counts

2 → 49

simplify64.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
502×	`fma-def_binary64`
413×	`associate-l_binary64`
298×	`associate-r_binary64`
288×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	402
1	24	289
2	54	289
3	89	289
4	189	289
5	480	289
6	1631	289
7	2307	289
8	2627	289
9	2887	289
10	3230	289
11	3714	289
12	4373	289

Stop Event

1×	node limit

Counts

85 → 60

prune36.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	60	3	63

Error

Counts

63 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 772 to 448 computations (42% saved)

regimes203.0ms (11.5%)

Accuracy

Total 0.0b remaining (60%)

Threshold costs 0.0b (60%)

Counts

29 → 1

Compiler

Compiled 1988 to 1224 computations (38.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	8	12

Stop Event

1×

saturated

end48.0ms (2.7%)

Stop Event

1×

done

Compiler

Compiled 55 to 32 computations (41.8% saved)

Details

analyze113.0ms (6.4%)

sample774.0ms (43.8%)

preprocess18.0ms (1%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite34.0ms (1.9%)

simplify58.0ms (3.3%)

prune22.0ms (1.2%)

localize10.0ms (0.6%)

series9.0ms (0.5%)

rewrite61.0ms (3.5%)

simplify97.0ms (5.5%)

prune138.0ms (7.8%)

localize5.0ms (0.3%)

series8.0ms (0.5%)

rewrite45.0ms (2.5%)

simplify64.0ms (3.6%)

prune36.0ms (2.1%)

regimes203.0ms (11.5%)

simplify2.0ms (0.1%)

end48.0ms (2.7%)

Profiling