Details

analyze891.0ms (14.6%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
49.9%	49.9%	0.1%	7
49.9%	49.9%	0.1%	8
49.9%	49.9%	0.1%	9
49.9%	43.9%	6.2%	10
49.9%	43.8%	6.3%	11
49.9%	40.8%	9.3%	12
49.9%	30.8%	19.3%	13
49.9%	30.6%	19.5%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.3s (21.5%)

Infinites

72.8% of outputs are infinite.

Results

1.0s	8256×	body	128	valid
161.0ms	1562×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify103.0ms (1.7%)

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

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(/.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))
✓	4.7b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series585.0ms (9.6%)

Counts

2 → 72

Calls

2 calls:

340.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
244.0ms	(*.f64 a (pow.f64 k m))

rewrite11.0ms (0.2%)

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))

simplify80.0ms (1.3%)

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 (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Error

1.3b

Counts

98 → 5

Alt Table

Status	Error	Program
	13.3b	(*.f64 a (pow.f64 k m))
	6.1b	(*.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))))
▶	5.3b	(/.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)))
✓	5.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
	22.3b	(/.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 2442 to 1346 computations (44.9% saved)

localize9.0ms (0.2%)

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))

series648.0ms (10.6%)

Counts

3 → 84

Calls

3 calls:

357.0ms

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

289.0ms

(/.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))

rewrite71.0ms (1.2%)

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))

simplify291.0ms (4.8%)

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

prune445.0ms (7.3%)

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
✓	5.3b	(/.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)))
✓	5.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
▶	13.3b	(*.f64 a (pow.f64 k m))
	31.3b	(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)))))))
	22.3b	(/.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 10766 to 6658 computations (38.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))

prune36.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	38	5	43

Error

0.0b

Counts

43 → 5

Alt Table

Status	Error	Program
✓	5.3b	(/.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)))
✓	5.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	13.3b	(*.f64 a (pow.f64 k m))
	31.3b	(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)))))))
▶	22.3b	(/.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 646 to 281 computations (56.5% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))
✓	4.0b	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))

series798.0ms (13.1%)

Counts

2 → 48

Calls

2 calls:

485.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))
313.0ms	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64`
42×	`prod-exp_binary64`
16×	`add-cbrt-cube_binary64`
14×	`pow-exp_binary64`
14×	`pow-to-exp_binary64`

Counts

2 → 70

Calls

2 calls:

12.0ms	(.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m))
7.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (sqrt.f64 k) m)) (pow.f64 (sqrt.f64 k) m)) (fma.f64 k (+.f64 k 10) 1))

simplify108.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
475×	`associate-/r*_binary64`
471×	`associate-*l/_binary64`
383×	`associate-/l/_binary64`
314×	`associate-/r/_binary64`

Counts

118 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2763
1	369	2403
2	1462	2387
3	4218	2379
4	4958	2379
5	4991	2379

prune90.0ms (1.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	105	5	110

Error

0.0b

Counts

110 → 5

Alt Table

Status	Error	Program
✓	5.3b	(/.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)))
✓	5.1b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))
✓	13.3b	(*.f64 a (pow.f64 k m))
	31.3b	(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)))))))
✓	22.3b	(/.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 2922 to 1266 computations (56.7% saved)

regimes355.0ms (5.8%)

Accuracy

Total 1.7b remaining (99.1%)

Threshold costs 0b (0%)

Counts

66 → 2

Compiler

Compiled 6088 to 4198 computations (31% saved)

bsearch18.0ms (0.3%)

Steps

Iters	Range		Point
6	1.037825958433997e+26	1.2069510207862494e+27	1.0596384614903166e+26

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	32	46
2	42	46
3	46	46
4	48	46
5	46	46

end100.0ms (1.6%)

Compiler: Compiled 183 to 109 computations (40.4% saved)

Details

analyze891.0ms (14.6%)

sample1.3s (21.5%)

simplify103.0ms (1.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series585.0ms (9.6%)

rewrite11.0ms (0.2%)

simplify80.0ms (1.3%)

prune84.0ms (1.4%)

localize9.0ms (0.2%)

series648.0ms (10.6%)

rewrite71.0ms (1.2%)

simplify291.0ms (4.8%)

prune445.0ms (7.3%)

localize4.0ms (0.1%)

prune36.0ms (0.6%)

localize12.0ms (0.2%)

series798.0ms (13.1%)

rewrite25.0ms (0.4%)

simplify108.0ms (1.8%)

prune90.0ms (1.5%)

regimes355.0ms (5.8%)

bsearch18.0ms (0.3%)

simplify3.0ms (0.1%)

end100.0ms (1.6%)

Profiling