Details

analyze272.0ms (6.9%)

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)

sample47.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms	183×	body	128	valid
6.0ms	38×	body	1024	valid
5.0ms	256×	pre	128	true
2.0ms	20×	body	512	valid
1.0ms	13×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify274.0ms (6.9%)

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

17.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.8b	(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 (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite15.0ms (0.4%)

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)

series53.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
19.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

simplify108.0ms (2.7%)

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 → 206

Iterations

Useful iterations: 2 (0.0ms)

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

prune138.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	200	6	206
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	201	6	207

Error

0.1b

Counts

207 → 6

Alt Table

Status	Error	Program
	18.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	17.8b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
▶	17.8b	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)
	44.8b	(-.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)))))
	43.8b	(/.f64 (+.f64 beta 1) alpha)
	17.8b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 4437 to 2733 computations (38.4% saved)

localize15.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha)))
✓	1.9b	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
96×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
44×	`distribute-lft-out--_binary64`
38×	`add-cube-cbrt_binary64`

Counts

2 → 134

Calls

2 calls:

11.0ms	(/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha)))
0.0ms	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)

series60.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)
22.0ms	(/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha)))

simplify156.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

496×	`sub-neg_binary64`
230×	`div-sub_binary64`
220×	`+-commutative_binary64`
197×	`fma-def_binary64`
195×	`fma-neg_binary64`

Counts

182 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	390	5963
1	1133	5825
2	4070	5781
3	5270	5781

prune129.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	280	6	286

Error

0.1b

Counts

286 → 6

Alt Table

Status	Error	Program
	18.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	17.8b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	17.8b	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)
	44.8b	(-.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)))))
	43.8b	(/.f64 (+.f64 beta 1) alpha)
▶	17.8b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 5168 to 2912 computations (43.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.9b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
✓	5.9b	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64`
62×	`exp-prod_binary64`
50×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
32×	`log-pow_binary64`

Counts

3 → 98

Calls

3 calls:

11.0ms

(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))

10.0ms

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

0.0ms

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

series126.0ms (3.2%)

Counts

3 → 72

Calls

3 calls:

57.0ms

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

37.0ms

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

32.0ms

(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))

simplify116.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

320×	`fma-def_binary64`
310×	`times-frac_binary64`
262×	`associate-+l+_binary64`
254×	`associate-/r*_binary64`
236×	`associate-/l*_binary64`

Counts

170 → 322

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	500	5750
1	1450	5592
2	5177	5592

prune279.0ms (7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	469	0	469
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	469	6	475

Error

0.1b

Counts

475 → 6

Alt Table

Status	Error	Program
	18.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (cbrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
▶	17.8b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	17.8b	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)
	44.8b	(-.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)))))
	43.8b	(/.f64 (+.f64 beta 1) alpha)
✓	17.8b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 10483 to 6648 computations (36.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.9b	(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×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series99.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

57.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
42.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify116.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

350×	`sub-neg_binary64`
288×	`times-frac_binary64`
247×	`associate-+r+_binary64`
240×	`+-commutative_binary64`
239×	`fma-def_binary64`

Counts

80 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4055
1	1082	3907
2	4529	3863
3	5124	3863

prune264.0ms (6.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	492	2	494
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	494	6	500

Error

0.0b

Counts

500 → 6

Alt Table

Status	Error	Program
	18.3b	(*.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	32.5b	(-.f64 (+.f64 (log.f64 (exp.f64 (-.f64 1/2 (.f64 1/2 (/.f64 alpha (+.f64 2 alpha)))))) (+.f64 (.f64 1/2 (/.f64 beta (+.f64 2 alpha))) (.f64 1/2 (/.f64 (.f64 beta alpha) (pow.f64 (+.f64 2 alpha) 2))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 beta 2) alpha) (pow.f64 (+.f64 2 alpha) 3))) (*.f64 1/2 (/.f64 (pow.f64 beta 2) (pow.f64 (+.f64 2 alpha) 2)))))
✓	17.8b	(fma.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (-.f64 -2 (+.f64 beta alpha))) -1/2 1/2)
	44.8b	(-.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)))))
	43.8b	(/.f64 (+.f64 beta 1) alpha)
✓	17.8b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 9231 to 6125 computations (33.6% saved)

regimes431.0ms (10.9%)

Accuracy

Total 0.1b remaining (63.7%)

Threshold costs 0.1b (63.7%)

Compiler

Compiled 5852 to 4483 computations (23.4% saved)

bsearch2.0ms (0.1%)

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

simplify5.0ms (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

end1.0ms (0%)

Compiler: Compiled 56 to 32 computations (42.9% saved)

sample1.2s (29.5%)

Algorithm

1×

intervals

Results

265.0ms	5926×	body	128	valid
169.0ms	1047×	body	1024	valid
159.0ms	8000×	pre	128	true
76.0ms	621×	body	512	valid
31.0ms	109×	body	2048	valid
25.0ms	297×	body	256	valid

Compiler

Compiled 240 to 163 computations (32.1% saved)

Details

analyze272.0ms (6.9%)

sample47.0ms (1.2%)

simplify274.0ms (6.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite15.0ms (0.4%)

series53.0ms (1.3%)

simplify108.0ms (2.7%)

prune138.0ms (3.5%)

localize15.0ms (0.4%)

rewrite24.0ms (0.6%)

series60.0ms (1.5%)

simplify156.0ms (3.9%)

prune129.0ms (3.3%)

localize12.0ms (0.3%)

rewrite29.0ms (0.7%)

series126.0ms (3.2%)

simplify116.0ms (2.9%)

prune279.0ms (7%)

localize11.0ms (0.3%)

rewrite5.0ms (0.1%)

series99.0ms (2.5%)

simplify116.0ms (2.9%)

prune264.0ms (6.6%)

regimes431.0ms (10.9%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (29.5%)

Profiling