Details

analyze479.0ms (12.7%)

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
12.5%	87.4%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample945.0ms (25.1%)

Results

933.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess50.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

930×	`fma-neg_binary64`
478×	`fma-def_binary64`
469×	`div-sub_binary64`
332×	`times-frac_binary64`
288×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	72
1	60	72
2	98	72
3	143	72
4	221	72
5	354	72
6	549	72
7	806	72
8	1175	72
9	1662	64
10	2534	64
11	4284	64
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-def_binary64`
768×	`fma-neg_binary64`
655×	`div-sub_binary64`
305×	`associate-/l/_binary64`
251×	`times-frac_binary64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	35	18
3	52	18
4	81	18
5	127	18
6	205	18
7	293	18
8	396	18
9	539	16
10	727	16
11	1179	16
12	2241	16
13	4295	16

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	3.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 z) y)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
✓	0.1b	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))
✓	0.1b	(fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)

series105.0ms (2.8%)

Counts

4 → 112

Calls

33 calls:

17.0ms	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))	z	0
9.0ms	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))	z	inf
8.0ms	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))	z	inf
8.0ms	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))	z	-inf
8.0ms	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))	z	-inf

rewrite64.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

681×	`prod-diff_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
118×	`add-sqr-sqrt_binary64`
115×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	233	45
2	3074	45

Stop Event

1×	node limit

Counts

4 → 115

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-/l*_binary64`
622×	`associate-/r*_binary64`
497×	`fma-def_binary64`
150×	`distribute-rgt-in_binary64`
133×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2813
1	467	2793
2	1699	2634

Stop Event

1×	node limit

Counts

227 → 185

prune148.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	183	4	187

Error

Counts

187 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	25.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
	5.8b	(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x) 2))) (/.f64 -1 (cbrt.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))) x)
▶	3.6b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4188 to 2464 computations (41.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.8b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	10.2b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series96.0ms (2.6%)

Counts

4 → 112

Calls

30 calls:

22.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))	y	inf
8.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))	z	inf
8.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))	z	-inf
8.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))	z	inf
7.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))	z	-inf

rewrite129.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`fma-def_binary64`
275×	`fma-neg_binary64`
242×	`egg-rr`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	252	51
2	3605	51

Stop Event

1×	node limit

Counts

4 → 242

simplify127.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

635×	`associate-/l*_binary64`
572×	`fma-def_binary64`
524×	`associate-/r*_binary64`
194×	`associate-*l/_binary64`
157×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2764
1	427	2744
2	1558	2629

Stop Event

1×	node limit

Counts

354 → 315

prune284.0ms (7.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	316	3	319

Error

Counts

319 → 3

Alt Table

Status	Error	Program
	25.7b	(+.f64 x (/.f64 (*.f64 5000000000000000/5641895835477563 y) (exp.f64 z)))
▶	3.6b	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))

Compiler

Compiled 7566 to 3345 computations (55.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x))))
✓	0.8b	(fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))
✓	2.4b	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)

series78.0ms (2.1%)

Counts

3 → 108

Calls

27 calls:

7.0ms	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)	z	-inf
7.0ms	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)	z	inf
6.0ms	(/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x))))	z	-inf
6.0ms	(/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x))))	z	inf
5.0ms	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)	x	0

rewrite87.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

482×	`log-prod_binary64`
298×	`prod-diff_binary64`
228×	`egg-rr`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	238	39
2	2847	39

Stop Event

1×	node limit

Counts

3 → 228

simplify100.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

862×	`associate-/r*_binary64`
780×	`fma-def_binary64`
236×	`associate-/r/_binary64`
174×	`cancel-sign-sub-inv_binary64`
165×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2744
1	556	2714
2	2171	2633

Stop Event

1×	node limit

Counts

336 → 295

prune272.0ms (7.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	295	3	298

Error

Counts

298 → 3

Alt Table

Status	Error	Program
✓	3.6b	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)
▶	25.7b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))

Compiler

Compiled 8608 to 4093 computations (52.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 5000000000000000/5641895835477563 (exp.f64 z))
✓	0.1b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)

series26.0ms (0.7%)

Counts

2 → 40

Calls

12 calls:

3.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)	z	-inf
3.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)	z	inf
3.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)	y	inf
2.0ms	(/.f64 5000000000000000/5641895835477563 (exp.f64 z))	z	-inf
2.0ms	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)	x	0

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
84×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	162	16
2	1929	16

Stop Event

1×	node limit

Counts

2 → 45

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
544×	`cancel-sign-sub-inv_binary64`
405×	`associate-l_binary64`
275×	`fma-neg_binary64`
272×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	414
1	111	410
2	325	395
3	1135	372
4	4448	372

Stop Event

1×	node limit

Counts

85 → 64

prune72.0ms (1.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	64	3	67

Error

Counts

67 → 3

Alt Table

Status	Error	Program
✓	3.6b	(fma.f64 y (/.f64 1 (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (*.f64 y (neg.f64 x)))) x)
✓	25.7b	(fma.f64 y (/.f64 5000000000000000/5641895835477563 (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))

Compiler

Compiled 762 to 458 computations (39.9% saved)

regimes398.0ms (10.6%)

Accuracy

Total 0.1b remaining (82.3%)

Threshold costs 0.1b (82.3%)

Counts

65 → 1

Compiler

Compiled 6215 to 4298 computations (30.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16

Stop Event

1×

saturated

end58.0ms (1.6%)

Stop Event

1×

done

Compiler

Compiled 68 to 48 computations (29.4% saved)

Details

analyze479.0ms (12.7%)

sample945.0ms (25.1%)

preprocess50.0ms (1.3%)

simplify30.0ms (0.8%)

prune6.0ms (0.2%)

localize8.0ms (0.2%)

series105.0ms (2.8%)

rewrite64.0ms (1.7%)

simplify80.0ms (2.1%)

prune148.0ms (3.9%)

localize8.0ms (0.2%)

series96.0ms (2.6%)

rewrite129.0ms (3.4%)

simplify127.0ms (3.4%)

prune284.0ms (7.5%)

localize9.0ms (0.2%)

series78.0ms (2.1%)

rewrite87.0ms (2.3%)

simplify100.0ms (2.7%)

prune272.0ms (7.2%)

localize5.0ms (0.1%)

series26.0ms (0.7%)

rewrite52.0ms (1.4%)

simplify41.0ms (1.1%)

prune72.0ms (1.9%)

regimes398.0ms (10.6%)

simplify2.0ms (0.1%)

end58.0ms (1.6%)

Profiling