Details

analyze397.0ms (7.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.3s (66.7%)

Results

1.6s	2607×	body	1024	valid
760.0ms	1272×	body	2048	valid
525.0ms	1266×	body	512	valid
279.0ms	2445×	body	128	valid
146.0ms	621×	body	256	valid
34.0ms	45×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

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

47.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	47.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(+.f64 x (hypot.f64 1 x))
✓	4.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
2.0ms	(+.f64 x (hypot.f64 1 x))

rewrite109.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
347×	`fma-udef_binary64`
185×	`fma-def_binary64`

Counts

2 → 67

Calls

2 calls:

107.0ms	(+.f64 x (hypot.f64 1 x))
107.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	120	16
2	1436	16
3	4831	16
4	4804	16
5	4976	16
0	0	0
1	0	0

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
387×	`associate-l_binary64`
364×	`cancel-sign-sub-inv_binary64`
308×	`associate-r_binary64`

Counts

91 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	411
1	253	397
2	680	391
3	1945	391
4	4405	391
5	4908	391

prune63.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
▶	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.5b	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))
	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))

Compiler

Compiled 1555 to 1158 computations (25.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

rewrite107.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
281×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
208×	`prod-diff_binary64`

Counts

1 → 36

Calls

1 calls:

106.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	126	8
2	1280	8
3	4889	8
4	5010	8
0	0	0
1	0	0

simplify167.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1705×	`fma-def_binary64`
865×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
615×	`sqr-pow_binary64`
528×	`cube-prod_binary64`

Counts

48 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	59	87
3	147	87
4	298	87
5	774	87
6	1120	87
7	1710	87
8	3217	87
9	4164	87
10	4277	87
11	4261	87
12	4044	87
13	3304	87
14	3939	87
15	4360	87
16	4810	87
17	4770	87

prune23.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Error

0.0b

Counts

46 → 5

Alt Table

Status	Error	Program
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
	47.5b	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))
▶	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))

Compiler

Compiled 591 to 452 computations (23.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
✓	0.3b	(/.f64 1/8 (pow.f64 x 3))
✓	11.9b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series13.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

7.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite70.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`prod-diff_binary64`
193×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Counts

3 → 104

Calls

3 calls:

69.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
69.0ms	(/.f64 1/8 (pow.f64 x 3))
69.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	230	31
2	2886	31
3	4884	31
0	0	0
1	0	0

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-neg_binary64`
732×	`fma-def_binary64`
685×	`times-frac_binary64`
524×	`cancel-sign-sub-inv_binary64`
387×	`associate-l_binary64`

Counts

128 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	410
1	180	402
2	497	400
3	1626	396
4	4148	396
5	5672	396

prune69.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Error

0.0b

Counts

136 → 5

Alt Table

Status	Error	Program
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	47.5b	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))
✓	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))

Compiler

Compiled 2218 to 1756 computations (20.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 x 1 (hypot.f64 1 x))
✓	4.0b	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))
2.0ms	(fma.f64 x 1 (hypot.f64 1 x))

rewrite81.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

790×	`log1p-udef_binary64`
430×	`log1p-expm1-u_binary64`
430×	`expm1-log1p-u_binary64`
302×	`prod-diff_binary64`
270×	`unpow-prod-down_binary64`

Counts

2 → 93

Calls

2 calls:

79.0ms	(fma.f64 x 1 (hypot.f64 1 x))
79.0ms	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	110	16
2	1129	16
3	4634	16
4	6296	16
0	0	0
1	0	0

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-neg_binary64`
426×	`associate-/r*_binary64`
387×	`associate-l_binary64`
364×	`cancel-sign-sub-inv_binary64`
308×	`associate-r_binary64`

Counts

117 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	411
1	253	397
2	680	391
3	1945	391
4	4405	391
5	4908	391

prune123.0ms (2.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))
✓	30.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	47.5b	(log.f64 (fma.f64 x 1 (hypot.f64 1 x)))
✓	46.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	60.1b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))

Compiler

Compiled 2034 to 1564 computations (23.1% saved)

regimes118.0ms (2.3%)

Accuracy

Total 0.1b remaining (84.4%)

Threshold costs 0.1b (84.4%)

Counts

32 → 3

Compiler

Compiled 972 to 742 computations (23.7% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
8	2.861332380623058e-6	0.021286450759173393	0.0010906364138287723
9	-4.83044265941669	-9.161204285302546e-6	-1.0730541910957112

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	27	42
2	26	42

end85.0ms (1.7%)

Compiler: Compiled 111 to 81 computations (27% saved)

Details

analyze397.0ms (7.9%)

sample3.3s (66.7%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite109.0ms (2.2%)

simplify57.0ms (1.1%)

prune63.0ms (1.3%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite107.0ms (2.1%)

simplify167.0ms (3.3%)

prune23.0ms (0.5%)

localize7.0ms (0.1%)

series13.0ms (0.3%)

rewrite70.0ms (1.4%)

simplify52.0ms (1%)

prune69.0ms (1.4%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite81.0ms (1.6%)

simplify57.0ms (1.1%)

prune123.0ms (2.5%)

regimes118.0ms (2.3%)

bsearch36.0ms (0.7%)

simplify2.0ms (0%)

end85.0ms (1.7%)

Profiling