Details

analyze173.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample1.8s (11.7%)

Results

1.1s	6743×	body	128	valid
338.0ms	636×	body	1024	valid
227.0ms	527×	body	512	valid
80.0ms	296×	body	256	valid
36.0ms	54×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
537×	`div-sub_binary64`
535×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	110	37
3	435	37
4	1672	37
5	2494	37
6	3358	37
7	5392	37

prune5.0ms (0%)

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

17.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	21.1b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Status

Error

Program

▶

17.5b

(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

21.1b

(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	10.5b	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓	16.1b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series1.1s (6.8%)

Counts

3 → 108

Calls

3 calls:

737.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

274.0ms

(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

39.0ms

(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

rewrite135.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

270×	`expm1-udef_binary64`
270×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Counts

3 → 95

Calls

3 calls:

130.0ms

(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

130.0ms

(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

130.0ms

(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	82
1	296	82
2	4200	82
3	4952	82
0	0	0
1	0	0

simplify318.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

555×	`+-commutative_binary64`
488×	`fma-def_binary64`
486×	`associate-+r+_binary64`
378×	`*-commutative_binary64`
291×	`associate-*r/_binary64`

Counts

203 → 220

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1298	17686
1	5193	17686

prune1.0s (6.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	2	222

Error

0.1b

Counts

222 → 2

Alt Table

Status	Error	Program
	51.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	10.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Status

Error

Program

51.6b

(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

▶

10.4b

(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Compiler

Compiled 24620 to 15975 computations (35.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))
✓	0.1b	(*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
✓	10.5b	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)

series1.6s (10.1%)

Counts

4 → 144

Calls

4 calls:

873.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)
532.0ms	(*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
84.0ms	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))
78.0ms	(/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))

rewrite100.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

301×	`log1p-udef_binary64`
170×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`
159×	`add-log-exp_binary64`

Counts

4 → 138

Calls

4 calls:

96.0ms	(/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))
96.0ms	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha)))
96.0ms	(*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
96.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 beta alpha))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	89
1	332	89
2	4758	89
3	5198	89
0	0	0
1	0	0

simplify209.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-def_binary64`
543×	`associate-+r+_binary64`
364×	`associate-*r/_binary64`
171×	`associate-/l*_binary64`
147×	`associate-/r*_binary64`

Counts

282 → 310

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1542	21193
1	5062	21193

prune866.0ms (5.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	310	2	312

Error

0.1b

Counts

312 → 2

Alt Table

Status	Error	Program
	51.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	10.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Status

Error

Program

51.6b

(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

▶

10.4b

(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Compiler

Compiled 30404 to 19496 computations (35.9% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 beta (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
✓	10.5b	(fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)

series865.0ms (5.6%)

Counts

4 → 144

Calls

4 calls:

418.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)
245.0ms	(*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
121.0ms	(-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta))))
81.0ms	(/.f64 beta (fma.f64 2 i (+.f64 alpha beta)))

rewrite237.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

939×	`prod-diff_binary64`
297×	`egg-rr`
185×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`

Counts

4 → 297

Calls

4 calls:

213.0ms	(/.f64 beta (fma.f64 2 i (+.f64 alpha beta)))
213.0ms	(-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta))))
213.0ms	(*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha)))))
213.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	86
1	361	86
2	4768	86
3	6698	86
0	0	0
1	0	0

simplify410.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

456×	`+-commutative_binary64`
358×	`associate-+r+_binary64`
325×	`fma-def_binary64`
271×	`*-commutative_binary64`
263×	`sub-neg_binary64`

Counts

441 → 474

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1105	14886
1	4247	14882
2	4977	14882

prune1.9s (12.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	474	2	476

Error

0.1b

Counts

476 → 2

Alt Table

Status	Error	Program
▶	51.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	10.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Status

Error

Program

▶

51.6b

(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

✓

10.4b

(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Compiler

Compiled 37578 to 21731 computations (42.2% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

series30.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

30.0ms

(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

rewrite91.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
286×	`prod-diff_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
164×	`log-pow_binary64`

Counts

1 → 36

Calls

1 calls:

89.0ms

(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	215	12
2	2618	12
3	4986	12
4	5143	12
0	0	0
1	0	0

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

187×	`fma-def_binary64`
30×	`*-commutative_binary64`
22×	`distribute-rgt-in_binary64`
20×	`associate-/l*_binary64`
19×	`associate-/r/_binary64`

Counts

72 → 46

Iterations

Useful iterations: 13 (0.0ms)

Iter	Nodes	Cost
0	25	646
1	49	644
2	83	584
3	106	584
4	123	554
5	150	494
6	164	494
7	202	494
8	212	494
9	221	494
10	240	494
11	253	494
12	275	494
13	292	404
14	289	404
15	295	404
16	297	404
17	298	404
18	292	404

prune69.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	43	5	48

Error

0.1b

Counts

48 → 5

Alt Table

Status	Error	Program
	51.7b	(/.f64 (.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (/.f64 1 alpha))) 2)
	51.9b	(/.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) 2) (.f64 (cbrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (/.f64 1 alpha))) 2)
✓	51.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	52.6b	(/.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 2 beta (fma.f64 i 4 2)) alpha))) 2)
✓	10.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (-.f64 (/.f64 beta (fma.f64 2 i (+.f64 alpha beta))) (/.f64 alpha (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 2 (fma.f64 2 i (+.f64 beta alpha))))) 1) 2)

Compiler

Compiled 892 to 676 computations (24.2% saved)

regimes4.1s (26.4%)

Accuracy

Total 1.3b remaining (85.2%)

Threshold costs 0b (0%)

Counts

179 → 2

Compiler

Compiled 37381 to 25112 computations (32.8% saved)

bsearch18.0ms (0.1%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
13×	`*-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	105
1	57	105
2	74	103
3	95	103
4	109	103
5	113	103
6	109	103

end274.0ms (1.8%)

Compiler: Compiled 269 to 180 computations (33.1% saved)

Iter	Nodes	Cost
0	25	646
1	49	644
2	83	584
3	106	584
4	123	554
5	150	494
6	164	494
7	202	494
8	212	494
9	221	494
10	240	494
11	253	494
12	275	494
13	292	404
14	289	404
15	295	404
16	297	404
17	298	404
18	292	404

Iter	Nodes	Cost
0	25	646
1	49	644
2	83	584
3	106	584
4	123	554
5	150	494
6	164	494
7	202	494
8	212	494
9	221	494
10	240	494
11	253	494
12	275	494
13	292	404
14	289	404
15	295	404
16	297	404
17	298	404
18	292	404

Details

analyze173.0ms (1.1%)

sample1.8s (11.7%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series1.1s (6.8%)

rewrite135.0ms (0.9%)

simplify318.0ms (2.1%)

prune1.0s (6.7%)

localize26.0ms (0.2%)

series1.6s (10.1%)

rewrite100.0ms (0.6%)

simplify209.0ms (1.3%)

prune866.0ms (5.6%)

localize32.0ms (0.2%)

series865.0ms (5.6%)

rewrite237.0ms (1.5%)

simplify410.0ms (2.6%)

prune1.9s (12.3%)

localize13.0ms (0.1%)

series30.0ms (0.2%)

rewrite91.0ms (0.6%)

simplify97.0ms (0.6%)

prune69.0ms (0.4%)

regimes4.1s (26.4%)

bsearch18.0ms (0.1%)

simplify10.0ms (0.1%)

end274.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	25	646
1	49	644
2	83	584
3	106	584
4	123	554
5	150	494
6	164	494
7	202	494
8	212	494
9	221	494
10	240	494
11	253	494
12	275	494
13	292	404
14	289	404
15	295	404
16	297	404
17	298	404
18	292	404