Details

analyze448.0ms (13.2%)

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)

sample960.0ms (28.3%)

Results

899.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify28.0ms (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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize7.0ms (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	(fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)
✓	0.1b	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))

series92.0ms (2.7%)

Counts

4 → 112

Calls

4 calls:

38.0ms	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
34.0ms	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))
14.0ms	(fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)
6.0ms	(/.f64 (exp.f64 z) y)

rewrite83.0ms (2.4%)

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

Calls

4 calls:

81.0ms	(/.f64 (exp.f64 z) y)
81.0ms	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
81.0ms	(fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)
81.0ms	(/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x))

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-/l*_binary64`
620×	`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 → 186

prune147.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	183	5	188

Error

Counts

188 → 5

Alt Table

Status	Error	Program
	11.4b	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
▶	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	24.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	27.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))) (/.f64 (/.f64 1 (pow.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x) 2)) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))))

Compiler

Compiled 4250 to 2505 computations (41.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	1.4b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	8.3b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series80.0ms (2.4%)

Counts

4 → 112

Calls

4 calls:

39.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
31.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
8.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite80.0ms (2.4%)

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

Calls

4 calls:

75.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
75.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
75.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
75.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

simplify69.0ms (2%)

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

prune265.0ms (7.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	315	5	320

Error

Counts

320 → 5

Alt Table

Status	Error	Program
▶	11.4b	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	24.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	27.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))) (/.f64 (/.f64 1 (pow.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x) 2)) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))))

Compiler

Compiled 7655 to 3399 computations (55.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -5641895835477563/5000000000000000 y))
✓	0.0b	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
✓	0.2b	(/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y)))
✓	0.3b	(/.f64 -5641895835477563/5000000000000000 y)

series23.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

8.0ms	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
8.0ms	(/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y)))
6.0ms	(+.f64 x (/.f64 -5641895835477563/5000000000000000 y))
1.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite62.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

463×	`log-prod_binary64`
356×	`fma-def_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
188×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	207	34
2	2930	34

Stop Event

1×	node limit

Counts

4 → 151

Calls

4 calls:

60.0ms	(+.f64 x (/.f64 -5641895835477563/5000000000000000 y))
60.0ms	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
60.0ms	(/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y)))
60.0ms	(/.f64 -5641895835477563/5000000000000000 y)

simplify56.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

414×	`unswap-sqr_binary64`
313×	`fma-def_binary64`
239×	`cancel-sign-sub-inv_binary64`
208×	`associate-l_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1197
1	206	1173
2	627	1167
3	2537	1161

Stop Event

1×	node limit

Counts

223 → 185

prune133.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	185	5	190

Error

Counts

190 → 5

Alt Table

Status	Error	Program
✓	11.4b	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	24.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	27.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))) (/.f64 (/.f64 1 (pow.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x) 2)) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))))

Compiler

Compiled 3111 to 2172 computations (30.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series37.0ms (1.1%)

Counts

2 → 40

Calls

2 calls:

21.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
16.0ms	(/.f64 y (exp.f64 z))

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

741×	`log1p-expm1-u_binary64`
741×	`expm1-log1p-u_binary64`
148×	`log1p-udef_binary64`
84×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	161	16
2	1985	16

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

41.0ms	(/.f64 y (exp.f64 z))
41.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

simplify40.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

661×	`cancel-sign-sub-inv_binary64`
524×	`associate-l_binary64`
449×	`associate-r_binary64`
369×	`fma-neg_binary64`
157×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	423
1	116	419
2	352	412
3	1322	401
4	4980	401

Stop Event

1×	node limit

Counts

96 → 75

prune43.0ms (1.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	75	5	80

Error

Counts

80 → 5

Alt Table

Status	Error	Program
✓	11.4b	(+.f64 x (/.f64 -1 (+.f64 x (/.f64 -5641895835477563/5000000000000000 y))))
✓	3.5b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	24.7b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))
	27.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))) (/.f64 (/.f64 1 (pow.f64 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x) 2)) (+.f64 x (/.f64 1 (fma.f64 -5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y) x)))))

Compiler

Compiled 996 to 508 computations (49% saved)

regimes527.0ms (15.6%)

Accuracy

Total 0.1b remaining (94.7%)

Threshold costs 0.1b (94.7%)

Counts

72 → 1

Compiler

Compiled 9981 to 6729 computations (32.6% 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

end75.0ms (2.2%)

Compiler: Compiled 121 to 81 computations (33.1% saved)

Details

analyze448.0ms (13.2%)

sample960.0ms (28.3%)

simplify28.0ms (0.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series92.0ms (2.7%)

rewrite83.0ms (2.4%)

simplify64.0ms (1.9%)

prune147.0ms (4.3%)

localize7.0ms (0.2%)

series80.0ms (2.4%)

rewrite80.0ms (2.4%)

simplify69.0ms (2%)

prune265.0ms (7.8%)

localize9.0ms (0.3%)

series23.0ms (0.7%)

rewrite62.0ms (1.8%)

simplify56.0ms (1.7%)

prune133.0ms (3.9%)

localize5.0ms (0.1%)

series37.0ms (1.1%)

rewrite42.0ms (1.2%)

simplify40.0ms (1.2%)

prune43.0ms (1.3%)

regimes527.0ms (15.6%)

simplify2.0ms (0.1%)

end75.0ms (2.2%)

Profiling