Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.8s (36.5%)

Results

736.0ms	6132×	body	128	valid
460.0ms	1098×	body	1024	valid
177.0ms	609×	body	512	valid
66.0ms	319×	body	256	valid
64.0ms	98×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify209.0ms (4.3%)

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

17.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.2b	(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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series58.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
21.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite15.0ms (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:

10.0ms	(/.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)

simplify102.0ms (2.1%)

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

prune110.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
✓	17.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	45.7b	(-.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 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
▶	45.3b	(-.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)))))

Compiler

Compiled 4371 to 2675 computations (38.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	3.3b	(-.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)))))
✓	3.4b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	8.6b	(/.f64 beta (*.f64 alpha alpha))

series146.0ms (3%)

Counts

4 → 96

Calls

4 calls:

41.0ms	(-.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)))))
41.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
33.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
30.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite60.0ms (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:

22.0ms	(-.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)))))
7.0ms	(+.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)))

simplify220.0ms (4.5%)

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

prune169.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	203	3	206

Error

Counts

206 → 3

Alt Table

Status	Error	Program
✓	17.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
▶	45.7b	(-.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 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	45.3b	(-.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)))))

Compiler

Compiled 11569 to 4225 computations (63.5% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.9b	(+.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))))))
	8.6b	(/.f64 beta (*.f64 alpha alpha))
✓	13.0b	(-.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 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	14.6b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

series163.0ms (3.3%)

Counts

3 → 72

Calls

3 calls:

62.0ms

(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

56.0ms

(-.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 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

45.0ms

(+.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))))))

rewrite150.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

261×	`*-un-lft-identity_binary64`
155×	`distribute-lft-out_binary64`
53×	`add-log-exp_binary64`
49×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`

Counts

3 → 215

Calls

3 calls:

58.0ms

(-.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 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

22.0ms

(+.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))))))

5.0ms

(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))

simplify506.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

527×	`distribute-rgt-in_binary64`
505×	`distribute-lft-in_binary64`
346×	`fma-def_binary64`
171×	`fma-neg_binary64`
133×	`times-frac_binary64`

Counts

287 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	21708
1	1408	20079
2	4842	20079
3	4992	20079
4	4978	20079

prune553.0ms (11.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	261	3	264

Error

Counts

264 → 3

Alt Table

Status	Error	Program
✓	17.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	45.7b	(-.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 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	45.3b	(-.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)))))

Compiler

Compiled 27890 to 14347 computations (48.6% saved)

regimes478.0ms (9.8%)

Accuracy

Total 0.0b remaining (50.2%)

Threshold costs 0.0b (50.2%)

Counts

50 → 2

Compiler

Compiled 6580 to 4301 computations (34.6% saved)

bsearch2.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-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	40	104
1	52	104
2	66	104
3	81	104
4	88	104
5	90	104
6	88	104

end101.0ms (2.1%)

Compiler: Compiled 249 to 146 computations (41.4% saved)

Details

analyze2.0ms (0%)

sample1.8s (36.5%)

simplify209.0ms (4.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series58.0ms (1.2%)

rewrite15.0ms (0.3%)

simplify102.0ms (2.1%)

prune110.0ms (2.3%)

localize13.0ms (0.3%)

series146.0ms (3%)

rewrite60.0ms (1.2%)

simplify220.0ms (4.5%)

prune169.0ms (3.5%)

localize30.0ms (0.6%)

series163.0ms (3.3%)

rewrite150.0ms (3.1%)

simplify506.0ms (10.3%)

prune553.0ms (11.3%)

regimes478.0ms (9.8%)

bsearch2.0ms (0%)

simplify6.0ms (0.1%)

end101.0ms (2.1%)

Profiling