Details

analyze61.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample874.0ms (43.8%)

Results

753.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify82.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
365×	`times-frac_binary64`
331×	`div-sub_binary64`
156×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	52	10
5	81	10
6	124	10
7	191	10
8	300	10
9	641	10
10	822	10
11	1299	10
12	1328	10
13	1343	10
14	1357	10
15	1377	10
16	1377	10
17	1276	10

prune2.0ms (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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

series9.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 48

Calls

1 calls:

6.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

simplify78.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

610×	`div-sub_binary64`
586×	`fma-neg_binary64`
530×	`cancel-sign-sub-inv_binary64`
194×	`distribute-neg-frac_binary64`
184×	`fma-def_binary64`

Counts

72 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1287
1	283	1239
2	748	1195
3	2488	1183
4	4383	1183
5	5485	1183

prune35.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	3	60

Error

Counts

60 → 3

Alt Table

Status	Error	Program
	32.5b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
▶	31.1b	(fma.f64 (/.f64 y x) -2 1)
	32.0b	(fma.f64 2 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

Compiler

Compiled 962 to 305 computations (68.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

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 (/.f64 y x) -2 1)

simplify67.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
706×	`fma-neg_binary64`
521×	`distribute-rgt-in_binary64`
476×	`distribute-lft-in_binary64`
388×	`associate-*l/_binary64`

Counts

34 → 22

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	331
1	36	278
2	66	277
3	202	277
4	805	277
5	3945	277
6	4338	277
7	4897	277

prune11.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

Counts

25 → 3

Alt Table

Status	Error	Program
	32.5b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
✓	31.1b	(fma.f64 (/.f64 y x) -2 1)
▶	32.0b	(fma.f64 2 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

Compiler

Compiled 288 to 178 computations (38.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 x y) (/.f64 x y))
✓	4.5b	(-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y)))

series54.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
25.0ms	(-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y)))

rewrite27.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 118

Calls

2 calls:

9.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
8.0ms	(-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y)))

simplify129.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
499×	`times-frac_binary64`
367×	`associate-/l/_binary64`
345×	`fma-def_binary64`
242×	`*-commutative_binary64`

Counts

166 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2835
1	453	2422
2	1413	2058
3	3948	1880
4	4949	1880
5	4939	1880

prune83.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	187	3	190

Error

Counts

190 → 3

Alt Table

Status	Error	Program
▶	32.5b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
✓	31.1b	(fma.f64 (/.f64 y x) -2 1)
✓	32.0b	(fma.f64 2 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

Compiler

Compiled 4160 to 1396 computations (66.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
✓	0.1b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

series61.0ms (3.1%)

Counts

2 → 28

Calls

2 calls:

39.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
22.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

rewrite48.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
40×	`add-cube-cbrt_binary64`

Counts

2 → 134

Calls

2 calls:

21.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
6.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))

simplify115.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
471×	`associate-/r*_binary64`
301×	`associate-/l/_binary64`
223×	`fma-neg_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

162 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3775
1	617	3487
2	2081	3370
3	4602	3358
4	4974	3358

prune61.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	167	3	170

Error

Counts

170 → 3

Alt Table

Status	Error	Program
✓	32.5b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
✓	31.1b	(fma.f64 (/.f64 y x) -2 1)
✓	32.0b	(fma.f64 2 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

Compiler

Compiled 4018 to 943 computations (76.5% saved)

regimes100.0ms (5%)

Accuracy

Total -0.3b remaining (-1007.3%)

Threshold costs -0.3b (-1007.3%)

Counts

36 → 1

Compiler

Compiled 1305 to 822 computations (37% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	19	10
3	21	10
4	22	10
5	20	10

end56.0ms (2.8%)

Compiler: Compiled 57 to 31 computations (45.6% saved)

Details

analyze61.0ms (3.1%)

sample874.0ms (43.8%)

simplify82.0ms (4.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.5%)

rewrite12.0ms (0.6%)

simplify78.0ms (3.9%)

prune35.0ms (1.7%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite1.0ms (0%)

simplify67.0ms (3.4%)

prune11.0ms (0.6%)

localize7.0ms (0.3%)

series54.0ms (2.7%)

rewrite27.0ms (1.4%)

simplify129.0ms (6.5%)

prune83.0ms (4.2%)

localize6.0ms (0.3%)

series61.0ms (3.1%)

rewrite48.0ms (2.4%)

simplify115.0ms (5.7%)

prune61.0ms (3%)

regimes100.0ms (5%)

simplify3.0ms (0.1%)

end56.0ms (2.8%)

Profiling