Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample2.0s (70.7%)

Results

813.0ms	5521×	body	128	valid
472.0ms	935×	body	1024	valid
402.0ms	1086×	body	512	valid
168.0ms	690×	body	256	valid
18.0ms	24×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

512×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
429×	`fma-def_binary64`
372×	`unswap-sqr_binary64`
314×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	45	13
3	143	13
4	475	8
5	1778	8
6	4244	8
7	4680	8
8	4952	8
9	4802	8

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))
	17.1b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 eps (fma.f64 2 x eps))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

7.0ms

(*.f64 eps (fma.f64 2 x eps))

simplify78.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
610×	`distribute-lft-in_binary64`
426×	`fma-def_binary64`
354×	`*-commutative_binary64`
330×	`associate-/l/_binary64`

Counts

46 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	507
1	84	413
2	239	413
3	617	413
4	2304	413
5	2439	413
6	3040	413
7	4552	413
8	4968	413

prune21.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
	8.4b	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))
▶	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))

Compiler

Compiled 402 to 227 computations (43.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
✓	0.0b	(.f64 2 (.f64 eps x))

series13.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
6.0ms	(.f64 2 (.f64 eps x))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
4.0ms	(.f64 2 (.f64 eps x))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
514×	`associate-l_binary64`
373×	`associate-r_binary64`
301×	`distribute-rgt-out_binary64`
274×	`distribute-rgt-in_binary64`

Counts

40 → 46

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	461
1	164	431
2	506	410
3	1775	410
4	4269	408
5	4971	408

prune29.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	8.4b	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))
✓	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))

Compiler

Compiled 739 to 467 computations (36.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	0.1b	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))
✓	15.6b	(sqrt.f64 (*.f64 eps (fma.f64 2 x eps)))

series46.0ms (1.6%)

Counts

2 → 36

Calls

2 calls:

27.0ms	(sqrt.f64 (*.f64 eps (fma.f64 2 x eps)))
19.0ms	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
11×	`pow1/2_binary64`
10×	`pow-prod-up_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))
3.0ms	(sqrt.f64 (*.f64 eps (fma.f64 2 x eps)))

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
554×	`times-frac_binary64`
542×	`unswap-sqr_binary64`
486×	`associate-l_binary64`
330×	`associate-r_binary64`

Counts

100 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	1106
1	157	984
2	492	937
3	2171	901
4	3956	828
5	4793	828
6	4948	828

prune123.0ms (4.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	193	3	196

Error

Counts

196 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
✓	8.4b	(.f64 (sqrt.f64 (.f64 eps (fma.f64 2 x eps))) (sqrt.f64 (*.f64 eps (fma.f64 2 x eps))))
✓	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))

Compiler

Compiled 3607 to 2203 computations (38.9% saved)

regimes110.0ms (3.9%)

Accuracy

Total 0.0b remaining (73.6%)

Threshold costs 0.0b (73.6%)

Counts

18 → 1

Compiler

Compiled 688 to 477 computations (30.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end107.0ms (3.8%)

Compiler: Compiled 52 to 34 computations (34.6% saved)

Details

analyze2.0ms (0.1%)

sample2.0s (70.7%)

simplify86.0ms (3.1%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify78.0ms (2.8%)

prune21.0ms (0.7%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite10.0ms (0.4%)

simplify56.0ms (2%)

prune29.0ms (1%)

localize7.0ms (0.2%)

series46.0ms (1.6%)

rewrite14.0ms (0.5%)

simplify86.0ms (3.1%)

prune123.0ms (4.4%)

regimes110.0ms (3.9%)

simplify2.0ms (0.1%)

end107.0ms (3.8%)

Profiling