Details

analyze41.0ms (1.2%)

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)

sample1.5s (44.4%)

Results

620.0ms	5182×	body	128	valid
409.0ms	1170×	body	1024	valid
306.0ms	1154×	body	512	valid
138.0ms	712×	body	256	valid
16.0ms	38×	body	2048	valid
8.0ms	76×	body	128	invalid

Compiler

Compiled 60 to 40 computations (33.3% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
29×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (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

25.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	3.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series31.0ms (0.9%)

Counts

3 → 56

Calls

3 calls:

14.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
12.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))
4.0ms	(-.f64 (*.f64 x x) eps)

rewrite50.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
104×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	162	28
2	2356	28

Stop Event

1×	node limit

Counts

3 → 104

Calls

3 calls:

48.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))
48.0ms	(-.f64 (*.f64 x x) eps)
48.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

simplify35.0ms (1%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
324×	`fma-neg_binary64`
230×	`associate-/r/_binary64`
224×	`associate-/l/_binary64`
193×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	858
1	214	844
2	615	834
3	2433	816

Stop Event

1×	node limit

Counts

160 → 155

prune81.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	5	156

Error

0.0b

Counts

156 → 5

Alt Table

Status	Error	Program
	25.3b	(-.f64 x (sqrt.f64 (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
▶	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	0.4b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (-.f64 (.f64 x x) (*.f64 x x)) eps)))
✓	25.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	36.3b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))

Compiler

Compiled 2572 to 1026 computations (60.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series55.0ms (1.6%)

Counts

2 → 32

Calls

2 calls:

43.0ms	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
13.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite63.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
308×	`fma-neg_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
177×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	261	24
2	3924	24

Stop Event

1×	node limit

Counts

2 → 177

Calls

2 calls:

58.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
58.0ms	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

759×	`cancel-sign-sub-inv_binary64`
355×	`fma-neg_binary64`
304×	`times-frac_binary64`
279×	`distribute-neg-frac_binary64`
214×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	786
1	202	759
2	613	751
3	2862	717

Stop Event

1×	node limit

Counts

209 → 206

prune157.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)
▶	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	25.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 7703 to 1947 computations (74.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.0b	(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x))
✓	0.4b	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x)

series94.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

46.0ms

(/.f64 (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) x))

29.0ms

(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) x)

19.0ms

(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)

rewrite49.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`fma-def_binary64`
220×	`fma-neg_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
130×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	62
1	278	37
2	3815	37

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

48.0ms

(pow.f64 (-.f64 (*.f64 x x) eps) 1/4)

48.0ms

(/.f64 (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) x))

48.0ms

(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) (pow.f64 (-.f64 (*.f64 x x) eps) 1/4) x)

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

542×	`cancel-sign-sub-inv_binary64`
225×	`times-frac_binary64`
218×	`sub-neg_binary64`
212×	`unswap-sqr_binary64`
203×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	2936
1	976	2810
2	3723	2716

Stop Event

1×	node limit

Counts

146 → 176

prune220.0ms (6.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	320	5	325

Error

Counts

325 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
▶	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)
✓	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	25.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 11051 to 4723 computations (57.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)
✓	0.3b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)

series63.0ms (1.8%)

Counts

2 → 32

Calls

2 calls:

43.0ms	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)
19.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)

rewrite50.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

462×	`fma-def_binary64`
263×	`fma-neg_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
177×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	227	30
2	3251	28

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

48.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)
48.0ms	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-neg_binary64`
430×	`times-frac_binary64`
283×	`associate-/l*_binary64`
279×	`unswap-sqr_binary64`
271×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	799
1	268	766
2	845	758
3	3851	726

Stop Event

1×	node limit

Counts

109 → 122

prune130.0ms (3.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	223	5	228

Error

Counts

228 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 x x) eps)) 3))))
✓	0.4b	(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps) -1)
✓	0.4b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) 1/4) (pow.f64 (-.f64 (.f64 x x) eps) 1/4) x))
✓	0.3b	(/.f64 (+.f64 (-.f64 (.f64 x x) (.f64 x x)) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
✓	25.1b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 4126 to 1675 computations (59.4% saved)

regimes517.0ms (15%)

Accuracy

Total 0.3b remaining (97.5%)

Threshold costs 0.3b (97.5%)

Counts

124 → 1

Compiler

Compiled 6503 to 3918 computations (39.8% saved)

simplify2.0ms (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	10	19
1	13	19
2	18	19
3	20	19
4	21	19

Stop Event

1×

saturated

end102.0ms (3%)

Compiler: Compiled 123 to 66 computations (46.3% saved)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12

Details

analyze41.0ms (1.2%)

sample1.5s (44.4%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series31.0ms (0.9%)

rewrite50.0ms (1.4%)

simplify35.0ms (1%)

prune81.0ms (2.3%)

localize8.0ms (0.2%)

series55.0ms (1.6%)

rewrite63.0ms (1.8%)

simplify37.0ms (1.1%)

prune157.0ms (4.6%)

localize11.0ms (0.3%)

series94.0ms (2.7%)

rewrite49.0ms (1.4%)

simplify62.0ms (1.8%)

prune220.0ms (6.4%)

localize7.0ms (0.2%)

series63.0ms (1.8%)

rewrite50.0ms (1.5%)

simplify38.0ms (1.1%)

prune130.0ms (3.8%)

regimes517.0ms (15%)

simplify2.0ms (0.1%)

end102.0ms (3%)

Profiling

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	55	12
5	103	12
6	196	12
7	269	12
8	363	12
9	441	12
10	497	12
11	501	12