Details

analyze1.3s (11%)

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 (16.3%)

Results

1.2s	8256×	body	128	valid
612.0ms	3936×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify103.0ms (0.9%)

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

3.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.1b	(/.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))
✓	3.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series524.0ms (4.3%)

Counts

2 → 72

Calls

2 calls:

294.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
230.0ms	(*.f64 a (pow.f64 k m))

rewrite13.0ms (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:

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

simplify85.0ms (0.7%)

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

prune99.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

3.1b

Counts

98 → 3

Alt Table

Status	Error	Program
	3.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	32.7b	(fma.f64 1/2 (.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) (fma.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (log.f64 k) m) (/.f64 a (fma.f64 k (+.f64 k 10) 1))))
▶	3.1b	(/.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 2441 to 1348 computations (44.8% saved)

localize10.0ms (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)))
✓	16.3b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series594.0ms (4.9%)

Counts

3 → 84

Calls

3 calls:

300.0ms

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

292.0ms

(/.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))

rewrite83.0ms (0.7%)

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))

simplify229.0ms (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

prune375.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	334	4	338

Error

0.0b

Counts

338 → 4

Alt Table

Status	Error	Program
	29.8b	(fma.f64 99 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 4)) (fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (fma.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10 (/.f64 -980 (/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))))))
▶	3.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	32.7b	(fma.f64 1/2 (.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (pow.f64 (log.f64 k) 2) (.f64 m m))) (fma.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (.f64 (log.f64 k) m) (/.f64 a (fma.f64 k (+.f64 k 10) 1))))
✓	3.1b	(/.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 10813 to 6694 computations (38.1% 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))))
✓	3.1b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series566.0ms (4.7%)

Counts

2 → 72

Calls

2 calls:

288.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
277.0ms	(/.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:

6.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
5.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

simplify121.0ms (1%)

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

prune205.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	200	5	205

Error

Counts

205 → 5

Alt Table

Status	Error	Program
	29.8b	(fma.f64 99 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 4)) (fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (fma.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10 (/.f64 -980 (/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))))))
✓	3.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	3.2b	(/.f64 (/.f64 1 (/.f64 1 a)) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
	16.2b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
✓	3.1b	(/.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 5404 to 3068 computations (43.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 1 a))
✓	3.1b	(/.f64 (/.f64 1 (/.f64 1 a)) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))

series296.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

295.0ms	(/.f64 (/.f64 1 (/.f64 1 a)) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
1.0ms	(/.f64 1 (/.f64 1 a))

rewrite381.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

3836×	`times-frac_binary64`
1584×	`*-un-lft-identity_binary64`
1584×	`add-sqr-sqrt_binary64`
1584×	`add-cube-cbrt_binary64`
405×	`unpow-prod-down_binary64`

Counts

2 → 1327

Calls

2 calls:

38.0ms	(/.f64 (/.f64 1 (/.f64 1 a)) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
5.0ms	(/.f64 1 (/.f64 1 a))

simplify1.1s (9.2%)

Algorithm

1×	egg-herbie

Rules

573×	`associate-*l/_binary64`
562×	`associate-/l/_binary64`
493×	`associate-/r/_binary64`
437×	`associate-/l*_binary64`
344×	`associate-*r/_binary64`

Counts

1375 → 1431

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	54016
1	1455	52506
2	5099	52506

prune1.9s (15.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1431	0	1431
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1431	5	1436

Error

Counts

1436 → 5

Alt Table

Status	Error	Program
	29.8b	(fma.f64 99 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 4)) (fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (fma.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10 (/.f64 -980 (/.f64 (pow.f64 k 5) (*.f64 a (pow.f64 k m)))))))
✓	3.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	3.2b	(/.f64 (/.f64 1 (/.f64 1 a)) (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
	16.2b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
✓	3.1b	(/.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 54818 to 35966 computations (34.4% saved)

regimes1.9s (15.9%)

Accuracy

Total 0.2b remaining (89.6%)

Threshold costs 0.2b (89.6%)

Counts

240 → 2

Compiler

Compiled 23404 to 16118 computations (31.1% saved)

bsearch34.0ms (0.3%)

Steps

Iters	Range		Point
7	3.0731720481010663e+57	8.854361968888062e+59	4.9377061128398556e+58

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (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	31	68
1	37	68
2	35	68

end113.0ms (0.9%)

Compiler: Compiled 219 to 129 computations (41.1% saved)

Details

analyze1.3s (11%)

sample2.0s (16.3%)

simplify103.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series524.0ms (4.3%)

rewrite13.0ms (0.1%)

simplify85.0ms (0.7%)

prune99.0ms (0.8%)

localize10.0ms (0.1%)

series594.0ms (4.9%)

rewrite83.0ms (0.7%)

simplify229.0ms (1.9%)

prune375.0ms (3.1%)

localize9.0ms (0.1%)

series566.0ms (4.7%)

rewrite19.0ms (0.2%)

simplify121.0ms (1%)

prune205.0ms (1.7%)

localize9.0ms (0.1%)

series296.0ms (2.4%)

rewrite381.0ms (3.1%)

simplify1.1s (9.2%)

prune1.9s (15.7%)

regimes1.9s (15.9%)

bsearch34.0ms (0.3%)

simplify2.0ms (0%)

end113.0ms (0.9%)

Profiling