Details

analyze1.5s (18.6%)

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 (23.5%)

Results

1.2s	8256×	body	128	valid
559.0ms	3898×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify101.0ms (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))

series516.0ms (6.4%)

Counts

2 → 72

Calls

2 calls:

293.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
222.0ms	(*.f64 a (pow.f64 k m))

rewrite11.0ms (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))

simplify83.0ms (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

prune84.0ms (1%)

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

2.1b

Counts

98 → 3

Alt Table

Status	Error	Program
	2.5b	(/.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)))
▶	2.2b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	19.7b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 2397 to 1316 computations (45.1% 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))))
✓	2.2b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series562.0ms (6.9%)

Counts

2 → 72

Calls

2 calls:

312.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
249.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite16.0ms (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:

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

simplify153.0ms (1.9%)

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

prune192.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	201	3	204

Error

0.0b

Counts

204 → 3

Alt Table

Status	Error	Program
	12.6b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
▶	2.5b	(/.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)))
	19.7b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 5325 to 3023 computations (43.2% saved)

localize53.0ms (0.7%)

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)))
✓	0.1b	(/.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)))
✓	18.2b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series675.0ms (8.3%)

Counts

3 → 84

Calls

3 calls:

338.0ms

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

335.0ms

(/.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))

rewrite49.0ms (0.6%)

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)))

4.0ms

(/.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))

simplify262.0ms (3.2%)

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

prune362.0ms (4.5%)

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
	12.6b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
✓	2.5b	(/.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)))
	19.7b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
▶	2.5b	(.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))) (/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))))

Compiler

Compiled 10761 to 6676 computations (38% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	9.1b	(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	18.2b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))
✓	18.7b	(cbrt.f64 (fma.f64 k (+.f64 k 10) 1))

series16.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

5.0ms

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

5.0ms

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

5.0ms

(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
18×	`pow1_binary64`
13×	`pow1/3_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 76

Calls

3 calls:

18.0ms

(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))

3.0ms

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

1.0ms

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

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-neg_binary64`
402×	`cancel-sign-sub-inv_binary64`
354×	`*-commutative_binary64`
234×	`fma-def_binary64`
230×	`sub-neg_binary64`

Counts

112 → 118

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1968
1	270	1930
2	624	1731
3	1648	1697
4	3231	1451
5	4482	1451
6	4814	1451
7	4991	1451

prune337.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	216	4	220

Error

0.0b

Counts

220 → 4

Alt Table

Status	Error	Program
	12.6b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
✓	2.5b	(/.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)))
	19.7b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
✓	2.5b	(.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))) (/.f64 (/.f64 (*.f64 a (pow.f64 k m)) (sqrt.f64 (fma.f64 k (+.f64 k 10) 1))) (sqrt.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))))

Compiler

Compiled 10042 to 7051 computations (29.8% saved)

regimes903.0ms (11.1%)

Accuracy

Total 0.0b remaining (38.9%)

Threshold costs 0.0b (38.9%)

Counts

134 → 2

Compiler

Compiled 12284 to 8698 computations (29.2% saved)

bsearch33.0ms (0.4%)

Steps

Iters	Range		Point
7	1.1364609866682856e+116	3.6778013973139975e+117	3.6283882401935997e+117

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	24	39
2	23	39

end101.0ms (1.2%)

Compiler: Compiled 163 to 107 computations (34.4% saved)

Details

analyze1.5s (18.6%)

sample1.9s (23.5%)

simplify101.0ms (1.3%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series516.0ms (6.4%)

rewrite11.0ms (0.1%)

simplify83.0ms (1%)

prune84.0ms (1%)

localize9.0ms (0.1%)

series562.0ms (6.9%)

rewrite16.0ms (0.2%)

simplify153.0ms (1.9%)

prune192.0ms (2.4%)

localize53.0ms (0.7%)

series675.0ms (8.3%)

rewrite49.0ms (0.6%)

simplify262.0ms (3.2%)

prune362.0ms (4.5%)

localize17.0ms (0.2%)

series16.0ms (0.2%)

rewrite25.0ms (0.3%)

simplify116.0ms (1.4%)

prune337.0ms (4.2%)

regimes903.0ms (11.1%)

bsearch33.0ms (0.4%)

simplify2.0ms (0%)

end101.0ms (1.2%)

Profiling