Details

analyze43.0ms (1.4%)

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 (49.8%)

Results

604.0ms	5201×	body	128	valid
431.0ms	1123×	body	1024	valid
320.0ms	1158×	body	512	valid
146.0ms	739×	body	256	valid
15.0ms	35×	body	2048	valid
7.0ms	67×	body	128	invalid

Compiler

Compiled 60 to 40 computations (33.3% saved)

simplify15.0ms (0.5%)

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

24.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series20.0ms (0.6%)

Counts

1 → 16

Calls

1 calls:

20.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
19×	`*-un-lft-identity_binary64`
17×	`sqrt-prod_binary64`
17×	`add-cube-cbrt_binary64`

Counts

1 → 47

Calls

1 calls:

9.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

simplify87.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
530×	`div-sub_binary64`
335×	`fma-def_binary64`
308×	`associate-l_binary64`
272×	`associate-r_binary64`

Counts

63 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	1837
1	310	1328
2	846	1035
3	3299	1035
4	4385	1035
5	5158	1035

prune40.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
✓	24.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	36.1b	(*.f64 1/2 (/.f64 eps x))
	39.8b	(fma.f64 1/2 (/.f64 eps x) (.f64 1/8 (/.f64 (.f64 eps eps) (pow.f64 x 3))))
▶	13.3b	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

Compiler

Compiled 1997 to 510 computations (74.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series184.0ms (5.8%)

Counts

3 → 39

Calls

3 calls:

109.0ms	(/.f64 eps (+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
39.0ms	(+.f64 x (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))
36.0ms	(hypot.f64 (sqrt.f64 (neg.f64 eps)) x)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 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))
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 eps)) x)

simplify81.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
781×	`times-frac_binary64`
580×	`associate-/l*_binary64`
460×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`

Counts

101 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	2207
1	489	2027
2	1464	1923
3	4681	1919
4	5361	1919

prune68.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	24.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	13.5b	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))

Compiler

Compiled 2515 to 972 computations (61.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series94.0ms (3%)

Counts

2 → 32

Calls

2 calls:

75.0ms	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
19.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite13.0ms (0.4%)

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:

6.0ms	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
5.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-neg_binary64`
395×	`div-sub_binary64`
353×	`times-frac_binary64`
295×	`associate-/l*_binary64`
239×	`associate-/r*_binary64`

Counts

84 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1891
1	334	1777
2	925	1696
3	3646	1696
4	5060	1696

prune42.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	24.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	13.5b	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))

Compiler

Compiled 2168 to 576 computations (73.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
✓	0.1b	(sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))
✓	0.3b	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

series232.0ms (7.4%)

Counts

4 → 44

Calls

4 calls:

112.0ms	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))
50.0ms	(sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))
35.0ms	(+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
34.0ms	(*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`

Counts

4 → 115

Calls

4 calls:

6.0ms	(*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))
3.0ms	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))
2.0ms	(+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))))
1.0ms	(sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x))

simplify111.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-neg_binary64`
593×	`times-frac_binary64`
522×	`fma-def_binary64`
470×	`associate-/l*_binary64`
273×	`cancel-sign-sub-inv_binary64`

Counts

159 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3275
1	608	2942
2	1788	2774
3	4716	2770
4	5267	2770

prune177.0ms (5.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	255	3	258

Error

Counts

258 → 3

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	24.3b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	13.5b	(/.f64 eps (+.f64 x (*.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 eps)) x)))))

Compiler

Compiled 6301 to 1778 computations (71.8% saved)

regimes177.0ms (5.6%)

Accuracy

Total 0.3b remaining (95.3%)

Threshold costs 0.3b (95.3%)

Counts

52 → 1

Compiler

Compiled 2729 to 1445 computations (47.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	11	15
2	16	15
3	18	15
4	19	15
5	19	15

end48.0ms (1.5%)

Compiler: Compiled 65 to 36 computations (44.6% 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

analyze43.0ms (1.4%)

sample1.6s (49.8%)

simplify15.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series20.0ms (0.6%)

rewrite13.0ms (0.4%)

simplify87.0ms (2.8%)

prune40.0ms (1.3%)

localize6.0ms (0.2%)

series184.0ms (5.8%)

rewrite9.0ms (0.3%)

simplify81.0ms (2.6%)

prune68.0ms (2.2%)

localize6.0ms (0.2%)

series94.0ms (3%)

rewrite13.0ms (0.4%)

simplify75.0ms (2.4%)

prune42.0ms (1.3%)

localize8.0ms (0.3%)

series232.0ms (7.4%)

rewrite19.0ms (0.6%)

simplify111.0ms (3.5%)

prune177.0ms (5.6%)

regimes177.0ms (5.6%)

simplify4.0ms (0.1%)

end48.0ms (1.5%)

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