Details

analyze802.0ms (14.7%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.9s (52.9%)

Results

1.1s	1754×	body	1024	valid
661.0ms	4771×	body	128	valid
434.0ms	1023×	body	512	valid
164.0ms	170×	body	2048	valid
146.0ms	538×	body	256	valid
97.0ms	167×	body	1024	invalid
89.0ms	226×	body	512	invalid
53.0ms	426×	body	128	invalid
43.0ms	156×	body	256	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	13
2	25	13
3	53	13
4	116	13
5	276	13
6	665	13
7	2268	13
8	4318	13
9	4902	13

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

8.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.7b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 44 to 22 computations (50% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	5.8b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series63.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
26.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`times-frac_binary64`
100×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
70×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`

Counts

2 → 143

Calls

2 calls:

8.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
5.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify156.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

338×	`associate-/l*_binary64`
326×	`fma-def_binary64`
313×	`times-frac_binary64`
240×	`associate-/r*_binary64`
228×	`associate-r_binary64`

Counts

191 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	538	6736
1	1340	6562
2	4956	6562
3	5133	6562

prune149.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

0.0b

Counts

227 → 4

Alt Table

Status	Error	Program
	8.7b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	12.6b	(/.f64 (exp.f64 (neg.f64 y)) x)
▶	7.9b	(/.f64 1 x)
✓	8.7b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 6914 to 2741 computations (60.4% saved)

localize2.0ms (0%)

prune3.0ms (0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
▶	8.7b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	12.6b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.9b	(/.f64 1 x)
✓	8.7b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 72 to 36 computations (50% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
✓	0.0b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))
✓	0.7b	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
✓	5.1b	(sqrt.f64 (/.f64 x (+.f64 x y)))

series390.0ms (7.2%)

Counts

4 → 51

Calls

4 calls:

185.0ms	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
114.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))
69.0ms	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
22.0ms	(sqrt.f64 (/.f64 x (+.f64 x y)))

rewrite83.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`unpow-prod-down_binary64`
142×	`sqrt-prod_binary64`
125×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
98×	`times-frac_binary64`

Counts

4 → 235

Calls

4 calls:

23.0ms	(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))
17.0ms	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
6.0ms	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
4.0ms	(sqrt.f64 (/.f64 x (+.f64 x y)))

simplify229.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary64`
289×	`associate-r_binary64`
249×	`associate-l_binary64`
228×	`times-frac_binary64`
211×	`fma-neg_binary64`

Counts

286 → 360

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	8432
1	958	7993
2	4083	7928
3	4976	7928
4	4978	7928

prune314.0ms (5.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	490	0	490
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	490	4	494

Error

0.0b

Counts

494 → 4

Alt Table

Status	Error	Program
✓	8.7b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
▶	12.6b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.9b	(/.f64 1 x)
✓	8.7b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 14918 to 3708 computations (75.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

series8.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

8.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

4.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-neg_binary64`
511×	`fma-def_binary64`
397×	`div-sub_binary64`
389×	`associate-/l*_binary64`
297×	`unswap-sqr_binary64`

Counts

39 → 46

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	565
1	149	524
2	369	516
3	905	516
4	2769	509
5	4190	509
6	5158	509

prune23.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	46	4	50

Error

0.0b

Counts

50 → 4

Alt Table

Status	Error	Program
✓	8.7b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
✓	12.6b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.9b	(/.f64 1 x)
✓	8.7b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 581 to 204 computations (64.9% saved)

regimes62.0ms (1.1%)

Accuracy

Total 1.0b remaining (98.4%)

Threshold costs 0b (0%)

Counts

7 → 3

Compiler

Compiled 311 to 174 computations (44.1% saved)

bsearch58.0ms (1.1%)

Steps

Iters	Range		Point
7	1.6221968140826545e-43	4.2769937615816464e-42	4.224512276303508e-42
8	-53.174701297037416	-0.018788335373431407	-2.863265023023429

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	20	32
2	22	32
3	23	32
4	22	32

end53.0ms (1%)

Compiler: Compiled 90 to 49 computations (45.6% saved)

Details

analyze802.0ms (14.7%)

sample2.9s (52.9%)

simplify51.0ms (0.9%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series63.0ms (1.2%)

rewrite28.0ms (0.5%)

simplify156.0ms (2.9%)

prune149.0ms (2.7%)

localize2.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series390.0ms (7.2%)

rewrite83.0ms (1.5%)

simplify229.0ms (4.2%)

prune314.0ms (5.8%)

localize4.0ms (0.1%)

series8.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify67.0ms (1.2%)

prune23.0ms (0.4%)

regimes62.0ms (1.1%)

bsearch58.0ms (1.1%)

simplify3.0ms (0%)

end53.0ms (1%)

Profiling