Details

analyze1.3s (15.4%)

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 (22.7%)

Results

1.2s	8256×	body	128	valid
576.0ms	3931×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify108.0ms (1.3%)

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

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(/.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 2 expressions with local error:

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

series553.0ms (6.6%)

Counts

2 → 72

Calls

2 calls:

308.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
244.0ms	(*.f64 a (pow.f64 k m))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 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))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
426×	`fma-neg_binary64`
424×	`associate-/r*_binary64`
331×	`associate-/r/_binary64`
315×	`associate-/l/_binary64`

Counts

124 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2471
1	511	2183
2	1953	2003
3	4480	1999
4	4945	1999

prune153.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

2.1b

Counts

98 → 4

Alt Table

Status	Error	Program
	21.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 (*.f64 k 10) a)))
	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	2.2b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	31.1b	(+.f64 (/.f64 a (+.f64 (.f64 10 k) (+.f64 1 (pow.f64 k 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 a (.f64 (pow.f64 (log.f64 k) 2) (pow.f64 m 2))) (+.f64 (.f64 10 k) (+.f64 1 (pow.f64 k 2))))) (/.f64 (.f64 a (.f64 (log.f64 k) m)) (+.f64 (.f64 10 k) (+.f64 1 (pow.f64 k 2))))))

Compiler

Compiled 2491 to 1390 computations (44.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	0.0b	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	16.4b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series530.0ms (6.3%)

Counts

4 → 96

Calls

4 calls:

411.0ms	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
69.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
47.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
2.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`add-sqr-sqrt_binary64`
152×	`times-frac_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`
85×	`sqrt-prod_binary64`

Counts

4 → 242

Calls

4 calls:

22.0ms	(*.f64 (/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))))
5.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
3.0ms	(/.f64 a (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify294.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
411×	`fma-neg_binary64`
274×	`associate-r_binary64`
259×	`associate-*l/_binary64`
254×	`*-commutative_binary64`

Counts

338 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	10930
1	1170	9931
2	3836	9583
3	4903	9583
4	4999	9583

prune442.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	423	4	427

Error

0.0b

Counts

427 → 4

Alt Table

Status	Error	Program
	21.6b	(.f64 (pow.f64 k m) (-.f64 a (.f64 (*.f64 k 10) a)))
▶	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	28.3b	(+.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (log.f64 k) m)))
	26.4b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 13756 to 8613 computations (37.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	2.2b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series646.0ms (7.7%)

Counts

2 → 72

Calls

2 calls:

351.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))
294.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
36×	`times-frac_binary64`
26×	`div-exp_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

2 → 89

Calls

2 calls:

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

simplify132.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
214×	`associate-r_binary64`
162×	`neg-mul-1_binary64`

Counts

161 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4810
1	696	4018
2	2746	3945
3	4282	3936
4	4879	3936

prune191.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	202	3	205

Error

Counts

205 → 3

Alt Table

Status	Error	Program
	16.1b	(/.f64 1 (fma.f64 k (/.f64 k (.f64 a (pow.f64 k m))) (fma.f64 k (/.f64 10 (.f64 a (pow.f64 k m))) (/.f64 (pow.f64 k (neg.f64 m)) a))))
▶	2.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	26.4b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 5341 to 3023 computations (43.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))
✓	2.0b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))

series355.0ms (4.2%)

Counts

2 → 60

Calls

2 calls:

308.0ms	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
47.0ms	(/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

2 → 97

Calls

2 calls:

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

simplify129.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary64`
592×	`fma-def_binary64`
399×	`fma-neg_binary64`
388×	`cancel-sign-sub-inv_binary64`
218×	`associate-r_binary64`

Counts

157 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	4566
1	722	4205
2	2577	3821
3	4685	3821
4	4973	3821

prune165.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	189	3	192

Error

Counts

192 → 3

Alt Table

Status	Error	Program
	16.1b	(/.f64 1 (fma.f64 k (/.f64 k (.f64 a (pow.f64 k m))) (fma.f64 k (/.f64 10 (.f64 a (pow.f64 k m))) (/.f64 (pow.f64 k (neg.f64 m)) a))))
✓	2.2b	(*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))
	26.4b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))

Compiler

Compiled 4961 to 2811 computations (43.3% saved)

regimes1.2s (13.8%)

Accuracy

Total 0.2b remaining (89.2%)

Threshold costs 0.2b (89.2%)

Counts

170 → 2

Compiler

Compiled 14984 to 9962 computations (33.5% saved)

bsearch23.0ms (0.3%)

Steps

Iters	Range		Point
5	4.5608308133363766e+60	1.507549934261767e+68	8.720811547314525e+67

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	25	36
2	24	36

end95.0ms (1.1%)

Compiler: Compiled 123 to 70 computations (43.1% saved)

Details

analyze1.3s (15.4%)

sample1.9s (22.7%)

simplify108.0ms (1.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series553.0ms (6.6%)

rewrite10.0ms (0.1%)

simplify89.0ms (1.1%)

prune153.0ms (1.8%)

localize10.0ms (0.1%)

series530.0ms (6.3%)

rewrite59.0ms (0.7%)

simplify294.0ms (3.5%)

prune442.0ms (5.2%)

localize9.0ms (0.1%)

series646.0ms (7.7%)

rewrite19.0ms (0.2%)

simplify132.0ms (1.6%)

prune191.0ms (2.3%)

localize7.0ms (0.1%)

series355.0ms (4.2%)

rewrite19.0ms (0.2%)

simplify129.0ms (1.5%)

prune165.0ms (2%)

regimes1.2s (13.8%)

bsearch23.0ms (0.3%)

simplify3.0ms (0%)

end95.0ms (1.1%)

Profiling