Details

analyze1.3s (11.4%)

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)

sample1.9s (16.8%)

Results

1.2s	8256×	body	128	valid
626.0ms	3739×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify111.0ms (1%)

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

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

1.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.2b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series595.0ms (5.1%)

Counts

3 → 84

Calls

3 calls:

365.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
227.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(fma.f64 k (+.f64 k 10) 1)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

4.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
4.0ms	(*.f64 a (pow.f64 k m))
0.0ms	(fma.f64 k (+.f64 k 10) 1)

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
533×	`fma-neg_binary64`
331×	`associate-/r/_binary64`
315×	`associate-/l/_binary64`
249×	`cancel-sign-sub-inv_binary64`

Counts

146 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	2692
1	520	2369
2	1962	2188
3	4053	2184
4	4928	2184
5	4971	2184

prune117.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Error

1.2b

Counts

119 → 5

Alt Table

Status	Error	Program
	1.2b	(/.f64 (.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
	1.2b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	19.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 (*.f64 k 10) a)))
	32.3b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
▶	1.2b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))

Compiler

Compiled 2768 to 1507 computations (45.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.3b	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))
✓	1.2b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))

series288.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

285.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

2 → 80

Calls

2 calls:

7.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-neg_binary64`
520×	`fma-def_binary64`
422×	`associate-/l*_binary64`
325×	`times-frac_binary64`
316×	`cancel-sign-sub-inv_binary64`

Counts

128 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	3037
1	540	2683
2	1829	2461
3	4204	2452
4	4960	2452
5	4989	2452

prune192.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	200	5	205

Error

1.2b

Counts

205 → 5

Alt Table

Status	Error	Program
▶	1.2b	(/.f64 (.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
	1.2b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
	16.8b	(.f64 (.f64 a (pow.f64 k m)) (fma.f64 k -10 1))
	32.3b	(/.f64 (.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (pow.f64 k m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.2b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))

Compiler

Compiled 4697 to 2727 computations (41.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m))
✓	0.5b	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
✓	0.6b	(cbrt.f64 k)
✓	1.2b	(/.f64 (.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))

series4.4s (37.8%)

Counts

4 → 96

Calls

4 calls:

2.9s	(.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m))
1.4s	(/.f64 (.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
36.0ms	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
29.0ms	(cbrt.f64 k)

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64`
61×	`prod-exp_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
22×	`pow-exp_binary64`

Counts

4 → 131

Calls

4 calls:

10.0ms	(.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m))
8.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
5.0ms	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
1.0ms	(cbrt.f64 k)

simplify162.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-r_binary64`
389×	`associate-l_binary64`
265×	`fma-neg_binary64`
232×	`associate-/l*_binary64`
213×	`*-commutative_binary64`

Counts

227 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	6164
1	919	5194
2	4194	5137
3	4903	5137
4	4907	5137

prune269.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	251	5	256

Error

0.0b

Counts

256 → 5

Alt Table

Status	Error	Program
	18.5b	(/.f64 (.f64 (pow.f64 (pow.f64 k 2/3) m) (.f64 a (pow.f64 (cbrt.f64 k) m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.2b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))
	16.8b	(.f64 (.f64 a (pow.f64 k m)) (fma.f64 k -10 1))
	38.6b	(fma.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 1 k) -2/3) m) k) (/.f64 (.f64 a (pow.f64 (pow.f64 (/.f64 1 k) -1/3) m)) k) (.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (/.f64 1 k) -2/3) m) (.f64 a (pow.f64 (pow.f64 (/.f64 1 k) -1/3) m))) (pow.f64 k 3)) -10))
▶	1.2b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))

Compiler

Compiled 8690 to 4341 computations (50% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	12.6b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series620.0ms (5.4%)

Counts

3 → 84

Calls

3 calls:

309.0ms

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

309.0ms

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

2.0ms

(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
63×	`sqrt-prod_binary64`
52×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

3 → 143

Calls

3 calls:

7.0ms

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

5.0ms

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

1.0ms

(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify225.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
487×	`cancel-sign-sub-inv_binary64`
351×	`fma-neg_binary64`
193×	`associate-r_binary64`
167×	`associate-/l*_binary64`

Counts

227 → 259

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	8152
1	896	7370
2	2897	6812
3	4807	6731
4	4983	6731
5	4985	6731

prune377.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	335	5	340

Error

0.0b

Counts

340 → 5

Alt Table

Status	Error	Program
	18.5b	(/.f64 (.f64 (pow.f64 (pow.f64 k 2/3) m) (.f64 a (pow.f64 (cbrt.f64 k) m))) (fma.f64 k (+.f64 k 10) 1))
✓	1.2b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k (+.f64 k 10) 1)))
	16.8b	(fma.f64 (.f64 k (.f64 a (pow.f64 k m))) -10 (*.f64 a (pow.f64 k m)))
	38.6b	(fma.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 1 k) -2/3) m) k) (/.f64 (.f64 a (pow.f64 (pow.f64 (/.f64 1 k) -1/3) m)) k) (.f64 (/.f64 (.f64 (pow.f64 (pow.f64 (/.f64 1 k) -2/3) m) (.f64 a (pow.f64 (pow.f64 (/.f64 1 k) -1/3) m))) (pow.f64 k 3)) -10))
✓	1.2b	(/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))

Compiler

Compiled 10706 to 6637 computations (38% saved)

regimes470.0ms (4.1%)

Accuracy

Total 0.0b remaining (45.5%)

Threshold costs 0.0b (45.5%)

Counts

87 → 2

Compiler

Compiled 6668 to 4474 computations (32.9% saved)

bsearch12.0ms (0.1%)

Steps

Iters	Range		Point
3	1.6866957539148825e+152	4.731935048203124e+154	1.3978715154187448e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	41	91
2	40	91

end127.0ms (1.1%)

Compiler: Compiled 257 to 178 computations (30.7% saved)

Details

analyze1.3s (11.4%)

sample1.9s (16.8%)

simplify111.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series595.0ms (5.1%)

rewrite13.0ms (0.1%)

simplify109.0ms (0.9%)

prune117.0ms (1%)

localize8.0ms (0.1%)

series288.0ms (2.5%)

rewrite17.0ms (0.1%)

simplify122.0ms (1.1%)

prune192.0ms (1.7%)

localize14.0ms (0.1%)

series4.4s (37.8%)

rewrite36.0ms (0.3%)

simplify162.0ms (1.4%)

prune269.0ms (2.3%)

localize9.0ms (0.1%)

series620.0ms (5.4%)

rewrite29.0ms (0.3%)

simplify225.0ms (1.9%)

prune377.0ms (3.3%)

regimes470.0ms (4.1%)

bsearch12.0ms (0.1%)

simplify5.0ms (0%)

end127.0ms (1.1%)

Profiling