Details

analyze1.4s (10.7%)

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 (14.9%)

Results

1.3s	8256×	body	128	valid
606.0ms	3894×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify103.0ms (0.8%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	2.2b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series598.0ms (4.5%)

Counts

3 → 84

Calls

3 calls:

334.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
261.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
5.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
4.0ms	(*.f64 a (pow.f64 k m))

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
543×	`fma-neg_binary64`
321×	`distribute-rgt-in_binary64`
285×	`cancel-sign-sub-inv_binary64`
191×	`associate-r_binary64`

Counts

156 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	2902
1	603	2584
2	2391	2295
3	4340	2291
4	4966	2291
5	4913	2291

prune159.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	4	152

Error

0.0b

Counts

152 → 4

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
	28.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) (-.f64 (/.f64 99 k) 10)))
	17.9b	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
	2.2b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 3833 to 2028 computations (47.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
✓	0.0b	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	14.9b	(sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
✓	14.9b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series602.0ms (4.5%)

Counts

4 → 84

Calls

4 calls:

534.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
63.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))
2.0ms	(sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 112

Calls

4 calls:

12.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
4.0ms	(sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
3.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify162.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
634×	`fma-neg_binary64`
412×	`cancel-sign-sub-inv_binary64`
185×	`distribute-rgt-neg-in_binary64`
170×	`neg-mul-1_binary64`

Counts

196 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	307	5053
1	800	4038
2	2690	3800
3	4241	3786
4	4953	3786
5	4913	3786

prune232.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	211	4	215

Error

0.0b

Counts

215 → 4

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
	28.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) (-.f64 (/.f64 99 k) 10)))
	17.9b	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
▶	2.2b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 6891 to 4178 computations (39.4% 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))
✓	0.6b	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
✓	0.6b	(cbrt.f64 k)
✓	2.2b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series5.0s (37.2%)

Counts

4 → 96

Calls

4 calls:

3.2s	(.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m))
1.7s	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
43.0ms	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
36.0ms	(cbrt.f64 k)

rewrite39.0ms (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 → 133

Calls

4 calls:

11.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
8.0ms	(*.f64 (cbrt.f64 k) (cbrt.f64 k))
7.0ms	(.f64 (.f64 a (pow.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m))
1.0ms	(cbrt.f64 k)

simplify146.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-r_binary64`
409×	`associate-l_binary64`
259×	`associate-/l*_binary64`
240×	`times-frac_binary64`
234×	`fma-neg_binary64`

Counts

229 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6396
1	971	5314
2	4623	5308
3	5033	5308

prune280.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	253	4	257

Error

0.0b

Counts

257 → 4

Alt Table

Status	Error	Program
▶	17.9b	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
✓	2.2b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
✓	2.2b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	38.2b	(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))

Compiler

Compiled 9484 to 4585 computations (51.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1))
✓	2.2b	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
✓	16.3b	(-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4))
✓	19.1b	(/.f64 (-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1))

series505.0ms (3.8%)

Counts

4 → 72

Calls

4 calls:

491.0ms	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
7.0ms	(/.f64 (-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1))
3.0ms	(-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4))
3.0ms	(*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
67×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
33×	`difference-of-squares_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1))
10.0ms	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
5.0ms	(-.f64 (*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4))
3.0ms	(*.f64 (fma.f64 k 10 1) (fma.f64 k 10 1))

simplify216.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

301×	`associate-r_binary64`
299×	`fma-neg_binary64`
293×	`associate-/l*_binary64`
257×	`associate-l_binary64`
185×	`fma-def_binary64`

Counts

248 → 358

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	469	9886
1	1208	8730
2	4790	8724
3	5014	8724

prune472.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	358	0	358
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	358	4	362

Error

0.0b

Counts

362 → 4

Alt Table

Status	Error	Program
✓	17.9b	(/.f64 (.f64 a (pow.f64 k m)) (/.f64 (-.f64 (.f64 (fma.f64 k 10 1) (fma.f64 k 10 1)) (pow.f64 k 4)) (fma.f64 k (-.f64 10 k) 1)))
✓	2.2b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (pow.f64 k m)) (sqrt.f64 (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
✓	2.2b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	38.2b	(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))

Compiler

Compiled 15203 to 10106 computations (33.5% saved)

regimes992.0ms (7.5%)

Accuracy

Total 0.0b remaining (51%)

Threshold costs 0.0b (51%)

Counts

165 → 2

Compiler

Compiled 15142 to 10342 computations (31.7% saved)

bsearch19.0ms (0.1%)

Steps

Iters	Range		Point
3	1.56628887520654e+150	4.2405313429828645e+150	2.343786894830444e+150

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (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	34	94
1	42	94
2	41	94

end137.0ms (1%)

Compiler: Compiled 264 to 184 computations (30.3% saved)

Details

analyze1.4s (10.7%)

sample2.0s (14.9%)

simplify103.0ms (0.8%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series598.0ms (4.5%)

rewrite20.0ms (0.1%)

simplify125.0ms (0.9%)

prune159.0ms (1.2%)

localize16.0ms (0.1%)

series602.0ms (4.5%)

rewrite29.0ms (0.2%)

simplify162.0ms (1.2%)

prune232.0ms (1.7%)

localize14.0ms (0.1%)

series5.0s (37.2%)

rewrite39.0ms (0.3%)

simplify146.0ms (1.1%)

prune280.0ms (2.1%)

localize14.0ms (0.1%)

series505.0ms (3.8%)

rewrite47.0ms (0.4%)

simplify216.0ms (1.6%)

prune472.0ms (3.5%)

regimes992.0ms (7.5%)

bsearch19.0ms (0.1%)

simplify3.0ms (0%)

end137.0ms (1%)

Profiling