Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (49.3%)

Results

656.0ms	2095×	body	1024	valid
451.0ms	4399×	body	128	valid
248.0ms	1001×	body	512	valid
88.0ms	536×	body	256	valid
87.0ms	225×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify101.0ms (3%)

Algorithm

1×	egg-herbie

Rules

742×	`rules-20_binary64`
268×	`rules-21_binary64`
249×	`fma-neg_binary64`
191×	`rules-6-rev_binary64`
173×	`rules-5-rev_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	20	19
2	46	19
3	145	19
4	689	19
5	3220	19
6	4628	19
7	4965	19
8	4918	19

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	4.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite102.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

858×	`prod-diff_binary64`
839×	`fma-neg_binary64`
168×	`egg-rr`
156×	`expm1-udef_binary64`
156×	`log1p-udef_binary64`

Counts

3 → 168

Calls

3 calls:

97.0ms	(/.f64 x (+.f64 x 1))
97.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
97.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	198	36
2	2703	36
3	5207	36
0	0	0
1	0	0

simplify78.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

629×	`rules-21_binary64`
404×	`rules-10-rev_binary64`
378×	`fma-def_binary64`
338×	`rules-13_binary64`
225×	`rules-14-rev_binary64`

Counts

204 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	475
1	249	452
2	980	389
3	3574	375
4	4714	375
5	5045	375

prune168.0ms (5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	3	208

Error

0.0b

Counts

208 → 3

Alt Table

Status	Error	Program
▶	30.4b	(fma.f64 x (+.f64 3 x) 1)
	33.2b	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
	33.3b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 5398 to 4002 computations (25.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 3 x) 1)

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 x (+.f64 3 x) 1)

rewrite110.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

558×	`log1p-expm1-u_binary64`
558×	`expm1-log1p-u_binary64`
440×	`fma-neg_binary64`
286×	`fma-def_binary64`
170×	`fma-udef_binary64`

Counts

1 → 30

Calls

1 calls:

110.0ms

(fma.f64 x (+.f64 3 x) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	139	8
2	1606	8
3	4947	8
4	4914	8
5	4912	8
0	0	0
1	0	0

simplify79.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

650×	`rules-20_binary64`
644×	`fma-neg_binary64`
365×	`rules-15-rev_binary64`
276×	`rules-4_binary64`
199×	`fma-def_binary64`

Counts

42 → 39

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	114
1	27	82
2	72	76
3	182	76
4	466	76
5	2045	76
6	4537	76
7	4994	76
8	5068	76

prune19.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Error

0.0b

Counts

42 → 3

Alt Table

Status	Error	Program
✓	30.4b	(fma.f64 x (+.f64 3 x) 1)
▶	33.2b	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
	33.3b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 476 to 365 computations (23.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3)))
✓	0.3b	(/.f64 1 (pow.f64 x 4))
✓	4.6b	(/.f64 (+.f64 3 x) (pow.f64 x 3))
✓	10.3b	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))

series12.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

3.0ms	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
3.0ms	(/.f64 (+.f64 3 x) (pow.f64 x 3))
3.0ms	(-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3)))
3.0ms	(/.f64 1 (pow.f64 x 4))

rewrite96.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
152×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`

Counts

4 → 152

Calls

4 calls:

93.0ms	(-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3)))
93.0ms	(/.f64 1 (pow.f64 x 4))
93.0ms	(/.f64 (+.f64 3 x) (pow.f64 x 3))
93.0ms	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	347	56
2	4394	56
3	4997	56
0	0	0
1	0	0

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-neg_binary64`
694×	`rules-14-rev_binary64`
594×	`fma-def_binary64`
393×	`rules-20_binary64`
343×	`rules-15-rev_binary64`

Counts

188 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	609
1	91	609
2	299	609
3	1657	433
4	4442	433
5	5090	433

prune145.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Error

0.0b

Counts

175 → 4

Alt Table

Status	Error	Program
✓	30.4b	(fma.f64 x (+.f64 3 x) 1)
	33.8b	(*.f64 (cbrt.f64 (-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (pow.f64 x -4))) (pow.f64 (cbrt.f64 (-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (pow.f64 x -4))) 2))
✓	33.2b	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
▶	33.3b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 4354 to 3423 computations (21.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (pow.f64 x 3))
✓	0.5b	(/.f64 1 (pow.f64 x 2))
✓	6.8b	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
✓	8.2b	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))

series13.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
3.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
3.0ms	(/.f64 1 (pow.f64 x 3))
2.0ms	(/.f64 1 (pow.f64 x 2))

rewrite95.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

296×	`log1p-udef_binary64`
188×	`prod-diff_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
172×	`add-sqr-sqrt_binary64`

Counts

4 → 151

Calls

4 calls:

93.0ms	(/.f64 1 (pow.f64 x 3))
93.0ms	(/.f64 1 (pow.f64 x 2))
93.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
93.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	42
1	459	42
2	4555	42
3	5245	42
0	0	0
1	0	0

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Rules

331×	`rules-21_binary64`
321×	`rules-15-rev_binary64`
315×	`rules-13_binary64`
304×	`fma-def_binary64`
301×	`rules-14-rev_binary64`

Counts

163 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	147
1	57	147
2	190	147
3	783	123
4	3010	123
5	4654	123
6	5071	123

prune157.0ms (4.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	164	4	168

Error

0.0b

Counts

168 → 4

Alt Table

Status	Error	Program
✓	30.4b	(fma.f64 x (+.f64 3 x) 1)
	55.4b	(neg.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 x -4) (+.f64 (/.f64 3 x) (fma.f64 3 (pow.f64 x -3) (pow.f64 x -2)))) 3) 1/3))
✓	33.2b	(-.f64 (-.f64 (neg.f64 (/.f64 3 x)) (/.f64 (+.f64 3 x) (pow.f64 x 3))) (/.f64 1 (pow.f64 x 4)))
✓	33.3b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))

Compiler

Compiled 4599 to 3749 computations (18.5% saved)

regimes240.0ms (7.2%)

Accuracy

Total 0.5b remaining (55.3%)

Threshold costs 0.5b (55.3%)

Counts

72 → 2

Compiler

Compiled 2968 to 2392 computations (19.4% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	58
1	26	58
2	25	58

end93.0ms (2.8%)

Compiler: Compiled 155 to 121 computations (21.9% saved)

Details

analyze6.0ms (0.2%)

sample1.7s (49.3%)

simplify101.0ms (3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite102.0ms (3%)

simplify78.0ms (2.3%)

prune168.0ms (5%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite110.0ms (3.3%)

simplify79.0ms (2.3%)

prune19.0ms (0.6%)

localize11.0ms (0.3%)

series12.0ms (0.4%)

rewrite96.0ms (2.9%)

simplify59.0ms (1.8%)

prune145.0ms (4.3%)

localize15.0ms (0.5%)

series13.0ms (0.4%)

rewrite95.0ms (2.8%)

simplify68.0ms (2%)

prune157.0ms (4.7%)

regimes240.0ms (7.2%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end93.0ms (2.8%)

Profiling