Details

analyze172.0ms (4.3%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample932.0ms (23.4%)

Results

793.0ms	8256×	body	128	valid
25.0ms	260×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	14

prune3.0ms (0.1%)

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

9.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.8b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 47 to 27 computations (42.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	9.2b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series22.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
9.0ms	(fma.f64 x (/.f64 x y) x)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 45

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
338×	`sub-neg_binary64`
265×	`distribute-rgt-in_binary64`
240×	`associate-/l/_binary64`

Counts

93 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1641
1	245	1554
2	714	1484
3	2409	1453
4	4439	1453
5	5061	1453

prune49.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

0.0b

Counts

75 → 4

Alt Table

Status	Error	Program
▶	9.9b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	37.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
	17.6b	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
	35.7b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 1363 to 614 computations (55% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (/.f64 x y) x)
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
✓	9.2b	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))

series29.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))
14.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
92×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

2 → 125

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
4.0ms	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))

simplify161.0ms (4%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-neg_binary64`
504×	`times-frac_binary64`
477×	`fma-def_binary64`
289×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Counts

173 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	4807
1	492	4497
2	1657	4212
3	4225	4193
4	4954	4193
5	5185	4193

prune175.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	225	2	227
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	225	6	231

Error

Counts

231 → 6

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	37.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
	17.6b	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
▶	10.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))))
	30.5b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (sqrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))
	35.7b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 5496 to 2649 computations (51.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))
✓	0.5b	(cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	9.2b	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))

series285.0ms (7.2%)

Counts

3 → 72

Calls

3 calls:

206.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))

61.0ms

(cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))

18.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))

rewrite76.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 181

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))

20.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))

3.0ms

(cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))

simplify241.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
631×	`times-frac_binary64`
271×	`*-commutative_binary64`
224×	`+-commutative_binary64`
162×	`associate-+r+_binary64`

Counts

253 → 364

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	887	16689
1	2852	15794
2	5069	15794

prune865.0ms (21.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	778	0	778
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	778	6	784

Error

Counts

784 → 6

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 1 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	37.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
▶	17.6b	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
✓	10.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))))
	30.5b	(/.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (sqrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))))
	35.7b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 51185 to 28100 computations (45.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (pow.f64 x 2) y) x)
✓	9.2b	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
✓	9.4b	(/.f64 (pow.f64 x 2) y)

series32.0ms (0.8%)

Counts

3 → 30

Calls

3 calls:

13.0ms	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
11.0ms	(/.f64 (pow.f64 x 2) y)
8.0ms	(+.f64 (/.f64 (pow.f64 x 2) y) x)

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
64×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
28×	`fma-def_binary64`

Counts

3 → 135

Calls

3 calls:

14.0ms	(/.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (+.f64 x 1))
9.0ms	(+.f64 (/.f64 (pow.f64 x 2) y) x)
3.0ms	(/.f64 (pow.f64 x 2) y)

simplify165.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

351×	`fma-def_binary64`
314×	`associate-/l*_binary64`
239×	`associate-l_binary64`
212×	`associate--l+_binary64`
211×	`times-frac_binary64`

Counts

165 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2572
1	422	2350
2	1204	2290
3	4515	2290
4	4747	2290
5	4996	2290
6	4936	2290

prune146.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	3	0	3
Picked	1	0	1
Done	1	1	2
Total	210	4	214

Error

Counts

214 → 4

Alt Table

Status	Error	Program
✓	10.7b	(/.f64 1 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))) (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))))
	17.6b	(/.f64 (fma.f64 (pow.f64 x 2) (/.f64 1 y) x) (+.f64 x 1))
	9.9b	(/.f64 (+.f64 (/.f64 x (/.f64 y x)) x) (+.f64 x 1))
	0.0b	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x (+.f64 x 1)))

Compiler

Compiled 4085 to 2279 computations (44.2% saved)

regimes284.0ms (7.1%)

Accuracy

Total 0.0b remaining (79.8%)

Threshold costs 0.0b (79.8%)

Counts

87 → 1

Compiler

Compiled 5060 to 3149 computations (37.8% saved)

simplify2.0ms (0.1%)

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	9	16
1	14	16
2	13	16

end76.0ms (1.9%)

Compiler: Compiled 105 to 65 computations (38.1% saved)

Details

analyze172.0ms (4.3%)

sample932.0ms (23.4%)

simplify88.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify78.0ms (2%)

prune49.0ms (1.2%)

localize7.0ms (0.2%)

series29.0ms (0.7%)

rewrite25.0ms (0.6%)

simplify161.0ms (4%)

prune175.0ms (4.4%)

localize12.0ms (0.3%)

series285.0ms (7.2%)

rewrite76.0ms (1.9%)

simplify241.0ms (6.1%)

prune865.0ms (21.8%)

localize6.0ms (0.2%)

series32.0ms (0.8%)

rewrite33.0ms (0.8%)

simplify165.0ms (4.1%)

prune146.0ms (3.7%)

regimes284.0ms (7.1%)

simplify2.0ms (0.1%)

end76.0ms (1.9%)

Profiling