Details

analyze552.0ms (10.3%)

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)

sample1.2s (21.6%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify140.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

prune4.0ms (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
▶	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	2.2b	(+.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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series102.0ms (1.9%)

Counts

4 → 108

Calls

4 calls:

43.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
43.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite121.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

675×	`prod-diff_binary64`
487×	`fma-udef_binary64`
256×	`fma-def_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`

Counts

4 → 115

Calls

4 calls:

119.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
119.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
119.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
119.0ms	(/.f64 -5641895835477563/5000000000000000 y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	234	43
2	2881	43
3	4890	43
4	4781	43
5	4923	43
0	0	0
1	0	0

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

711×	`associate-/l*_binary64`
623×	`associate-/r*_binary64`
481×	`fma-def_binary64`
150×	`distribute-rgt-in_binary64`
135×	`distribute-neg-in_binary64`

Counts

223 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	2745
1	436	2727
2	1581	2570
3	5204	2570

prune152.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Error

Counts

180 → 4

Alt Table

Status	Error	Program
	24.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	0.4b	(+.f64 x (*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)))
	2.2b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3988 to 2495 computations (37.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2))
✓	0.2b	(/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x)))
✓	0.4b	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)
✓	0.4b	(cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))

series1.1s (19.6%)

Counts

4 → 144

Calls

4 calls:

384.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)
339.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x)))
285.0ms	(cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))
42.0ms	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2))

rewrite75.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
209×	`log-pow_binary64`
134×	`add-sqr-sqrt_binary64`

Counts

4 → 120

Calls

4 calls:

72.0ms	(*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2))
72.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x)))
72.0ms	(pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)
72.0ms	(cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	80
1	282	63
2	3039	63
3	5185	63
0	0	0
1	0	0

simplify174.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

456×	`fma-def_binary64`
354×	`times-frac_binary64`
315×	`associate-/l*_binary64`
288×	`associate-/r*_binary64`
193×	`*-commutative_binary64`

Counts

264 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	581	7009
1	1859	6870
2	4963	6860
3	5025	6860

prune539.0ms (10%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	407	0	407
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	407	4	411

Error

Counts

411 → 4

Alt Table

Status	Error	Program
	24.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.4b	(+.f64 x (*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)))
▶	2.2b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 19127 to 13270 computations (30.6% saved)

localize8.0ms (0.1%)

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))
✓	0.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	7.7b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series84.0ms (1.6%)

Counts

4 → 112

Calls

4 calls:

36.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
35.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
10.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite96.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 246

Calls

4 calls:

90.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
90.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
90.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
90.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	248	51
2	3364	51
3	4999	51
0	0	0
1	0	0

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Rules

636×	`associate-/l*_binary64`
572×	`fma-def_binary64`
527×	`associate-/r*_binary64`
199×	`fma-neg_binary64`
196×	`associate-*l/_binary64`

Counts

358 → 313

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	2764
1	422	2744
2	1493	2629
3	4889	2621
4	4988	2621

prune263.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	313	0	313
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	313	4	317

Error

Counts

317 → 4

Alt Table

Status	Error	Program
▶	24.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.4b	(+.f64 x (*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)))
✓	2.2b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 7560 to 3536 computations (53.2% 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)

series34.0ms (0.6%)

Counts

2 → 40

Calls

2 calls:

21.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
13.0ms	(/.f64 y (exp.f64 z))

rewrite52.0ms (1%)

Algorithm

2×	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`

Counts

2 → 58

Calls

2 calls:

51.0ms	(/.f64 y (exp.f64 z))
51.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	161	16
2	1919	16
3	4942	16
0	0	0
1	0	0

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

783×	`distribute-rgt-neg-in_binary64`
660×	`cancel-sign-sub-inv_binary64`
609×	`distribute-lft-neg-in_binary64`
532×	`associate-l_binary64`
448×	`associate-r_binary64`

Counts

98 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	423
1	115	419
2	325	412
3	1035	401
4	3272	401
5	4631	401
6	5117	401

prune53.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	74	4	78

Error

Counts

78 → 4

Alt Table

Status	Error	Program
✓	24.2b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
✓	0.1b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.4b	(+.f64 x (*.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) (pow.f64 (/.f64 -1 (cbrt.f64 (fma.f64 (/.f64 -5641895835477563/5000000000000000 y) (exp.f64 z) x))) 2)))
✓	2.2b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 963 to 484 computations (49.7% saved)

regimes352.0ms (6.6%)

Accuracy

Total 0.0b remaining (92.9%)

Threshold costs 0.0b (92.9%)

Counts

60 → 1

Compiler

Compiled 6811 to 4916 computations (27.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end75.0ms (1.4%)

Compiler: Compiled 95 to 67 computations (29.5% saved)

Details

analyze552.0ms (10.3%)

sample1.2s (21.6%)

simplify140.0ms (2.6%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series102.0ms (1.9%)

rewrite121.0ms (2.3%)

simplify74.0ms (1.4%)

prune152.0ms (2.8%)

localize14.0ms (0.3%)

series1.1s (19.6%)

rewrite75.0ms (1.4%)

simplify174.0ms (3.2%)

prune539.0ms (10%)

localize8.0ms (0.1%)

series84.0ms (1.6%)

rewrite96.0ms (1.8%)

simplify105.0ms (2%)

prune263.0ms (4.9%)

localize5.0ms (0.1%)

series34.0ms (0.6%)

rewrite52.0ms (1%)

simplify81.0ms (1.5%)

prune53.0ms (1%)

regimes352.0ms (6.6%)

simplify2.0ms (0%)

end75.0ms (1.4%)

Profiling