Details

analyze435.0ms (18.5%)

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
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
27.3%	67.1%	5.6%	9
41%	50.3%	8.7%	10
43.9%	47%	9.1%	11
48.3%	38%	13.7%	12
56.3%	27.4%	16.2%	13
58.2%	25.4%	16.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify20.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`
1×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	12	8
3	14	8
4	15	8
5	15	8

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (/.f64 y z) x)
	6.6b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)

series13.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 y (/.f64 y z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (/.f64 y z) x)

simplify47.0ms (2%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
604×	`associate-+l+_binary64`
543×	`associate-l_binary64`
462×	`fma-def_binary64`
424×	`associate-/r*_binary64`

Counts

46 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	376
1	28	359
2	59	359
3	151	359
4	551	359
5	2861	359
6	5394	359

prune11.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
	33.4b	(exp.f64 (log.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
▶	6.6b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 208 to 71 computations (65.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	11.2b	(/.f64 (*.f64 y y) z)

series28.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

18.0ms	(+.f64 x (/.f64 (*.f64 y y) z))
10.0ms	(/.f64 (*.f64 y y) z)

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(+.f64 x (/.f64 (*.f64 y y) z))
3.0ms	(/.f64 (*.f64 y y) z)

simplify84.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-neg_binary64`
567×	`fma-def_binary64`
363×	`cancel-sign-sub-inv_binary64`
282×	`distribute-rgt-out_binary64`
269×	`*-commutative_binary64`

Counts

100 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	924
1	177	897
2	469	819
3	1624	819
4	3220	819
5	4792	819
6	5203	819

prune28.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)
✓	6.6b	(+.f64 x (/.f64 (*.f64 y y) z))
▶	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
	33.8b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 z)) (/.f64 y (sqrt.f64 z))))

Compiler

Compiled 775 to 232 computations (70.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.2b	(/.f64 y (/.f64 z y))

series27.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(+.f64 x (/.f64 y (/.f64 z y)))
10.0ms	(/.f64 y (/.f64 z y))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

2 → 89

Calls

2 calls:

10.0ms	(+.f64 x (/.f64 y (/.f64 z y)))
4.0ms	(/.f64 y (/.f64 z y))

simplify119.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary64`
532×	`associate-/l*_binary64`
507×	`associate-/r/_binary64`
346×	`associate-l_binary64`
308×	`fma-neg_binary64`

Counts

149 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	167	1992
1	373	1799
2	1160	1727
3	3066	1703
4	4514	1688
5	4960	1688
6	4955	1688

prune72.0ms (3.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)
✓	6.6b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
▶	34.5b	(+.f64 x (/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y))))

Compiler

Compiled 2191 to 628 computations (71.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y))))
✓	0.1b	(/.f64 z (sqrt.f64 y))
✓	2.6b	(/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y)))

series108.0ms (4.6%)

Counts

3 → 64

Calls

3 calls:

66.0ms	(/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y)))
23.0ms	(/.f64 z (sqrt.f64 y))
18.0ms	(+.f64 x (/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y))))

rewrite71.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

316×	`times-frac_binary64`
171×	`*-un-lft-identity_binary64`
169×	`add-sqr-sqrt_binary64`
169×	`add-cube-cbrt_binary64`
84×	`sqrt-prod_binary64`

Counts

3 → 262

Calls

3 calls:

27.0ms	(+.f64 x (/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y))))
11.0ms	(/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y)))
3.0ms	(/.f64 z (sqrt.f64 y))

simplify306.0ms (13%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-def_binary64`
592×	`associate-/r*_binary64`
481×	`*-commutative_binary64`
457×	`associate-r_binary64`
285×	`associate-/r/_binary64`

Counts

326 → 334

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	337	7052
1	671	6861
2	2243	6670
3	3805	6464
4	4870	6464
5	4993	6464
6	4963	6464

prune181.0ms (7.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	334	4	338

Error

Counts

338 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)
✓	6.6b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	34.5b	(+.f64 x (/.f64 (pow.f64 y 3/2) (/.f64 z (sqrt.f64 y))))

Compiler

Compiled 7021 to 2929 computations (58.3% saved)

regimes117.0ms (5%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Counts

20 → 1

Compiler

Compiled 1674 to 1030 computations (38.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample600.0ms (25.6%)

Algorithm

1×

intervals

Results

254.0ms	8000×	body	128	valid
37.0ms	946×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

Details

analyze435.0ms (18.5%)

sample21.0ms (0.9%)

simplify20.0ms (0.8%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series13.0ms (0.6%)

rewrite1.0ms (0%)

simplify47.0ms (2%)

prune11.0ms (0.5%)

localize4.0ms (0.2%)

series28.0ms (1.2%)

rewrite8.0ms (0.4%)

simplify84.0ms (3.6%)

prune28.0ms (1.2%)

localize8.0ms (0.3%)

series27.0ms (1.2%)

rewrite21.0ms (0.9%)

simplify119.0ms (5.1%)

prune72.0ms (3.1%)

localize8.0ms (0.3%)

series108.0ms (4.6%)

rewrite71.0ms (3%)

simplify306.0ms (13%)

prune181.0ms (7.7%)

regimes117.0ms (5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample600.0ms (25.6%)

Profiling