Details

analyze688.0ms (15.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
21.1%	78%	0.9%	9
37.3%	60.3%	2.5%	10
39.7%	56.1%	4.2%	11
45.6%	48.7%	5.7%	12
55.9%	35.1%	8.9%	13
57.6%	32.1%	10.3%	14

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample1.2s (25.8%)

Results

872.0ms	8256×	body	128	valid
123.0ms	1126×	body	128	invalid

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify113.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2064×	`fma-neg_binary64`
381×	`div-sub_binary64`
365×	`associate-/l*_binary64`
334×	`distribute-neg-frac_binary64`
322×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	11
2	25	11
3	47	11
4	82	11
5	143	11
6	228	11
7	442	11
8	1041	11
9	2472	11
10	2805	11
11	2944	11
12	3273	11
13	3441	11
14	3513	11
15	4986	11

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

9.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.6b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

Compiler

Compiled 42 to 21 computations (50% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	9.0b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

series38.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

26.0ms	(fma.f64 y (-.f64 z x) x)
12.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)

rewrite72.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

870×	`log1p-expm1-u_binary64`
870×	`expm1-log1p-u_binary64`
441×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-log-exp_binary64`

Counts

2 → 58

Calls

2 calls:

71.0ms	(fma.f64 y (-.f64 z x) x)
71.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	156	19
2	2144	19
3	6145	19
0	0	0
1	0	0

simplify237.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

972×	`div-sub_binary64`
791×	`*-commutative_binary64`
677×	`associate-/r/_binary64`
501×	`fma-def_binary64`
491×	`associate-/l/_binary64`

Counts

130 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	753
1	84	726
2	178	672
3	384	618
4	724	618
5	1858	618
6	2302	618
7	2599	618
8	2755	618
9	2875	618
10	2911	618
11	2808	618
12	3785	618
13	4284	618
14	4283	618
15	4842	618
16	4846	618
17	5144	618

prune89.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	4	80

Error

0.0b

Counts

80 → 4

Alt Table

Status	Error	Program
	22.1b	(-.f64 y (*.f64 (/.f64 x z) y))
▶	1.6b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
	38.0b	(*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 y (-.f64 z x) x) (sqrt.f64 z)))
	9.8b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))

Compiler

Compiled 1049 to 323 computations (69.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	4.9b	(/.f64 (*.f64 y x) z)

series30.0ms (0.7%)

Counts

2 → 9

Calls

2 calls:

17.0ms	(/.f64 (*.f64 y x) z)
13.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))

rewrite224.0ms (5%)

Algorithm

2×	batch-egg-rewrite

Rules

579×	`fma-def_binary64`
332×	`fma-neg_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
186×	`egg-rr`

Counts

2 → 186

Calls

2 calls:

114.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
114.0ms	(/.f64 (*.f64 y x) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	212	20
2	3301	20
3	4991	20
4	5025	20
0	0	0
1	0	0

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
366×	`fma-neg_binary64`
98×	`distribute-rgt-in_binary64`
84×	`distribute-lft-in_binary64`
69×	`associate-/l*_binary64`

Counts

195 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	66
1	52	66
2	133	66
3	218	57
4	473	57
5	829	57
6	960	57
7	987	57
8	982	57
9	910	57

prune228.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	193	5	198

Error

0.0b

Counts

198 → 5

Alt Table

Status	Error	Program
	22.1b	(-.f64 y (*.f64 (/.f64 x z) y))
✓	1.6b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
	38.0b	(*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 y (-.f64 z x) x) (sqrt.f64 z)))
▶	9.8b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	13.1b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z))))

Compiler

Compiled 4318 to 950 computations (78% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 y (-.f64 z x) x)
✓	9.2b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))

series13.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))

rewrite84.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

558×	`prod-diff_binary64`
457×	`log-prod_binary64`
202×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

1 → 33

Calls

1 calls:

82.0ms

(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	192	11
2	2370	11
3	4981	11
4	5252	11
0	0	0
1	0	0

simplify330.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

3586×	`fma-neg_binary64`
1263×	`div-sub_binary64`
699×	`associate-/r/_binary64`
690×	`*-commutative_binary64`
583×	`sub-neg_binary64`

Counts

69 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	408
1	67	408
2	155	354
3	323	354
4	638	354
5	1699	354
6	2326	354
7	2919	354
8	2821	354
9	2845	354
10	2882	354
11	2867	354
12	4057	354
13	4535	354
14	4228	354
15	4278	354
16	4302	354
17	4288	354
18	4445	354
19	4397	354
20	4435	354
21	7708	354

prune48.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	78	5	83

Error

0.0b

Counts

83 → 5

Alt Table

Status	Error	Program
	22.1b	(-.f64 y (*.f64 (/.f64 x z) y))
✓	1.6b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	9.8b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	38.0b	(/.f64 (/.f64 (fma.f64 y (-.f64 z x) x) (sqrt.f64 z)) (sqrt.f64 z))
▶	13.1b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z))))

Compiler

Compiled 1082 to 406 computations (62.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 y)
✓	2.0b	(*.f64 (cbrt.f64 y) (/.f64 x z))
✓	2.3b	(.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z)))
✓	24.0b	(cbrt.f64 (*.f64 y y))

series572.0ms (12.8%)

Counts

4 → 96

Calls

4 calls:

447.0ms	(*.f64 (cbrt.f64 y) (/.f64 x z))
52.0ms	(.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z)))
38.0ms	(cbrt.f64 (*.f64 y y))
34.0ms	(cbrt.f64 y)

rewrite66.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

908×	`log1p-expm1-u_binary64`
908×	`expm1-log1p-u_binary64`
98×	`egg-rr`
98×	`add-sqr-sqrt_binary64`
93×	`associate-r_binary64`

Counts

4 → 98

Calls

4 calls:

62.0ms	(cbrt.f64 y)
62.0ms	(*.f64 (cbrt.f64 y) (/.f64 x z))
62.0ms	(.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z)))
62.0ms	(cbrt.f64 (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	199	25
2	2392	25
3	5643	25
0	0	0
1	0	0

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1386×	`fma-def_binary64`
446×	`unswap-sqr_binary64`
440×	`associate-/l*_binary64`
394×	`associate-*l/_binary64`
393×	`*-commutative_binary64`

Counts

194 → 106

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	768
1	63	768
2	131	768
3	364	768
4	1009	768
5	2136	768
6	3276	768
7	4381	768
8	5076	768

prune67.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	106	5	111

Error

0.0b

Counts

111 → 5

Alt Table

Status	Error	Program
	22.1b	(-.f64 y (*.f64 (/.f64 x z) y))
✓	1.6b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	9.8b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	38.0b	(/.f64 (/.f64 (fma.f64 y (-.f64 z x) x) (sqrt.f64 z)) (sqrt.f64 z))
✓	13.1b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (cbrt.f64 (.f64 y y)) (*.f64 (cbrt.f64 y) (/.f64 x z))))

Compiler

Compiled 2071 to 557 computations (73.1% saved)

regimes179.0ms (4%)

Accuracy

Total 0.0b remaining (69.4%)

Threshold costs 0.0b (69.4%)

Counts

49 → 1

Compiler

Compiled 2400 to 1492 computations (37.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end71.0ms (1.6%)

Compiler: Compiled 100 to 57 computations (43% saved)

Details

analyze688.0ms (15.4%)

sample1.2s (25.8%)

simplify113.0ms (2.5%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series38.0ms (0.9%)

rewrite72.0ms (1.6%)

simplify237.0ms (5.3%)

prune89.0ms (2%)

localize7.0ms (0.2%)

series30.0ms (0.7%)

rewrite224.0ms (5%)

simplify43.0ms (1%)

prune228.0ms (5.1%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite84.0ms (1.9%)

simplify330.0ms (7.4%)

prune48.0ms (1.1%)

localize10.0ms (0.2%)

series572.0ms (12.8%)

rewrite66.0ms (1.5%)

simplify84.0ms (1.9%)

prune67.0ms (1.5%)

regimes179.0ms (4%)

simplify3.0ms (0.1%)

end71.0ms (1.6%)

Profiling