Details

analyze1.1s (30.8%)

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)

sample41.0ms (1.2%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
2.0ms	27×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify81.0ms (2.3%)

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

prune6.0ms (0.2%)

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

9.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	9.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 38 computations (42.4% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	9.3b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series51.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

36.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
15.0ms	(fma.f64 x (-.f64 y z) x)

rewrite11.0ms (0.3%)

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:

7.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
1.0ms	(fma.f64 x (-.f64 y z) x)

simplify149.0ms (4.3%)

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

prune81.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
	10.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
▶	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	2.8b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	10.9b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	10.1b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	10.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))

Compiler

Compiled 1159 to 293 computations (74.7% saved)

localize17.0ms (0.5%)

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))

series81.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

41.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
39.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite12.0ms (0.3%)

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:

7.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
1.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify160.0ms (4.6%)

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

prune68.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Error

0.0b

Counts

80 → 4

Alt Table

Status	Error	Program
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
▶	2.8b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	4.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.1b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 1421 to 295 computations (79.2% saved)

localize14.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series51.0ms (1.5%)

Counts

2 → 72

Calls

2 calls:

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

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 100

Calls

2 calls:

13.0ms	(-.f64 (/.f64 (fma.f64 y x x) z) x)
4.0ms	(/.f64 (fma.f64 y x x) z)

simplify150.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
431×	`fma-neg_binary64`
395×	`times-frac_binary64`
374×	`associate-/l*_binary64`
228×	`associate-*l/_binary64`

Counts

172 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	3072
1	267	2971
2	947	2007
3	3816	1989
4	4881	1989
5	4897	1989

prune70.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	149	4	153

Error

0.0b

Counts

153 → 4

Alt Table

Status	Error	Program
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.8b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
▶	4.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.1b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 3146 to 634 computations (79.8% saved)

localize7.0ms (0.2%)

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))
✓	4.7b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series44.0ms (1.2%)

Counts

3 → 75

Calls

3 calls:

18.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
17.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
9.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite43.0ms (1.2%)

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:

15.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
11.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
10.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify85.0ms (2.4%)

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

prune86.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

0.0b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.8b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
✓	4.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.1b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 2459 to 1143 computations (53.5% saved)

regimes240.0ms (6.9%)

Accuracy

Total 0.1b remaining (91.4%)

Threshold costs 0.1b (91.4%)

Counts

43 → 3

Compiler

Compiled 2696 to 1366 computations (49.3% saved)

bsearch29.0ms (0.8%)

Steps

Iters	Range		Point
7	3.846591825745724e-36	1.9672037864028695e-34	1.9249634187461288e-34
7	-2.375128798148829e+56	-1.0852454322593221e+55	-3.1371785873879285e+55

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	35	52
2	39	52
3	41	52
4	42	52
5	41	52

end1.0ms (0%)

Compiler: Compiled 39 to 24 computations (38.5% saved)

sample795.0ms (22.7%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	128	valid
103.0ms	970×	body	128	invalid

Compiler

Compiled 106 to 65 computations (38.7% saved)

Details

analyze1.1s (30.8%)

sample41.0ms (1.2%)

simplify81.0ms (2.3%)

prune6.0ms (0.2%)

localize11.0ms (0.3%)

series51.0ms (1.5%)

rewrite11.0ms (0.3%)

simplify149.0ms (4.3%)

prune81.0ms (2.3%)

localize17.0ms (0.5%)

series81.0ms (2.3%)

rewrite12.0ms (0.3%)

simplify160.0ms (4.6%)

prune68.0ms (1.9%)

localize14.0ms (0.4%)

series51.0ms (1.5%)

rewrite32.0ms (0.9%)

simplify150.0ms (4.3%)

prune70.0ms (2%)

localize7.0ms (0.2%)

series44.0ms (1.2%)

rewrite43.0ms (1.2%)

simplify85.0ms (2.4%)

prune86.0ms (2.5%)

regimes240.0ms (6.9%)

bsearch29.0ms (0.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample795.0ms (22.7%)

Profiling