Details

analyze1.3s (15.7%)

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
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.0s (23.6%)

Results

1.2s	8256×	body	128	valid
614.0ms	3773×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.4b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 96 to 61 computations (36.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 10 k))
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	0.2b	(*.f64 a (pow.f64 k m))
✓	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series453.0ms (5.3%)

Counts

4 → 96

Calls

4 calls:

248.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
201.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
1.0ms	(+.f64 1 (*.f64 10 k))

rewrite78.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

529×	`fma-def_binary64`
248×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`
218×	`fma-neg_binary64`
164×	`egg-rr`

Counts

4 → 164

Calls

4 calls:

75.0ms	(+.f64 1 (*.f64 10 k))
75.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
75.0ms	(*.f64 a (pow.f64 k m))
75.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	285	39
2	3705	37
3	5114	37

simplify196.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
526×	`associate-r_binary64`
494×	`associate-l_binary64`
483×	`fma-def_binary64`
279×	`associate-/l*_binary64`

Counts

260 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1699
1	347	1596
2	1109	1340
3	3981	1336
4	4871	1336
5	4918	1336

prune336.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	207	4	211
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	208	5	213

Error

0.0b

Counts

213 → 5

Alt Table

Status	Error	Program
	20.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 k (*.f64 10 a))))
	12.5b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 10 k) 1))) 2)
	7.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
▶	2.5b	(*.f64 (/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1))))
✓	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 4681 to 2519 computations (46.2% saved)

localize44.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)))
✓	0.2b	(pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)
✓	2.5b	(/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2))
✓	17.3b	(cbrt.f64 (fma.f64 k (+.f64 10 k) 1))

series1.1s (13%)

Counts

4 → 72

Calls

4 calls:

772.0ms	(/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2))
320.0ms	(/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)))
9.0ms	(pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)
5.0ms	(cbrt.f64 (fma.f64 k (+.f64 10 k) 1))

rewrite71.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
230×	`log-pow_binary64`
165×	`fma-def_binary64`
146×	`prod-diff_binary64`

Counts

4 → 111

Calls

4 calls:

69.0ms	(/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)))
69.0ms	(pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)
69.0ms	(/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2))
69.0ms	(cbrt.f64 (fma.f64 k (+.f64 10 k) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	299	55
2	3521	55
3	4967	55

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-def_binary64`
660×	`associate-l_binary64`
638×	`fma-neg_binary64`
432×	`cancel-sign-sub-inv_binary64`
169×	`distribute-rgt-neg-in_binary64`

Counts

183 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2048
1	563	1828
2	1640	1597
3	4300	1589
4	4951	1589
5	4944	1589

prune292.0ms (3.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	226	5	231

Error

0.0b

Counts

231 → 5

Alt Table

Status	Error	Program
	20.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 k (*.f64 10 a))))
	12.5b	(pow.f64 (sqrt.f64 (/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 10 k) 1))) 2)
▶	7.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	2.5b	(*.f64 (/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1))))
✓	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 7022 to 4850 computations (30.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
✓	0.0b	(fma.f64 k 10 1)
✓	0.1b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	0.3b	(sqrt.f64 (fma.f64 k 10 1))

series366.0ms (4.3%)

Counts

4 → 64

Calls

4 calls:

293.0ms	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
64.0ms	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
7.0ms	(sqrt.f64 (fma.f64 k 10 1))
2.0ms	(fma.f64 k 10 1)

rewrite73.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
221×	`log-pow_binary64`
151×	`log-div_binary64`
143×	`prod-diff_binary64`

Counts

4 → 136

Calls

4 calls:

69.0ms	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
69.0ms	(fma.f64 k 10 1)
69.0ms	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
69.0ms	(sqrt.f64 (fma.f64 k 10 1))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	273	43
2	3339	43
3	4951	43

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-neg_binary64`
491×	`associate-r_binary64`
423×	`associate-l_binary64`
385×	`fma-def_binary64`
257×	`cancel-sign-sub-inv_binary64`

Counts

200 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1202
1	305	1091
2	901	1028
3	3394	1021
4	4970	1021
5	4957	1021

prune296.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	242	7	249

Error

Counts

249 → 7

Alt Table

Status	Error	Program
	7.8b	(/.f64 (/.f64 (*.f64 a (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (sqrt.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
▶	7.8b	(/.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) (pow.f64 k m)))
✓	7.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	2.5b	(*.f64 (/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1))))
✓	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	20.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 k (*.f64 10 a))))
	31.6b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) 2) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Compiler

Compiled 6235 to 3980 computations (36.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))
	0.0b	(fma.f64 k 10 1)
✓	0.1b	(/.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) (pow.f64 k m)))
	0.3b	(sqrt.f64 (fma.f64 k 10 1))

series276.0ms (3.2%)

Counts

1 → 30

Calls

1 calls:

276.0ms

(/.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) (pow.f64 k m)))

rewrite116.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
210×	`fma-neg_binary64`
170×	`prod-diff_binary64`
161×	`fma-udef_binary64`

Counts

1 → 50

Calls

1 calls:

114.0ms

(/.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))) (pow.f64 k m)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	278	18
2	3595	18
3	4912	18
4	4961	18
5	4985	18

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
414×	`associate-r_binary64`
368×	`associate-l_binary64`
292×	`distribute-rgt-neg-in_binary64`
261×	`unswap-sqr_binary64`

Counts

80 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	802
1	222	723
2	665	675
3	2643	675
4	4883	675
5	4992	675

prune313.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	2	3
Picked	1	0	1
Done	0	3	3
Total	247	6	253

Error

Counts

253 → 6

Alt Table

Status	Error	Program
	7.8b	(*.f64 (/.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (neg.f64 (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) (neg.f64 (pow.f64 k m)))
✓	7.8b	(*.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))
✓	2.5b	(*.f64 (/.f64 a (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 10 k) 1)) 2)) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 10 k) 1))))
✓	2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	20.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 k (*.f64 10 a))))
	31.6b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 a (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1))))) 2) (/.f64 (pow.f64 k m) (hypot.f64 k (sqrt.f64 (fma.f64 k 10 1)))))

Compiler

Compiled 6343 to 4013 computations (36.7% saved)

regimes641.0ms (7.5%)

Accuracy

Total 0.0b remaining (63.5%)

Threshold costs 0.0b (63.5%)

Counts

121 → 2

Compiler

Compiled 9616 to 6646 computations (30.9% saved)

bsearch16.0ms (0.2%)

Steps

Iters	Range		Point
3	2.5386088862819462e+32	1.3417777866763047e+33	4.8368259749345016e+32

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	63
1	44	63
2	63	63
3	78	63
4	86	63
5	89	63
6	90	63
7	89	63

end129.0ms (1.5%)

Compiler: Compiled 225 to 156 computations (30.7% saved)

Details

analyze1.3s (15.7%)

sample2.0s (23.6%)

simplify102.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series453.0ms (5.3%)

rewrite78.0ms (0.9%)

simplify196.0ms (2.3%)

prune336.0ms (3.9%)

localize44.0ms (0.5%)

series1.1s (13%)

rewrite71.0ms (0.8%)

simplify101.0ms (1.2%)

prune292.0ms (3.4%)

localize10.0ms (0.1%)

series366.0ms (4.3%)

rewrite73.0ms (0.9%)

simplify75.0ms (0.9%)

prune296.0ms (3.5%)

localize13.0ms (0.2%)

series276.0ms (3.2%)

rewrite116.0ms (1.4%)

simplify62.0ms (0.7%)

prune313.0ms (3.7%)

regimes641.0ms (7.5%)

bsearch16.0ms (0.2%)

simplify4.0ms (0%)

end129.0ms (1.5%)

Profiling