Details

analyze140.0ms (4.7%)

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)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify74.0ms (2.5%)

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

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

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))

series15.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

15.0ms

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

rewrite28.0ms (0.9%)

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:

12.0ms

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

simplify105.0ms (3.6%)

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

prune36.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	5	60

Error

Counts

60 → 5

Alt Table

Status	Error	Program
	30.3b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (+.f64 x y))))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
	33.1b	(fma.f64 (/.f64 y x) -2 1)

Compiler

Compiled 1056 to 347 computations (67.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

series34.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)
16.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))

rewrite33.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
76×	`add-sqr-sqrt_binary64`
58×	`cbrt-prod_binary64`
52×	`cube-prod_binary64`

Counts

2 → 144

Calls

2 calls:

8.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
7.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3)

simplify164.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
319×	`unswap-sqr_binary64`
229×	`associate-/l/_binary64`
227×	`distribute-rgt-in_binary64`
206×	`distribute-lft-in_binary64`

Counts

192 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	4193
1	636	3904
2	1974	3788
3	4715	3762
4	5252	3762

prune139.0ms (4.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	205	3	208

Error

Counts

208 → 3

Alt Table

Status	Error	Program
	30.3b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
▶	0.0b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	33.1b	(fma.f64 (/.f64 y x) -2 1)

Compiler

Compiled 3861 to 1464 computations (62.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2))
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

series56.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
17.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2))
12.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)

rewrite33.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
57×	`cbrt-prod_binary64`
52×	`unpow-prod-down_binary64`

Counts

3 → 122

Calls

3 calls:

10.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2))
7.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)
5.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))

simplify370.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

659×	`times-frac_binary64`
345×	`fma-neg_binary64`
343×	`fma-def_binary64`
273×	`cancel-sign-sub-inv_binary64`
140×	`unswap-sqr_binary64`

Counts

194 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	4576
1	668	4348
2	1860	4193
3	4795	4193
4	4973	4193

prune421.0ms (14.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	289	3	292

Error

Counts

292 → 3

Alt Table

Status	Error	Program
▶	30.3b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	33.1b	(fma.f64 (/.f64 y x) -2 1)

Compiler

Compiled 8215 to 2628 computations (68% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))
✓	0.2b	(pow.f64 (/.f64 x y) 3)
✓	0.2b	(*.f64 (/.f64 x y) (/.f64 x y))
✓	7.8b	(-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y)))

series117.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))
32.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
27.0ms	(-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y)))
17.0ms	(pow.f64 (/.f64 x y) 3)

rewrite77.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
71×	`times-frac_binary64`
69×	`add-sqr-sqrt_binary64`
56×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

4 → 191

Calls

4 calls:

32.0ms	(-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y)))
20.0ms	(+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3))
8.0ms	(*.f64 (/.f64 x y) (/.f64 x y))
3.0ms	(pow.f64 (/.f64 x y) 3)

simplify184.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-neg_binary64`
341×	`log-prod_binary64`
326×	`associate-r_binary64`
279×	`associate-l_binary64`
266×	`exp-prod_binary64`

Counts

287 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	4761
1	722	4049
2	3220	3920
3	4058	3862
4	4913	3862

prune165.0ms (5.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	262	3	265

Error

Counts

265 → 3

Alt Table

Status	Error	Program
✓	30.3b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	33.1b	(fma.f64 (/.f64 y x) -2 1)

Compiler

Compiled 7662 to 3041 computations (60.3% saved)

regimes240.0ms (8.1%)

Accuracy

Total 0.0b remaining (59.2%)

Threshold costs 0.0b (59.2%)

Counts

99 → 1

Compiler

Compiled 4437 to 2874 computations (35.2% saved)

simplify3.0ms (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	11	19
1	14	19
2	19	19
3	21	19
4	22	19
5	22	19

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample478.0ms (16.1%)

Algorithm

1×

intervals

Results

229.0ms

8000×

body

128

valid

Compiler

Compiled 77 to 45 computations (41.6% saved)

Details

analyze140.0ms (4.7%)

sample19.0ms (0.6%)

simplify74.0ms (2.5%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series15.0ms (0.5%)

rewrite28.0ms (0.9%)

simplify105.0ms (3.6%)

prune36.0ms (1.2%)

localize7.0ms (0.2%)

series34.0ms (1.1%)

rewrite33.0ms (1.1%)

simplify164.0ms (5.5%)

prune139.0ms (4.7%)

localize9.0ms (0.3%)

series56.0ms (1.9%)

rewrite33.0ms (1.1%)

simplify370.0ms (12.5%)

prune421.0ms (14.2%)

localize8.0ms (0.3%)

series117.0ms (3.9%)

rewrite77.0ms (2.6%)

simplify184.0ms (6.2%)

prune165.0ms (5.6%)

regimes240.0ms (8.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample478.0ms (16.1%)

Profiling