Details

analyze963.0ms (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
0%	56.2%	43.8%	3
0%	56.2%	43.8%	4
3.5%	52.7%	43.8%	5
7%	49.2%	43.8%	6
14%	42.1%	43.8%	7
15.8%	40.4%	43.8%	8
17.8%	38.4%	43.8%	9
18.8%	37.4%	43.8%	10
19.8%	36.4%	43.8%	11
20.3%	35.9%	43.8%	12
20.9%	35.3%	43.8%	13
21.4%	34.8%	43.8%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.7s (20%)

Results

698.0ms	6124×	body	128	valid
402.0ms	1025×	body	1024	valid
188.0ms	655×	body	512	valid
70.0ms	106×	body	2048	valid
67.0ms	346×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify211.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0%)

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

16.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.8b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series76.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

45.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
31.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
1.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune141.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
▶	16.3b	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)
	16.3b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	46.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	16.3b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 4343 to 2669 computations (38.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2)))
✓	0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
✓	0.0b	(/.f64 beta (+.f64 (+.f64 beta alpha) 2))
✓	2.8b	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)

series115.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

47.0ms	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)
27.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2)))
21.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
19.0ms	(/.f64 beta (+.f64 (+.f64 beta alpha) 2))

rewrite218.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1180×	`*-un-lft-identity_binary64`
716×	`times-frac_binary64`
441×	`prod-diff_binary64`
438×	`distribute-lft-out_binary64`
434×	`add-sqr-sqrt_binary64`

Counts

4 → 605

Calls

4 calls:

37.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2)))
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
6.0ms	(/.f64 beta (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)

simplify808.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

339×	`fma-def_binary64`
213×	`associate-*r/_binary64`
212×	`fma-udef_binary64`
208×	`sub-neg_binary64`
201×	`times-frac_binary64`

Counts

701 → 605

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	743	53503
1	2053	30885
2	4562	29928
3	4962	29928
4	4980	29928

prune709.0ms (8.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	604	1	605
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	605	4	609

Error

0.0b

Counts

609 → 4

Alt Table

Status	Error	Program
▶	16.3b	(exp.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))
	46.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	16.3b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	16.3b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 32189 to 18302 computations (43.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 beta (+.f64 (+.f64 beta alpha) 2))
✓	0.2b	(exp.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))
✓	1.8b	(log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))
	2.8b	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)

series219.0ms (2.6%)

Counts

2 → 48

Calls

2 calls:

172.0ms

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

46.0ms

(exp.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

(exp.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))

1.0ms

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

simplify110.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

594×	`times-frac_binary64`
585×	`associate-/r*_binary64`
539×	`fma-def_binary64`
383×	`associate-/l*_binary64`
182×	`+-commutative_binary64`

Counts

79 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	6648
1	1885	6344
2	5229	6344

prune331.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	245	4	249

Error

0.0b

Counts

249 → 4

Alt Table

Status	Error	Program
▶	16.3b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))))
	46.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	16.3b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	16.3b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 13120 to 9097 computations (30.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))))
✓	0.5b	(*.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))
	1.8b	(log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))
	2.8b	(fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)

series767.0ms (9%)

Counts

2 → 48

Calls

2 calls:

600.0ms

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

166.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`log-prod_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms

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

3.0ms

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

simplify227.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

472×	`+-commutative_binary64`
418×	`associate-+r+_binary64`
388×	`fma-def_binary64`
350×	`*-commutative_binary64`
255×	`associate-*r/_binary64`

Counts

98 → 141

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1248	18200
1	4836	17018
2	5062	17018

prune1.3s (14.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	465	0	465
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	465	4	469

Error

0.0b

Counts

469 → 4

Alt Table

Status	Error	Program
✓	16.3b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2))) (log.f64 (fma.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 beta (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)))))
	46.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	16.3b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	16.3b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 62328 to 43575 computations (30.1% saved)

regimes358.0ms (4.2%)

Accuracy

Total 0.2b remaining (74.9%)

Threshold costs 0.2b (74.9%)

Counts

55 → 2

Compiler

Compiled 5905 to 4316 computations (26.9% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	89
1	44	89
2	60	89
3	77	89
4	86	89
5	89	89
6	87	89

end142.0ms (1.7%)

Compiler: Compiled 249 to 149 computations (40.2% saved)

Details

analyze963.0ms (11.3%)

sample1.7s (20%)

simplify211.0ms (2.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series76.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify108.0ms (1.3%)

prune141.0ms (1.6%)

localize9.0ms (0.1%)

series115.0ms (1.3%)

rewrite218.0ms (2.5%)

simplify808.0ms (9.5%)

prune709.0ms (8.3%)

localize12.0ms (0.1%)

series219.0ms (2.6%)

rewrite4.0ms (0.1%)

simplify110.0ms (1.3%)

prune331.0ms (3.9%)

localize15.0ms (0.2%)

series767.0ms (9%)

rewrite14.0ms (0.2%)

simplify227.0ms (2.7%)

prune1.3s (14.6%)

regimes358.0ms (4.2%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end142.0ms (1.7%)

Profiling