Details

analyze103.0ms (1.5%)

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)

sample3.2s (45.5%)

Results

1.3s	1749×	body	1024	valid
733.0ms	4646×	body	128	valid
582.0ms	1094×	body	512	valid
181.0ms	622×	body	256	valid
163.0ms	145×	body	2048	valid
20.0ms	165×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify81.0ms (1.2%)

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

13.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.4b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 44 to 22 computations (50% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	0.0b	(/.f64 x (+.f64 x y))
✓	6.7b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series248.0ms (3.6%)

Counts

3 → 72

Calls

3 calls:

102.0ms	(/.f64 x (+.f64 x y))
96.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
50.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite60.0ms (0.9%)

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:

14.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
11.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
6.0ms	(/.f64 x (+.f64 x y))

simplify380.0ms (5.5%)

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

prune506.0ms (7.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	267	6	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	6	274

Error

Counts

274 → 6

Alt Table

Status	Error	Program
	13.4b	(/.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 1) x)
	20.1b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
	13.4b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
	16.1b	(/.f64 1 x)
▶	11.2b	(/.f64 (exp.f64 (neg.f64 y)) x)
	27.1b	(-.f64 (/.f64 1 x) (/.f64 y x))

Compiler

Compiled 7737 to 3041 computations (60.7% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

10.0ms

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

rewrite7.0ms (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)

simplify154.0ms (2.2%)

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

prune64.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Error

Counts

52 → 5

Alt Table

Status	Error	Program
	13.4b	(/.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 1) x)
	20.1b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
	13.4b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
	16.1b	(/.f64 1 x)
▶	11.2b	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))

Compiler

Compiled 653 to 259 computations (60.3% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 (neg.f64 y)))
✓	0.0b	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))

series44.0ms (0.6%)

Counts

2 → 32

Calls

2 calls:

30.0ms	(/.f64 x (exp.f64 (neg.f64 y)))
14.0ms	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 111

Calls

2 calls:

13.0ms	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))
7.0ms	(/.f64 x (exp.f64 (neg.f64 y)))

simplify212.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
453×	`associate-/r/_binary64`
426×	`fma-neg_binary64`
384×	`associate-/l/_binary64`
205×	`div-sub_binary64`

Counts

143 → 181

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	202	2322
1	330	1961
2	707	1927
3	1885	1922
4	4383	1894
5	4985	1894

prune317.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	181	5	186

Error

Counts

186 → 5

Alt Table

Status	Error	Program
	13.4b	(/.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 1) x)
	20.1b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
▶	13.4b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
	16.1b	(/.f64 1 x)
✓	11.2b	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))

Compiler

Compiled 2942 to 1296 computations (55.9% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
	0.0b	(/.f64 x (+.f64 x y))
	6.7b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series88.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

88.0ms

(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
37×	`add-exp-log_binary64`
32×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
24×	`unpow-prod-down_binary64`

Counts

1 → 77

Calls

1 calls:

24.0ms

(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))

simplify196.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

216×	`fma-neg_binary64`
178×	`associate-r_binary64`
166×	`*-commutative_binary64`
165×	`fma-def_binary64`
153×	`sub-neg_binary64`

Counts

101 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	3198
1	851	2970
2	3006	2682
3	4814	2682
4	4961	2682

prune438.0ms (6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	262	5	267

Error

Counts

267 → 5

Alt Table

Status	Error	Program
	13.4b	(/.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 1) x)
	20.1b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
✓	13.4b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
	16.1b	(/.f64 1 x)
✓	11.2b	(/.f64 (exp.f64 0) (/.f64 x (exp.f64 (neg.f64 y))))

Compiler

Compiled 7342 to 3366 computations (54.2% saved)

regimes450.0ms (6.5%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Counts

42 → 3

Compiler

Compiled 1580 to 990 computations (37.3% saved)

bsearch72.0ms (1%)

Steps

Iters	Range		Point
8	7.038874824824338e-10	3.230438352927998e-5	3.137771231155085e-5
6	-3.2771569776339944	-0.38994988924039975	-1.2194538249148998

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-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	25	50
1	29	50
2	31	50
3	32	50
4	31	50

end215.0ms (3.1%)

Compiler: Compiled 128 to 83 computations (35.2% saved)

Details

analyze103.0ms (1.5%)

sample3.2s (45.5%)

simplify81.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series248.0ms (3.6%)

rewrite60.0ms (0.9%)

simplify380.0ms (5.5%)

prune506.0ms (7.3%)

localize9.0ms (0.1%)

series10.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify154.0ms (2.2%)

prune64.0ms (0.9%)

localize14.0ms (0.2%)

series44.0ms (0.6%)

rewrite32.0ms (0.5%)

simplify212.0ms (3.1%)

prune317.0ms (4.6%)

localize14.0ms (0.2%)

series88.0ms (1.3%)

rewrite41.0ms (0.6%)

simplify196.0ms (2.8%)

prune438.0ms (6.3%)

regimes450.0ms (6.5%)

bsearch72.0ms (1%)

simplify7.0ms (0.1%)

end215.0ms (3.1%)

Profiling