Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
56.2%	0%	43.8%	1

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.6s (30.7%)

Results

797.0ms	6133×	body	128	valid
313.0ms	1120×	body	1024	valid
119.0ms	571×	body	512	valid
49.0ms	343×	body	256	valid
28.0ms	89×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify204.0ms (4%)

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 (0.1%)

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

16.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.5b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.5b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series55.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
22.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite14.0ms (0.3%)

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

simplify89.0ms (1.7%)

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

prune109.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	3	143

Error

0.1b

Counts

143 → 3

Alt Table

Status	Error	Program
	45.5b	(-.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)))))
▶	16.5b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	48.0b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 4467 to 2745 computations (38.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.2b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	1.9b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	2.5b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series204.0ms (3.9%)

Counts

2 → 48

Calls

2 calls:

171.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
32.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite5.0ms (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 beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify95.0ms (1.8%)

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	556	6288
1	1886	6047
2	5229	6047

prune282.0ms (5.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	258	4	262

Error

0.1b

Counts

262 → 4

Alt Table

Status	Error	Program
▶	45.5b	(-.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)))))
	47.4b	(exp.f64 (log.f64 (-.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)))))))
	49.6b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	16.5b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 13209 to 9105 computations (31.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.1b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	2.8b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	4.8b	(-.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)))))
✓	9.4b	(/.f64 beta (*.f64 alpha alpha))

series136.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
35.0ms	(-.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)))))
31.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
29.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite64.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
48×	`prod-diff_binary64`
46×	`distribute-lft-out_binary64`
41×	`times-frac_binary64`
38×	`add-sqr-sqrt_binary64`

Counts

4 → 150

Calls

4 calls:

26.0ms	(-.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)))))
5.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
3.0ms	(/.f64 beta (*.f64 alpha alpha))
0.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))

simplify215.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
502×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
192×	`distribute-rgt-neg-in_binary64`
161×	`distribute-rgt-in_binary64`

Counts

246 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	10949
1	623	9056
2	2377	7436
3	4711	7436
4	4930	7436

prune189.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	203	4	207

Error

0.1b

Counts

207 → 4

Alt Table

Status	Error	Program
	45.8b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 3 (.f64 beta (/.f64 beta (.f64 alpha alpha))))))
▶	45.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))
	49.6b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	16.5b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 12353 to 4776 computations (61.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.1b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	4.8b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))
✓	6.7b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))
	9.4b	(/.f64 beta (*.f64 alpha alpha))

series78.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

44.0ms

(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))

34.0ms

(+.f64 (/.f64 2 (*.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))

rewrite66.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`*-un-lft-identity_binary64`
70×	`distribute-lft-out_binary64`
60×	`prod-diff_binary64`
45×	`times-frac_binary64`
40×	`div-inv_binary64`

Counts

2 → 137

Calls

2 calls:

24.0ms

(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))

7.0ms

(+.f64 (/.f64 2 (*.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))

simplify211.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
334×	`times-frac_binary64`
275×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-neg-in_binary64`
185×	`associate-/l*_binary64`

Counts

185 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	11456
1	556	9205
2	2283	5785
3	4502	5771
4	4938	5771

prune191.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	209	4	213

Error

0.1b

Counts

213 → 4

Alt Table

Status	Error	Program
	45.8b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (neg.f64 (+.f64 (/.f64 2 (.f64 alpha alpha)) (log.f64 (exp.f64 (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))
	49.6b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	16.5b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	45.5b	(+.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (.f64 (/.f64 beta (*.f64 alpha alpha)) (+.f64 3 beta))))

Compiler

Compiled 12292 to 5219 computations (57.5% saved)

regimes1.0s (19.5%)

Accuracy

Total 0.0b remaining (5.3%)

Threshold costs 0.0b (5.3%)

Counts

119 → 2

Compiler

Compiled 23544 to 13965 computations (40.7% saved)

bsearch8.0ms (0.2%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	43	80
2	57	80
3	72	80
4	79	80
5	81	80
6	79	80

end296.0ms (5.7%)

Compiler: Compiled 589 to 394 computations (33.1% saved)

Details

analyze1.0ms (0%)

sample1.6s (30.7%)

simplify204.0ms (4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series55.0ms (1.1%)

rewrite14.0ms (0.3%)

simplify89.0ms (1.7%)

prune109.0ms (2.1%)

localize11.0ms (0.2%)

series204.0ms (3.9%)

rewrite5.0ms (0.1%)

simplify95.0ms (1.8%)

prune282.0ms (5.5%)

localize14.0ms (0.3%)

series136.0ms (2.6%)

rewrite64.0ms (1.2%)

simplify215.0ms (4.2%)

prune189.0ms (3.7%)

localize16.0ms (0.3%)

series78.0ms (1.5%)

rewrite66.0ms (1.3%)

simplify211.0ms (4.1%)

prune191.0ms (3.7%)

regimes1.0s (19.5%)

bsearch8.0ms (0.2%)

simplify6.0ms (0.1%)

end296.0ms (5.7%)

Profiling