Details

analyze610.0ms (19%)

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
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (34.4%)

Results

883.0ms	8256×	body	128	valid
113.0ms	1043×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify54.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

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

11.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.4b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
▶	11.4b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 38 computations (42.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
✓	10.6b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

series22.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
9.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
6.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

555×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
516×	`associate-/l*_binary64`
469×	`times-frac_binary64`
227×	`fma-def_binary64`

Counts

123 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1568
1	273	1257
2	1027	1253
3	4803	1253
4	4971	1253

prune64.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
	5.6b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))
▶	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	4.7b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
	33.8b	(/.f64 (.f64 x (-.f64 (.f64 (-.f64 y z) (-.f64 y z)) (.f64 1 1))) (.f64 z (-.f64 (-.f64 y z) 1)))

Compiler

Compiled 1541 to 686 computations (55.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	0.0b	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
✓	5.1b	(/.f64 (*.f64 y x) z)

series45.0ms (1.4%)

Counts

3 → 45

Calls

3 calls:

19.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
14.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
12.0ms	(/.f64 (*.f64 y x) z)

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`

Counts

3 → 112

Calls

3 calls:

15.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
7.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify84.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary64`
420×	`associate-*l/_binary64`
295×	`associate-/r*_binary64`
291×	`distribute-rgt-in_binary64`
272×	`distribute-lft-in_binary64`

Counts

157 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	2368
1	356	2272
2	1418	1693
3	4646	1693
4	5000	1693

prune103.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
▶	2.6b	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	3.3b	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)
	4.7b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

Compiler

Compiled 3143 to 768 computations (75.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)
✓	5.0b	(*.f64 (+.f64 y 1) (/.f64 x z))

series28.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)
13.0ms	(*.f64 (+.f64 y 1) (/.f64 x z))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

2 → 59

Calls

2 calls:

6.0ms	(*.f64 (+.f64 y 1) (/.f64 x z))
6.0ms	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)

simplify75.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

523×	`times-frac_binary64`
498×	`fma-def_binary64`
466×	`associate-/l*_binary64`
432×	`distribute-rgt-in_binary64`
424×	`distribute-lft-in_binary64`

Counts

131 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1809
1	339	1780
2	1378	1418
3	4795	1418
4	5012	1418

prune56.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	4	106

Error

Counts

106 → 4

Alt Table

Status	Error	Program
✓	2.6b	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
▶	3.3b	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)
	4.7b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

Compiler

Compiled 1648 to 742 computations (55% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z))
✓	0.0b	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)
✓	0.6b	(/.f64 1 (/.f64 z (*.f64 y x)))
✓	5.1b	(/.f64 z (*.f64 y x))

series65.0ms (2%)

Counts

4 → 108

Calls

4 calls:

19.0ms	(+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z))
16.0ms	(/.f64 1 (/.f64 z (*.f64 y x)))
15.0ms	(/.f64 z (*.f64 y x))
15.0ms	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)

rewrite58.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
30×	`add-exp-log_binary64`

Counts

4 → 170

Calls

4 calls:

22.0ms	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)
18.0ms	(+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z))
5.0ms	(/.f64 1 (/.f64 z (*.f64 y x)))
3.0ms	(/.f64 z (*.f64 y x))

simplify111.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
327×	`distribute-rgt-in_binary64`
295×	`distribute-lft-in_binary64`
287×	`fma-neg_binary64`
273×	`associate-/l/_binary64`

Counts

278 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	3384
1	395	3047
2	1674	2559
3	4341	2559
4	4919	2559

prune137.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	213	4	217

Error

Counts

217 → 4

Alt Table

Status	Error	Program
✓	2.6b	(-.f64 (*.f64 (+.f64 y 1) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	3.3b	(-.f64 (+.f64 (/.f64 1 (/.f64 z (*.f64 y x))) (/.f64 x z)) x)
	4.7b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

Compiler

Compiled 4370 to 1569 computations (64.1% saved)

regimes359.0ms (11.2%)

Accuracy

Total 0.4b remaining (96.3%)

Threshold costs 0.4b (96.3%)

Counts

69 → 3

Compiler

Compiled 3927 to 2382 computations (39.3% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	78
1	42	78
2	51	78
3	55	78
4	57	78
5	56	78

end66.0ms (2.1%)

Compiler: Compiled 166 to 98 computations (41% saved)

Details

analyze610.0ms (19%)

sample1.1s (34.4%)

simplify54.0ms (1.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series22.0ms (0.7%)

rewrite15.0ms (0.5%)

simplify68.0ms (2.1%)

prune64.0ms (2%)

localize7.0ms (0.2%)

series45.0ms (1.4%)

rewrite33.0ms (1%)

simplify84.0ms (2.6%)

prune103.0ms (3.2%)

localize6.0ms (0.2%)

series28.0ms (0.9%)

rewrite17.0ms (0.5%)

simplify75.0ms (2.3%)

prune56.0ms (1.8%)

localize8.0ms (0.2%)

series65.0ms (2%)

rewrite58.0ms (1.8%)

simplify111.0ms (3.5%)

prune137.0ms (4.3%)

regimes359.0ms (11.2%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end66.0ms (2.1%)

Profiling