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)

sample1.7s (38%)

Results

708.0ms	6179×	body	128	valid
429.0ms	1084×	body	1024	valid
171.0ms	593×	body	512	valid
83.0ms	109×	body	2048	valid
66.0ms	291×	body	256	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify211.0ms (4.6%)

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

19.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series50.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms	(/.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)

simplify87.0ms (1.9%)

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

prune104.0ms (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

0.0b

Counts

143 → 3

Alt Table

Status	Error	Program
✓	19.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
▶	41.9b	(/.f64 (+.f64 beta 1) alpha)
	42.8b	(-.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)))))

Compiler

Compiled 4267 to 2615 computations (38.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 beta 1) alpha)

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(/.f64 (+.f64 beta 1) alpha)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 35

Calls

1 calls:

4.0ms

(/.f64 (+.f64 beta 1) alpha)

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
554×	`distribute-lft-in_binary64`
413×	`associate-+l+_binary64`
338×	`unsub-neg_binary64`
305×	`associate-+r+_binary64`

Counts

47 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	585
1	134	551
2	294	551
3	688	518
4	1731	518
5	3257	518
6	4763	518
7	5090	518

prune25.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	57	3	60

Error

0.0b

Counts

60 → 3

Alt Table

Status	Error	Program
✓	19.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	41.9b	(/.f64 (+.f64 beta 1) alpha)
▶	42.8b	(-.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)))))

Compiler

Compiled 751 to 476 computations (36.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	2.2b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	3.8b	(-.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)))))
✓	5.2b	(/.f64 beta (*.f64 alpha alpha))

series131.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

38.0ms	(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))))
27.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite61.0ms (1.3%)

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:

23.0ms	(-.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)))

simplify232.0ms (5.1%)

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

prune187.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	203	3	206

Error

Counts

206 → 3

Alt Table

Status	Error	Program
▶	43.0b	(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))))))
✓	19.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	41.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 11506 to 4185 computations (63.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(-.f64 (/.f64 -2 (.f64 alpha alpha)) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 3 (.f64 beta (/.f64 beta (.f64 alpha alpha)))))
✓	3.6b	(sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))
✓	4.6b	(.f64 beta (/.f64 beta (.f64 alpha alpha)))
	5.2b	(/.f64 beta (*.f64 alpha alpha))

series126.0ms (2.8%)

Counts

3 → 52

Calls

3 calls:

50.0ms

(sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))

40.0ms

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

36.0ms

(-.f64 (/.f64 -2 (*.f64 alpha alpha)) (fma.f64 (/.f64 beta (*.f64 alpha alpha)) 3 (*.f64 beta (/.f64 beta (*.f64 alpha alpha)))))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 111

Calls

3 calls:

12.0ms

(sqrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))

6.0ms

(-.f64 (/.f64 -2 (*.f64 alpha alpha)) (fma.f64 (/.f64 beta (*.f64 alpha alpha)) 3 (*.f64 beta (/.f64 beta (*.f64 alpha alpha)))))

6.0ms

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

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
626×	`associate-/l*_binary64`
249×	`distribute-rgt-in_binary64`
224×	`distribute-lft-in_binary64`
162×	`cancel-sign-sub-inv_binary64`

Counts

163 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	4403
1	504	3100
2	1677	2649
3	4889	2649

prune199.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	265	3	268

Error

Counts

268 → 3

Alt Table

Status	Error	Program
✓	43.0b	(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))))))
✓	19.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	41.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 13161 to 5296 computations (59.8% saved)

regimes1.1s (23.2%)

Accuracy

Total 0.1b remaining (55%)

Threshold costs 0.1b (55%)

Counts

126 → 2

Compiler

Compiled 21870 to 11771 computations (46.2% saved)

bsearch6.0ms (0.1%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	63
1	33	63
2	40	63
3	44	63
4	46	63
5	45	63

end68.0ms (1.5%)

Compiler: Compiled 150 to 89 computations (40.7% saved)

Details

analyze2.0ms (0%)

sample1.7s (38%)

simplify211.0ms (4.6%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series50.0ms (1.1%)

rewrite14.0ms (0.3%)

simplify87.0ms (1.9%)

prune104.0ms (2.3%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.7%)

prune25.0ms (0.6%)

localize14.0ms (0.3%)

series131.0ms (2.9%)

rewrite61.0ms (1.3%)

simplify232.0ms (5.1%)

prune187.0ms (4.1%)

localize18.0ms (0.4%)

series126.0ms (2.8%)

rewrite41.0ms (0.9%)

simplify90.0ms (2%)

prune199.0ms (4.3%)

regimes1.1s (23.2%)

bsearch6.0ms (0.1%)

simplify3.0ms (0.1%)

end68.0ms (1.5%)

Profiling