Details

analyze55.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample16.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms	249×	body	128	valid
0.0ms	3×	body	1024	valid
0.0ms	1×	body	2048	valid
0.0ms	2×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-neg_binary64`
32×	`cancel-sign-sub-inv_binary64`
30×	`fma-def_binary64`
29×	`sub-neg_binary64`
17×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

Compiler

Compiled 35 to 21 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-neg-out_binary64`
515×	`neg-mul-1_binary64`
507×	`neg-sub0_binary64`
481×	`distribute-rgt-out_binary64`
469×	`*-commutative_binary64`

Counts

34 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	374
1	26	353
2	55	353
3	125	353
4	320	353
5	990	353
6	1892	353
7	2461	353
8	3898	353
9	5066	353

prune24.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

0.0b

Counts

22 → 3

Alt Table

Status	Error	Program
	17.5b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 345 to 162 computations (53% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.6b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

series1.6s (23.1%)

Counts

3 → 72

Calls

3 calls:

830.0ms

(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

755.0ms

(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

11.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite50.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

14.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

9.0ms

(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

6.0ms

(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify198.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
393×	`*-commutative_binary64`
356×	`cancel-sign-sub-inv_binary64`
338×	`unswap-sqr_binary64`
309×	`fma-neg_binary64`

Counts

165 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3620
1	483	3205
2	1465	3016
3	3985	2880
4	5033	2880

prune420.0ms (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	334	4	338

Error

0.0b

Counts

338 → 4

Alt Table

Status	Error	Program
▶	17.5b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	29.5b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 11733 to 5790 computations (50.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	0.0b	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

series55.0ms (0.8%)

Counts

2 → 40

Calls

2 calls:

43.0ms	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
12.0ms	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
2.0ms	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify101.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
581×	`fma-def_binary64`
306×	`distribute-lft-in_binary64`
304×	`distribute-rgt-in_binary64`
283×	`fma-neg_binary64`

Counts

108 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1747
1	180	1580
2	499	1518
3	1804	1478
4	4926	1478
5	5056	1478

prune143.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	170	7	177

Error

0.0b

Counts

177 → 7

Alt Table

Status	Error	Program
✓	17.5b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	29.5b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	17.8b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 3))
▶	17.6b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	31.1b	(.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))

Compiler

Compiled 4364 to 2163 computations (50.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.1b	(sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

series1.8s (26.4%)

Counts

3 → 72

Calls

3 calls:

1.1s

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

669.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

8.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`sqrt-pow1_binary64`
51×	`pow1_binary64`
47×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
36×	`pow-prod-up_binary64`

Counts

3 → 121

Calls

3 calls:

21.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

11.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

2.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

simplify220.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
420×	`fma-neg_binary64`
385×	`times-frac_binary64`
250×	`associate-/r*_binary64`
238×	`associate-/l*_binary64`

Counts

193 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	4169
1	545	3787
2	1604	3639
3	4899	3637
4	5205	3637

prune553.0ms (8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	352	7	359

Error

Counts

359 → 7

Alt Table

Status	Error	Program
✓	17.5b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	31.1b	(.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
	17.8b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	17.8b	(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 3))
✓	17.6b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

Compiler

Compiled 13274 to 7189 computations (45.8% saved)

regimes311.0ms (4.5%)

Accuracy

Total 0.0b remaining (61.8%)

Threshold costs 0.0b (61.8%)

Counts

38 → 1

Compiler

Compiled 2744 to 1735 computations (36.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	7	10
1	11	10
2	18	10
3	23	10
4	26	10
5	27	10
6	27	10

end1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample1.1s (15.6%)

Algorithm

1×

intervals

Results

462.0ms	7717×	body	128	valid
24.0ms	82×	body	2048	valid
22.0ms	99×	body	1024	valid
13.0ms	77×	body	512	valid
4.0ms	25×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 221 to 129 computations (41.6% saved)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Details

analyze55.0ms (0.8%)

sample16.0ms (0.2%)

simplify17.0ms (0.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify94.0ms (1.4%)

prune24.0ms (0.3%)

localize18.0ms (0.3%)

series1.6s (23.1%)

rewrite50.0ms (0.7%)

simplify198.0ms (2.9%)

prune420.0ms (6.1%)

localize13.0ms (0.2%)

series55.0ms (0.8%)

rewrite21.0ms (0.3%)

simplify101.0ms (1.5%)

prune143.0ms (2.1%)

localize13.0ms (0.2%)

series1.8s (26.4%)

rewrite59.0ms (0.8%)

simplify220.0ms (3.2%)

prune553.0ms (8%)

regimes311.0ms (4.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (15.6%)

Profiling

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10