Details

analyze48.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.8%	87.2%	0
0%	12.8%	87.2%	1
0%	12.8%	87.2%	2
6.4%	6.4%	87.2%	3
6.4%	4.8%	88.8%	4
7.2%	3.2%	89.6%	5
7.2%	2.4%	90.4%	6
7.6%	1.6%	90.8%	7
7.6%	1.2%	91.2%	8
7.8%	0.8%	91.4%	9
7.8%	0.6%	91.5%	10
7.9%	0.4%	91.7%	11
8%	0.3%	91.7%	12
8.1%	0.2%	91.7%	13
8.1%	0.2%	91.8%	14

Compiler

Compiled 25 to 17 computations (32% saved)

sample1.6s (36.2%)

Results

599.0ms	5261×	body	128	valid
388.0ms	1073×	body	1024	valid
319.0ms	1159×	body	512	valid
173.0ms	729×	body	256	valid
19.0ms	34×	body	2048	valid
8.0ms	77×	body	128	invalid

Compiler

Compiled 60 to 40 computations (33.3% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

22.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	4.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series29.0ms (0.7%)

Counts

2 → 40

Calls

2 calls:

21.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
8.0ms	(-.f64 (*.f64 x x) eps)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_binary64`

Counts

2 → 68

Calls

2 calls:

6.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
3.0ms	(-.f64 (*.f64 x x) eps)

simplify112.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-neg_binary64`
538×	`fma-def_binary64`
326×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`
229×	`*-commutative_binary64`

Counts

108 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	2317
1	385	1758
2	1206	1434
3	4073	1426
4	4866	1426
5	4990	1426
6	4814	1426

prune70.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	6	116

Error

0.0b

Counts

116 → 6

Alt Table

Status	Error	Program
	48.0b	(fma.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3)) (fma.f64 1/2 (/.f64 eps x) (.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)))))
▶	12.8b	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
	41.8b	(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
	37.7b	(*.f64 1/2 (/.f64 eps x))
	29.7b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
	22.3b	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))

Compiler

Compiled 2608 to 743 computations (71.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))
✓	0.3b	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

series162.0ms (3.8%)

Counts

2 → 26

Calls

2 calls:

116.0ms	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
46.0ms	(+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
2.0ms	(+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
560×	`times-frac_binary64`
438×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`
296×	`fma-def_binary64`

Counts

78 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1885
1	426	1696
2	1266	1605
3	4697	1601
4	5307	1601

prune51.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Error

Counts

99 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
	13.0b	(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
	40.9b	(/.f64 eps (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2))))
	37.1b	(/.f64 eps (fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2)))
▶	12.8b	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))
	13.7b	(/.f64 (*.f64 (cbrt.f64 eps) (cbrt.f64 eps)) (/.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (cbrt.f64 eps)))

Compiler

Compiled 2015 to 749 computations (62.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x)
✓	0.3b	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))

series152.0ms (3.5%)

Counts

2 → 26

Calls

2 calls:

113.0ms	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))
39.0ms	(+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))
2.0ms	(+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x)

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-neg_binary64`
560×	`times-frac_binary64`
438×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`
294×	`fma-def_binary64`

Counts

78 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1892
1	426	1703
2	1266	1605
3	4701	1601
4	5312	1601

prune58.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	121	6	127

Error

Counts

127 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
▶	13.0b	(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
	40.9b	(/.f64 eps (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2))))
	37.1b	(/.f64 eps (fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2)))
✓	12.8b	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))
	13.7b	(/.f64 (*.f64 (cbrt.f64 eps) (cbrt.f64 eps)) (/.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (cbrt.f64 eps)))

Compiler

Compiled 2539 to 821 computations (67.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))
✓	0.1b	(sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
✓	0.2b	(/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
✓	0.3b	(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))

series367.0ms (8.6%)

Counts

3 → 23

Calls

3 calls:

166.0ms

(/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))

117.0ms

(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))

78.0ms

(sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac_binary64`
302×	`*-un-lft-identity_binary64`
228×	`sqrt-prod_binary64`
191×	`add-sqr-sqrt_binary64`
188×	`add-cube-cbrt_binary64`

Counts

3 → 308

Calls

3 calls:

13.0ms

(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))

5.0ms

(/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))

3.0ms

(sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

simplify336.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
595×	`associate-/l/_binary64`
574×	`associate-/l*_binary64`
395×	`fma-neg_binary64`
333×	`fma-def_binary64`

Counts

331 → 327

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	16048
1	822	14646
2	1956	13582
3	4789	13580
4	5020	13580

prune168.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	429	0	429
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	429	6	435

Error

Counts

435 → 6

Alt Table

Status	Error	Program
	22.3b	(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))
✓	13.0b	(/.f64 (/.f64 eps (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))) (sqrt.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
	40.9b	(/.f64 eps (fma.f64 (/.f64 (.f64 eps eps) (pow.f64 x 3)) -1/8 (fma.f64 x 2 (.f64 (/.f64 eps x) -1/2))))
	37.1b	(/.f64 eps (fma.f64 x 2 (*.f64 (/.f64 eps x) -1/2)))
✓	12.8b	(/.f64 eps (+.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x) x))
	13.7b	(/.f64 (*.f64 (cbrt.f64 eps) (cbrt.f64 eps)) (/.f64 (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (cbrt.f64 eps)))

Compiler

Compiled 14722 to 2514 computations (82.9% saved)

regimes762.0ms (17.8%)

Accuracy

Total 0.8b remaining (94.1%)

Threshold costs 0.8b (94.1%)

Counts

70 → 2

Compiler

Compiled 4196 to 2179 computations (48.1% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 10 to 6 computations (40% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	48
1	35	48
2	41	48
3	44	48
4	45	48
5	43	48

end114.0ms (2.7%)

Compiler: Compiled 161 to 98 computations (39.1% saved)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

Details

analyze48.0ms (1.1%)

sample1.6s (36.2%)

simplify13.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series29.0ms (0.7%)

rewrite14.0ms (0.3%)

simplify112.0ms (2.6%)

prune70.0ms (1.6%)

localize6.0ms (0.1%)

series162.0ms (3.8%)

rewrite9.0ms (0.2%)

simplify76.0ms (1.8%)

prune51.0ms (1.2%)

localize9.0ms (0.2%)

series152.0ms (3.5%)

rewrite9.0ms (0.2%)

simplify73.0ms (1.7%)

prune58.0ms (1.3%)

localize8.0ms (0.2%)

series367.0ms (8.6%)

rewrite79.0ms (1.8%)

simplify336.0ms (7.8%)

prune168.0ms (3.9%)

regimes762.0ms (17.8%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end114.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12