Details

analyze1.4s (26.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.2s (21.7%)

Results

1.0s	8252×	body	128	valid
65.0ms	514×	body	128	invalid
1.0ms	3×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	1.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series78.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

53.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
25.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite72.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

923×	`prod-diff_binary64`
140×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`
130×	`add-log-exp_binary64`

Counts

2 → 60

Calls

2 calls:

70.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
70.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	269	27
2	3662	27
3	5548	27
0	0	0
1	0	0

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
347×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
271×	`+-commutative_binary64`

Counts

156 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3917
1	882	3913
2	3755	3898
3	5215	3898

prune123.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Error

Counts

134 → 5

Alt Table

Status	Error	Program
	28.2b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 1 z)) (+.f64 (/.f64 (.f64 y (.f64 a t)) (pow.f64 (-.f64 1 z) 2)) x)) (+.f64 (/.f64 (.f64 y a) (-.f64 1 z)) (/.f64 (.f64 a (.f64 t z)) (pow.f64 (-.f64 1 z) 2))))
	38.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	12.0b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
▶	1.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 4261 to 2092 computations (50.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	10.4b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series108.0ms (2%)

Counts

3 → 144

Calls

3 calls:

54.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
42.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
11.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite88.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

291×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
151×	`add-log-exp_binary64`

Counts

3 → 121

Calls

3 calls:

84.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
84.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)
84.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	309	45
2	4627	45
3	5104	45
0	0	0
1	0	0

simplify141.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

453×	`associate-+r+_binary64`
418×	`fma-neg_binary64`
389×	`times-frac_binary64`
358×	`+-commutative_binary64`
343×	`associate-+l+_binary64`

Counts

265 → 214

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	355	5790
1	1111	5790
2	4647	5790
3	5053	5790

prune204.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	214	5	219

Error

Counts

219 → 5

Alt Table

Status	Error	Program
	38.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	12.0b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
▶	2.8b	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
✓	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	1.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 7355 to 3502 computations (52.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
✓	0.0b	(/.f64 (-.f64 1 z) a)
✓	1.4b	(+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))
✓	10.4b	(/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a)))

series207.0ms (3.8%)

Counts

4 → 160

Calls

4 calls:

121.0ms	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
61.0ms	(/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a)))
18.0ms	(+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))
7.0ms	(/.f64 (-.f64 1 z) a)

rewrite97.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

321×	`log1p-udef_binary64`
176×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
165×	`egg-rr`

Counts

4 → 165

Calls

4 calls:

90.0ms	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
90.0ms	(/.f64 (-.f64 1 z) a)
90.0ms	(+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))
90.0ms	(/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	334	61
2	4903	61
3	5435	61
0	0	0
1	0	0

simplify135.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-+r+_binary64`
379×	`times-frac_binary64`
354×	`associate-+l+_binary64`
295×	`fma-neg_binary64`
268×	`associate-/l*_binary64`

Counts

325 → 263

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	369	6771
1	1184	6697
2	4942	6697
3	5223	6697

prune231.0ms (4.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	263	5	268

Error

Counts

268 → 5

Alt Table

Status	Error	Program
	38.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
▶	12.0b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.8b	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
✓	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	1.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 9660 to 4625 computations (52.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	0.0b	(*.f64 a (-.f64 y z))
✓	11.3b	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))

series118.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

61.0ms	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
50.0ms	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))
6.0ms	(*.f64 a (-.f64 y z))

rewrite83.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
281×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Counts

3 → 106

Calls

3 calls:

80.0ms	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
80.0ms	(*.f64 a (-.f64 y z))
80.0ms	(/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	299	42
2	4312	42
3	5147	42
0	0	0
1	0	0

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

453×	`associate-+r+_binary64`
418×	`fma-neg_binary64`
389×	`times-frac_binary64`
355×	`+-commutative_binary64`
342×	`associate-+l+_binary64`

Counts

226 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	345	5358
1	1091	5349
2	4594	5349
3	4999	5349

prune155.0ms (2.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	194	5	199

Error

Counts

199 → 5

Alt Table

Status	Error	Program
	38.0b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
✓	12.0b	(-.f64 x (/.f64 (*.f64 a (-.f64 y z)) (-.f64 (+.f64 1 t) z)))
✓	2.8b	(-.f64 x (/.f64 (-.f64 y z) (+.f64 (/.f64 (-.f64 1 z) a) (/.f64 t a))))
✓	1.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	1.3b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 6933 to 3319 computations (52.1% saved)

regimes502.0ms (9.3%)

Accuracy

Total 0.3b remaining (96.7%)

Threshold costs 0.3b (96.7%)

Counts

69 → 1

Compiler

Compiled 9408 to 6354 computations (32.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	26	19
2	40	19
3	50	19
4	61	19
5	77	19
6	83	19
7	84	19
8	80	19

end87.0ms (1.6%)

Compiler: Compiled 131 to 87 computations (33.6% saved)

Details

analyze1.4s (26.7%)

sample1.2s (21.7%)

simplify98.0ms (1.8%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series78.0ms (1.4%)

rewrite72.0ms (1.3%)

simplify88.0ms (1.6%)

prune123.0ms (2.3%)

localize9.0ms (0.2%)

series108.0ms (2%)

rewrite88.0ms (1.6%)

simplify141.0ms (2.6%)

prune204.0ms (3.8%)

localize10.0ms (0.2%)

series207.0ms (3.8%)

rewrite97.0ms (1.8%)

simplify135.0ms (2.5%)

prune231.0ms (4.3%)

localize10.0ms (0.2%)

series118.0ms (2.2%)

rewrite83.0ms (1.5%)

simplify121.0ms (2.2%)

prune155.0ms (2.9%)

regimes502.0ms (9.3%)

simplify4.0ms (0.1%)

end87.0ms (1.6%)

Profiling