Details

analyze1.0s (19.8%)

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)

sample1.9s (36.6%)

Results

1.6s	8256×	body	128	valid
191.0ms	1036×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify88.0ms (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

prune5.0ms (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

11.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	11.1b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series47.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
13.0ms	(fma.f64 x (-.f64 y z) x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
1.0ms	(fma.f64 x (-.f64 y z) x)

simplify136.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
629×	`fma-def_binary64`
448×	`associate-/l/_binary64`
308×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`

Counts

111 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1522
1	160	1371
2	374	1332
3	1227	1332
4	4358	1332
5	5042	1332

prune71.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

Status	Error	Program
	12.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	11.9b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	37.5b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
▶	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 1073 to 257 computations (76% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.7b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series74.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

37.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))
36.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

6.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
1.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify142.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
438×	`associate-l_binary64`
352×	`associate-r_binary64`
336×	`fma-def_binary64`
307×	`distribute-rgt-out_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1698
1	160	1621
2	607	1157
3	2730	1152
4	4468	1152
5	4961	1152

prune76.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Error

Counts

78 → 5

Alt Table

Status	Error	Program
	12.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	11.9b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	37.5b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))
▶	2.6b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 1465 to 315 computations (78.5% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	2.6b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series94.0ms (1.8%)

Counts

3 → 75

Calls

3 calls:

43.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
36.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
14.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite90.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

3 → 89

Calls

3 calls:

27.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
26.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
26.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify154.0ms (3%)

Algorithm

1×	egg-herbie

Rules

757×	`times-frac_binary64`
585×	`fma-def_binary64`
393×	`fma-neg_binary64`
381×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`

Counts

164 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2112
1	301	2041
2	1225	1572
3	3819	1517
4	4989	1517

prune194.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
▶	4.4b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	2.6b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	25.8b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)

Compiler

Compiled 2491 to 1161 computations (53.4% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	4.2b	(*.f64 (/.f64 1 z) (fma.f64 x y x))

series54.0ms (1%)

Counts

2 → 72

Calls

2 calls:

28.0ms	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
25.0ms	(*.f64 (/.f64 1 z) (fma.f64 x y x))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
13×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 61

Calls

2 calls:

10.0ms	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
10.0ms	(*.f64 (/.f64 1 z) (fma.f64 x y x))

simplify176.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-def_binary64`
440×	`fma-neg_binary64`
329×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`
227×	`associate-/l*_binary64`

Counts

133 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1600
1	261	1388
2	993	1371
3	3418	1371
4	4697	1371
5	4967	1371
6	4874	1371

prune119.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
✓	4.4b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	2.6b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	25.8b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)

Compiler

Compiled 1825 to 748 computations (59% saved)

regimes512.0ms (9.9%)

Accuracy

Total 0.1b remaining (76.4%)

Threshold costs 0.1b (76.4%)

Counts

58 → 3

Compiler

Compiled 3064 to 1802 computations (41.2% saved)

bsearch3.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	73
1	40	73
2	49	73
3	53	73
4	55	73
5	54	73

end133.0ms (2.6%)

Compiler: Compiled 161 to 93 computations (42.2% saved)

Details

analyze1.0s (19.8%)

sample1.9s (36.6%)

simplify88.0ms (1.7%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

series47.0ms (0.9%)

rewrite7.0ms (0.1%)

simplify136.0ms (2.6%)

prune71.0ms (1.4%)

localize10.0ms (0.2%)

series74.0ms (1.4%)

rewrite11.0ms (0.2%)

simplify142.0ms (2.7%)

prune76.0ms (1.5%)

localize14.0ms (0.3%)

series94.0ms (1.8%)

rewrite90.0ms (1.7%)

simplify154.0ms (3%)

prune194.0ms (3.7%)

localize12.0ms (0.2%)

series54.0ms (1%)

rewrite26.0ms (0.5%)

simplify176.0ms (3.4%)

prune119.0ms (2.3%)

regimes512.0ms (9.9%)

bsearch3.0ms (0.1%)

simplify7.0ms (0.1%)

end133.0ms (2.6%)

Profiling