Details

analyze77.0ms (0.7%)

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
25%	74.9%	0.1%	3
37.5%	62.4%	0.1%	4
43.7%	56.2%	0.1%	5
53.1%	40.6%	6.3%	6
57.8%	32.8%	9.5%	7
63.2%	22.6%	14.1%	8
66%	17.6%	16.5%	9
68.9%	11.9%	19.2%	10
70.3%	9.1%	20.6%	11
71.9%	6.1%	22%	12
72.6%	4.6%	22.8%	13
73.4%	3.1%	23.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.1s (20.1%)

Infinites

11.9% of outputs are infinite.

Results

865.0ms	1773×	body	1024	valid
494.0ms	4587×	body	128	valid
375.0ms	1125×	body	512	valid
136.0ms	637×	body	256	valid
113.0ms	134×	body	2048	valid
13.0ms	157×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify54.0ms (0.5%)

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

12.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.4b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 44 to 22 computations (50% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series94.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

50.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
35.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
9.0ms	(/.f64 x (+.f64 x y))

rewrite155.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
80×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`

Counts

3 → 178

Calls

3 calls:

10.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
5.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
4.0ms	(/.f64 x (+.f64 x y))

simplify446.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

358×	`associate-/l*_binary64`
339×	`times-frac_binary64`
332×	`fma-def_binary64`
265×	`fma-neg_binary64`
253×	`associate-/r*_binary64`

Counts

250 → 273

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	564	7650
1	1419	7378
2	4947	7378
3	5165	7378

prune210.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	269	4	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	270	4	274

Error

0.0b

Counts

274 → 4

Alt Table

Status	Error	Program
	12.4b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
▶	10.8b	(/.f64 (exp.f64 (neg.f64 y)) x)
	12.4b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	14.4b	(/.f64 1 x)

Compiler

Compiled 7717 to 3007 computations (61% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

11.0ms

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

rewrite5.0ms (0%)

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)

simplify70.0ms (0.7%)

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

prune30.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
	12.4b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	33.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 y)) x) 3))
▶	12.4b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
	14.4b	(/.f64 1 x)

Compiler

Compiled 651 to 237 computations (63.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
	0.0b	(/.f64 x (+.f64 x y))
✓	0.8b	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
✓	4.3b	(sqrt.f64 (/.f64 x (+.f64 x y)))

series471.0ms (4.6%)

Counts

3 → 38

Calls

3 calls:

345.0ms	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
97.0ms	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
29.0ms	(sqrt.f64 (/.f64 x (+.f64 x y)))

rewrite988.0ms (9.6%)

Algorithm

1×	rewrite-expression-head

Rules

5846×	`times-frac_binary64`
3339×	`unpow-prod-down_binary64`
3237×	`*-un-lft-identity_binary64`
2880×	`sqrt-prod_binary64`
2280×	`add-sqr-sqrt_binary64`

Counts

3 → 2178

Calls

3 calls:

55.0ms	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
6.0ms	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
4.0ms	(sqrt.f64 (/.f64 x (+.f64 x y)))

simplify2.6s (24.8%)

Algorithm

1×	egg-herbie

Rules

2091×	`associate-/r/_binary64`
374×	`times-frac_binary64`
95×	`associate-/l*_binary64`
41×	`sqr-pow_binary64`
30×	`fma-def_binary64`

Counts

2216 → 2485

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2595	139672
1	4932	135918
2	5556	135918

prune1.3s (12.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	2675	0	2675
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	2675	4	2679

Error

Counts

2679 → 4

Alt Table

Status	Error	Program
▶	12.4b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	33.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 y)) x) 3))
✓	12.4b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
	14.4b	(/.f64 1 x)

Compiler

Compiled 118595 to 19089 computations (83.9% saved)

localize10.0ms (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))
	0.8b	(pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)
	4.3b	(sqrt.f64 (/.f64 x (+.f64 x y)))

series551.0ms (5.3%)

Counts

2 → 26

Calls

2 calls:

308.0ms

(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)

243.0ms

(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`unpow-prod-down_binary64`
106×	`sqrt-prod_binary64`
102×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
73×	`times-frac_binary64`

Counts

2 → 163

Calls

2 calls:

21.0ms

(*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))

15.0ms

(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)

simplify195.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

590×	`unswap-sqr_binary64`
507×	`fma-def_binary64`
262×	`pow-sqr_binary64`
251×	`associate-r_binary64`
231×	`associate-l_binary64`

Counts

189 → 227

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	337	6184
1	761	5851
2	3152	5811
3	4559	5795
4	4629	5514
5	4981	5514

prune275.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	419	0	419
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	419	4	423

Error

Counts

423 → 4

Alt Table

Status	Error	Program
✓	12.4b	(/.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) x)
	33.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 y)) x) 3))
✓	12.4b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (/.f64 x (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)))
	14.4b	(/.f64 1 x)

Compiler

Compiled 12851 to 3272 computations (74.5% saved)

regimes499.0ms (4.8%)

Accuracy

Total -0.1b remaining (-30.8%)

Threshold costs -0.1b (-30.8%)

Counts

87 → 3

Compiler

Compiled 3998 to 2379 computations (40.5% saved)

bsearch56.0ms (0.5%)

Steps

Iters	Range		Point
10	5.657068694699421e-23	1.1622935979344937e-7	1.1474851571757078e-7
10	-55168863466.39508	-2.753822385516796e-5	-0.18501999673040256

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	21	27
2	20	27

end67.0ms (0.6%)

Compiler: Compiled 97 to 58 computations (40.2% saved)

Details

analyze77.0ms (0.7%)

sample2.1s (20.1%)

simplify54.0ms (0.5%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series94.0ms (0.9%)

rewrite155.0ms (1.5%)

simplify446.0ms (4.3%)

prune210.0ms (2%)

localize4.0ms (0%)

series11.0ms (0.1%)

rewrite5.0ms (0%)

simplify70.0ms (0.7%)

prune30.0ms (0.3%)

localize10.0ms (0.1%)

series471.0ms (4.6%)

rewrite988.0ms (9.6%)

simplify2.6s (24.8%)

prune1.3s (12.9%)

localize10.0ms (0.1%)

series551.0ms (5.3%)

rewrite67.0ms (0.6%)

simplify195.0ms (1.9%)

prune275.0ms (2.7%)

regimes499.0ms (4.8%)

bsearch56.0ms (0.5%)

simplify3.0ms (0%)

end67.0ms (0.6%)

Profiling