Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	50%	50%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample798.0ms (53%)

Results

760.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	14	11
3	12	11

prune1.0ms (0.1%)

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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series11.0ms (0.7%)

Counts

1 → 4

Calls

1 calls:

11.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite67.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
10×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`
6×	`associate-r_binary64`

Counts

1 → 39

Calls

1 calls:

7.0ms

(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

simplify93.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-neg_binary64`
626×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
314×	`associate-l_binary64`
262×	`associate-/r*_binary64`

Counts

43 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	590
1	146	578
2	355	578
3	725	578
4	1829	568
5	4473	568
6	4973	568

prune69.0ms (4.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	2	52

Error

Counts

52 → 2

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
▶	0.5b	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))

Compiler

Compiled 692 to 454 computations (34.4% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
✓	0.0b	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
✓	0.5b	(/.f64 1/16 (*.f64 x x))

series8.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
3.0ms	(/.f64 1/16 (*.f64 x x))
2.0ms	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))

rewrite79.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
16×	`distribute-lft-out_binary64`
15×	`prod-diff_binary64`

Counts

3 → 94

Calls

3 calls:

57.0ms	(+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))
13.0ms	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
3.0ms	(/.f64 1/16 (*.f64 x x))

simplify153.0ms (10.1%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-def_binary64`
505×	`distribute-rgt-in_binary64`
481×	`distribute-lft-in_binary64`
343×	`times-frac_binary64`
291×	`fma-neg_binary64`

Counts

130 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2404
1	338	2026
2	1158	1744
3	4666	1744
4	4930	1744

prune105.0ms (7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	129	2	131

Error

Counts

131 → 2

Alt Table

Status	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
✓	0.5b	(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))

Compiler

Compiled 3113 to 2055 computations (34% saved)

regimes51.0ms (3.4%)

Accuracy

Total 0.3b remaining (98.5%)

Threshold costs 0.3b (98.5%)

Counts

21 → 1

Compiler

Compiled 481 to 359 computations (25.4% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`distribute-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	15	19
2	25	19
3	34	19
4	49	19
5	54	19
6	56	19
7	53	19

end44.0ms (2.9%)

Compiler: Compiled 50 to 36 computations (28% saved)

Details

analyze5.0ms (0.3%)

sample798.0ms (53%)

simplify9.0ms (0.6%)

prune1.0ms (0.1%)

localize5.0ms (0.3%)

series11.0ms (0.7%)

rewrite67.0ms (4.5%)

simplify93.0ms (6.2%)

prune69.0ms (4.6%)

localize7.0ms (0.5%)

series8.0ms (0.5%)

rewrite79.0ms (5.2%)

simplify153.0ms (10.1%)

prune105.0ms (7%)

regimes51.0ms (3.4%)

simplify3.0ms (0.2%)

end44.0ms (2.9%)

Profiling