Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 21 to 17 computations (19% saved)

sample1.7s (51.7%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 62 to 50 computations (19.4% saved)

simplify102.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
684×	`fma-neg_binary64`
640×	`associate-/l*_binary64`
583×	`associate-/r*_binary64`
496×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	59	22
3	94	22
4	131	22
5	171	20
6	250	20
7	423	20
8	810	20
9	1376	20
10	2197	20
11	2355	20
12	3878	20
13	4822	20
14	4656	20

prune8.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (.f64 x 27061/100000)) (+.f64 1 (.f64 x (+.f64 99229/100000 (.f64 x 4481/100000))))) x))
▶	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Status

Error

Program

0.1b

(*.f64 70711/100000 (-.f64 (/.f64 (+.f64 230753/100000 (*.f64 x 27061/100000)) (+.f64 1 (*.f64 x (+.f64 99229/100000 (*.f64 x 4481/100000))))) x))

▶

0.1b

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 107 to 83 computations (22.4% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	15.3b	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series15.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
4.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
3.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite118.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

509×	`unpow-prod-down_binary64`
418×	`log-prod_binary64`
268×	`pow2_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Counts

4 → 165

Calls

4 calls:

112.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
112.0ms	(fma.f64 x 4481/100000 99229/100000)
112.0ms	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
112.0ms	(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	35
2	2451	35
3	5654	35
0	0	0
1	0	0

simplify130.0ms (4%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
739×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
305×	`fma-def_binary64`
239×	`neg-mul-1_binary64`

Counts

213 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	459
1	130	417
2	295	389
3	716	369
4	2068	369
5	4656	369
6	4991	369
7	4998	369
8	4919	369

prune336.0ms (10.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	197	2	199

Error

0.1b

Counts

199 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Status

Error

Program

▶

0.1b

(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))

✓

0.1b

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 4440 to 3498 computations (21.2% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
✓	0.6b	(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)
✓	15.7b	(/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000))

series10.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms

(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)

5.0ms

(/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000))

rewrite83.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

484×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
190×	`pow3_binary64`
175×	`log-pow_binary64`

Counts

2 → 81

Calls

2 calls:

79.0ms

(pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1)

79.0ms

(/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	267	32
2	2833	32
3	4775	32
0	0	0
1	0	0

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
470×	`times-frac_binary64`
290×	`neg-mul-1_binary64`
274×	`sub-neg_binary64`
256×	`distribute-rgt-neg-in_binary64`

Counts

105 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	326
1	175	306
2	415	296
3	1051	284
4	2944	284
5	4645	284
6	4912	284

prune300.0ms (9.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

0.1b

Counts

187 → 2

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))
✓	0.1b	(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Status

Error

Program

✓

0.1b

(fma.f64 x -70711/100000 (pow.f64 (/.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) (fma.f64 x 1913510371/10000000000 16316775383/10000000000)) -1))

✓

0.1b

(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

Compiler

Compiled 4098 to 3255 computations (20.6% saved)

regimes191.0ms (6%)

Accuracy

Total 0.0b remaining (5%)

Threshold costs 0.0b (5%)

Counts

34 → 1

Compiler

Compiled 1409 to 1085 computations (23% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	17	23
2	16	23

end118.0ms (3.7%)

Compiler: Compiled 70 to 54 computations (22.9% saved)

Details

analyze5.0ms (0.2%)

sample1.7s (51.7%)

simplify102.0ms (3.2%)

prune8.0ms (0.2%)

localize18.0ms (0.6%)

series15.0ms (0.5%)

rewrite118.0ms (3.7%)

simplify130.0ms (4%)

prune336.0ms (10.4%)

localize20.0ms (0.6%)

series10.0ms (0.3%)

rewrite83.0ms (2.6%)

simplify94.0ms (2.9%)

prune300.0ms (9.3%)

regimes191.0ms (6%)

simplify4.0ms (0.1%)

end118.0ms (3.7%)

Profiling