Details

analyze1.0s (22.4%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (31%)

Results

1.1s	8256×	body	128	valid
220.0ms	733×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify99.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	7.7b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	4.8b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series63.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

39.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
16.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
7.0ms	(/.f64 2 (-.f64 y t))

rewrite90.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

473×	`prod-diff_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
193×	`fma-def_binary64`
182×	`log-pow_binary64`

Counts

3 → 91

Calls

3 calls:

88.0ms	(/.f64 2 (-.f64 y t))
88.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
88.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	226	30
2	3094	30
3	4978	30
4	5124	30
0	0	0
1	0	0

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
705×	`associate-/l*_binary64`
480×	`associate-/r*_binary64`
159×	`distribute-lft-out_binary64`
117×	`distribute-rgt-out_binary64`

Counts

199 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2577
1	446	2445
2	1620	2229
3	4985	2229

prune100.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Error

0.0b

Counts

138 → 8

Alt Table

Status	Error	Program
	29.2b	(.f64 x (/.f64 -2 (.f64 t z)))
	34.8b	(.f64 (/.f64 x z) (fma.f64 2 (/.f64 t (.f64 y y)) (/.f64 2 y)))
✓	5.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	31.5b	(.f64 (/.f64 x z) (fma.f64 -2 (/.f64 y (.f64 t t)) (/.f64 -2 t)))
	6.1b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	6.7b	(/.f64 (/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
▶	6.0b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.2b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))

Compiler

Compiled 2475 to 1427 computations (42.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(*.f64 x (/.f64 2 (-.f64 y t)))
✓	5.9b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

series53.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
18.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))

rewrite114.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

395×	`prod-diff_binary64`
318×	`fma-udef_binary64`
220×	`fma-def_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`

Counts

2 → 69

Calls

2 calls:

113.0ms	(*.f64 x (/.f64 2 (-.f64 y t)))
112.0ms	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	226	23
2	3112	23
3	4847	23
4	4849	23
5	5031	23
0	0	0
1	0	0

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
599×	`associate-/l*_binary64`
577×	`fma-def_binary64`
400×	`associate-/r*_binary64`
136×	`associate-/r/_binary64`

Counts

153 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1992
1	332	1902
2	1231	1698
3	5080	1698

prune104.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	141	6	147

Error

0.0b

Counts

147 → 6

Alt Table

Status	Error	Program
	5.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	6.1b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
▶	5.8b	(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))
	6.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.9b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
	6.2b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))

Compiler

Compiled 2452 to 1392 computations (43.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	5.5b	(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))

series35.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))

rewrite113.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

386×	`prod-diff_binary64`
307×	`fma-udef_binary64`
228×	`fma-def_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Counts

1 → 55

Calls

1 calls:

112.0ms

(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	229	13
2	3183	13
3	4853	13
4	4849	13
5	4982	13
0	0	0
1	0	0

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

806×	`times-frac_binary64`
504×	`associate-/l*_binary64`
345×	`associate-/r*_binary64`
326×	`fma-def_binary64`
239×	`fma-neg_binary64`

Counts

103 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1182
1	222	1110
2	905	1032
3	4919	1023
4	5109	1023

prune84.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

Counts

116 → 7

Alt Table

Status	Error	Program
	30.2b	(*.f64 (/.f64 x z) (cbrt.f64 (pow.f64 (/.f64 2 (-.f64 y t)) 3)))
	6.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	6.1b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	5.8b	(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))
▶	5.9b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
	6.2b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 2 (-.f64 y t)))))

Compiler

Compiled 1820 to 946 computations (48% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	0.3b	(*.f64 x (/.f64 1 z))
✓	5.5b	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))

series40.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

35.0ms	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))
5.0ms	(*.f64 x (/.f64 1 z))

rewrite113.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

377×	`prod-diff_binary64`
300×	`fma-udef_binary64`
228×	`fma-def_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`

Counts

2 → 61

Calls

2 calls:

111.0ms	(*.f64 x (/.f64 1 z))
111.0ms	(.f64 (/.f64 2 (-.f64 y t)) (.f64 x (/.f64 1 z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	262	17
2	3250	17
3	4864	17
4	4857	17
5	4903	17
0	0	0
1	0	0

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

806×	`times-frac_binary64`
504×	`associate-/l*_binary64`
345×	`associate-/r*_binary64`
326×	`fma-def_binary64`
239×	`fma-neg_binary64`

Counts

133 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1278
1	222	1206
2	905	1128
3	4919	1119
4	5109	1119

prune76.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	119	6	125

Error

Counts

125 → 6

Alt Table

Status	Error	Program
	30.2b	(*.f64 (/.f64 x z) (cbrt.f64 (pow.f64 (/.f64 2 (-.f64 y t)) 3)))
	6.0b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	5.9b	(/.f64 (*.f64 2 (/.f64 x (-.f64 y t))) z)
	6.2b	(/.f64 2 (/.f64 (-.f64 y t) (/.f64 x z)))
	6.1b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	5.8b	(*.f64 (/.f64 x z) (/.f64 2 (-.f64 y t)))

Compiler

Compiled 1912 to 1066 computations (44.2% saved)

regimes582.0ms (12.8%)

Accuracy

Total 1.1b remaining (98%)

Threshold costs 0b (0%)

Counts

49 → 3

Compiler

Compiled 4824 to 3445 computations (28.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

36×	`distribute-rgt-neg-in_binary64`
32×	`cancel-sign-sub-inv_binary64`
23×	`distribute-lft-neg-in_binary64`
21×	`distribute-lft-neg-out_binary64`
21×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	71
1	44	71
2	58	71
3	74	69
4	93	69
5	107	69
6	112	69
7	122	69
8	135	69
9	159	69
10	184	69
11	198	69
12	200	69
13	196	69

end168.0ms (3.7%)

Compiler: Compiled 185 to 113 computations (38.9% saved)

Iter	Nodes	Cost
0	28	71
1	44	71
2	58	71
3	74	69
4	93	69
5	107	69
6	112	69
7	122	69
8	135	69
9	159	69
10	184	69
11	198	69
12	200	69
13	196	69

Iter	Nodes	Cost
0	28	71
1	44	71
2	58	71
3	74	69
4	93	69
5	107	69
6	112	69
7	122	69
8	135	69
9	159	69
10	184	69
11	198	69
12	200	69
13	196	69

Details

analyze1.0s (22.4%)

sample1.4s (31%)

simplify99.0ms (2.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series63.0ms (1.4%)

rewrite90.0ms (2%)

simplify66.0ms (1.5%)

prune100.0ms (2.2%)

localize6.0ms (0.1%)

series53.0ms (1.2%)

rewrite114.0ms (2.5%)

simplify51.0ms (1.1%)

prune104.0ms (2.3%)

localize6.0ms (0.1%)

series35.0ms (0.8%)

rewrite113.0ms (2.5%)

simplify66.0ms (1.5%)

prune84.0ms (1.8%)

localize9.0ms (0.2%)

series40.0ms (0.9%)

rewrite113.0ms (2.5%)

simplify62.0ms (1.4%)

prune76.0ms (1.7%)

regimes582.0ms (12.8%)

bsearch1.0ms (0%)

simplify11.0ms (0.2%)

end168.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	28	71
1	44	71
2	58	71
3	74	69
4	93	69
5	107	69
6	112	69
7	122	69
8	135	69
9	159	69
10	184	69
11	198	69
12	200	69
13	196	69