Details

analyze64.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.2s (24%)

Results

903.0ms	8256×	body	128	valid
5.0ms	46×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify132.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series24.0ms (0.5%)

Counts

3 → 56

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite237.0ms (4.6%)

Algorithm

3×	egg-rewrite

Rules

63×	`egg`
58×	`egg`
39×	`egg`

Counts

3 → 160

Calls

3 calls:

96.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
86.0ms	(*.f64 m (-.f64 1 m))
53.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	201	16
2	2716	14
3	4997	14
4	5369	14
0	7	10
1	150	10
2	2027	10
3	5305	10
0	5	7
1	103	7
2	1237	7
3	4917	7
4	5441	7

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

577×	`unsub-neg_binary64`
458×	`fma-def_binary64`
426×	`associate-/l*_binary64`
379×	`fma-neg_binary64`
318×	`div-sub_binary64`

Counts

216 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	638
1	66	584
2	135	584
3	341	584
4	1077	584
5	3918	584
6	4987	584

prune161.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	178	6	184

Error

0.0b

Counts

184 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (-.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) 1) m)
	0.8b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 2) (.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) m))
▶	0.1b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	38.2b	(.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) (.f64 (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) m))
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 3075 to 1931 computations (37.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m)

series30.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m)
14.0ms	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))

rewrite162.0ms (3.1%)

Algorithm

2×	egg-rewrite

Rules

110×	`egg`
52×	`egg`

Counts

2 → 162

Calls

2 calls:

91.0ms	(.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m)
68.0ms	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	172	13
2	2340	13
3	4978	13
4	5327	13
0	10	16
1	225	12
2	2748	12
3	5234	12

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary64`
621×	`unsub-neg_binary64`
320×	`div-sub_binary64`
294×	`distribute-rgt-in_binary64`
284×	`associate-/r/_binary64`

Counts

210 → 175

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	614
1	62	614
2	149	614
3	416	614
4	1407	614
5	4198	614
6	5101	614

prune251.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	308	6	314

Error

Counts

314 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))
▶	0.3b	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
	6.2b	(+.f64 (/.f64 (*.f64 (pow.f64 m 2) (-.f64 1 m)) v) (neg.f64 m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	0.3b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (/.f64 m (sqrt.f64 v))) (neg.f64 m))
	0.8b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 2) (.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) m))

Compiler

Compiled 5457 to 2279 computations (58.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
✓	0.2b	(.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m)
✓	0.2b	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
✓	0.3b	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

series115.0ms (2.2%)

Counts

4 → 72

Calls

4 calls:

37.0ms	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
28.0ms	(.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m)
28.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
21.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))

rewrite312.0ms (6.1%)

Algorithm

4×	egg-rewrite

Rules

107×	`egg`
81×	`egg`
58×	`egg`
51×	`egg`

Counts

4 → 297

Calls

4 calls:

109.0ms	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
74.0ms	(.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m)
65.0ms	(/.f64 (/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v))
59.0ms	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	194	10
2	2696	10
3	5155	10
0	8	12
1	169	12
2	2219	12
3	5740	12
0	10	13
1	216	13
2	3018	13
3	5731	13
0	12	16
1	269	12
2	3389	12
3	4941	12
4	5062	12

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
413×	`fma-neg_binary64`
358×	`associate-/l*_binary64`
342×	`cancel-sign-sub-inv_binary64`
313×	`difference-of-squares_binary64`

Counts

369 → 320

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	875
1	86	875
2	171	875
3	434	875
4	1342	851
5	4073	851
6	4882	851

prune232.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	320	6	326

Error

Counts

326 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))
✓	0.3b	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
	6.2b	(+.f64 (/.f64 (*.f64 (pow.f64 m 2) (-.f64 1 m)) v) (neg.f64 m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
▶	0.2b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m)) (neg.f64 m))
	0.8b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 2) (.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) m))

Compiler

Compiled 6052 to 2619 computations (56.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m)) (neg.f64 m))
✓	0.2b	(*.f64 (pow.f64 v -1/2) m)
	0.2b	(/.f64 (*.f64 m (-.f64 1 m)) (sqrt.f64 v))
✓	0.3b	(.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m))

series137.0ms (2.7%)

Counts

3 → 56

Calls

3 calls:

69.0ms	(.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m))
53.0ms	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m)) (neg.f64 m))
15.0ms	(*.f64 (pow.f64 v -1/2) m)

rewrite265.0ms (5.1%)

Algorithm

3×	egg-rewrite

Rules

104×	`egg`
54×	`egg`
47×	`egg`

Counts

3 → 205

Calls

3 calls:

113.0ms	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m)) (neg.f64 m))
108.0ms	(.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m))
40.0ms	(*.f64 (pow.f64 v -1/2) m)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	260	16
2	3280	16
3	4956	16
4	5401	16
0	6	7
1	125	7
2	1353	7
3	4925	7
0	14	24
1	313	15
2	3691	15
3	4999	15
4	4885	15

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-def_binary64`
521×	`fma-neg_binary64`
420×	`cancel-sign-sub-inv_binary64`
378×	`div-sub_binary64`
311×	`difference-of-squares_binary64`

Counts

261 → 221

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	679
1	63	679
2	139	679
3	376	670
4	1115	646
5	3483	646
6	4880	646
7	5206	646

prune274.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	285	6	291

Error

Counts

291 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) m) (neg.f64 m))
✓	0.3b	(+.f64 (.f64 (/.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (sqrt.f64 v)) m) (neg.f64 m))
	6.2b	(+.f64 (/.f64 (*.f64 (pow.f64 m 2) (-.f64 1 m)) v) (neg.f64 m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
✓	0.2b	(+.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) (sqrt.f64 v)) (*.f64 (pow.f64 v -1/2) m)) (neg.f64 m))
	0.8b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) 2) (.f64 (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1)) m))

Compiler

Compiled 5992 to 3243 computations (45.9% saved)

regimes1.1s (20.7%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

323 → 1

Compiler

Compiled 16427 to 10700 computations (34.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`/-rgt-identity_binary64`
1×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	16
2	24	16
3	25	16
4	24	16

end92.0ms (1.8%)

Compiler: Compiled 140 to 93 computations (33.6% saved)

Details

analyze64.0ms (1.3%)

sample1.2s (24%)

simplify132.0ms (2.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series24.0ms (0.5%)

rewrite237.0ms (4.6%)

simplify67.0ms (1.3%)

prune161.0ms (3.1%)

localize7.0ms (0.1%)

series30.0ms (0.6%)

rewrite162.0ms (3.1%)

simplify75.0ms (1.4%)

prune251.0ms (4.9%)

localize9.0ms (0.2%)

series115.0ms (2.2%)

rewrite312.0ms (6.1%)

simplify81.0ms (1.6%)

prune232.0ms (4.5%)

localize12.0ms (0.2%)

series137.0ms (2.7%)

rewrite265.0ms (5.1%)

simplify95.0ms (1.8%)

prune274.0ms (5.3%)

regimes1.1s (20.7%)

simplify2.0ms (0%)

end92.0ms (1.8%)

Profiling