Details

analyze615.0ms (17%)

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
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
21.1%	78%	0.9%	9
37.3%	60.3%	2.5%	10
39.7%	56.1%	4.2%	11
45.6%	48.7%	5.7%	12
55.9%	35.1%	8.9%	13
57.6%	32.1%	10.3%	14

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample1.1s (31.4%)

Results

855.0ms	8256×	body	128	valid
112.0ms	1090×	body	128	invalid

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify112.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2064×	`fma-neg_binary64`
381×	`div-sub_binary64`
365×	`associate-/l*_binary64`
334×	`distribute-neg-frac_binary64`
322×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	11
2	25	11
3	47	11
4	82	11
5	143	11
6	228	11
7	442	11
8	1041	11
9	2472	11
10	2805	11
11	2944	11
12	3273	11
13	3441	11
14	3513	11
15	4986	11

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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

Compiler

Compiled 42 to 21 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	10.4b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

series20.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)
6.0ms	(fma.f64 y (-.f64 z x) x)

rewrite4.0ms (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:

2.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)
0.0ms	(fma.f64 y (-.f64 z x) x)

simplify90.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

615×	`distribute-rgt-in_binary64`
602×	`distribute-lft-in_binary64`
415×	`times-frac_binary64`
355×	`fma-def_binary64`
346×	`fma-neg_binary64`

Counts

111 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1462
1	170	1315
2	385	1259
3	1042	1259
4	4436	1259
5	4999	1259
6	4955	1259

prune44.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	4	66

Error

0.0b

Counts

66 → 4

Alt Table

Status	Error	Program
	11.2b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
▶	2.8b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
	3.6b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))

Compiler

Compiled 951 to 248 computations (73.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series29.0ms (0.8%)

Counts

2 → 9

Calls

2 calls:

18.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
11.0ms	(/.f64 (*.f64 y x) z)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
28×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify147.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
611×	`times-frac_binary64`
297×	`distribute-rgt-in_binary64`
229×	`fma-neg_binary64`
167×	`exp-prod_binary64`

Counts

91 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2607
1	440	1617
2	1522	1313
3	4223	1313
4	4901	1313
5	4995	1313
6	4998	1313
7	4999	1313
8	4810	1313

prune76.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Error

Counts

122 → 5

Alt Table

Status	Error	Program
	11.2b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	2.8b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
	3.6b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
▶	2.9b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z))))

Compiler

Compiled 2837 to 640 computations (77.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	4.5b	(.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z)))

series575.0ms (15.9%)

Counts

4 → 84

Calls

4 calls:

446.0ms	(/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
50.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z)))
42.0ms	(cbrt.f64 z)
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
32×	`add-exp-log_binary64`
31×	`times-frac_binary64`
30×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`

Counts

4 → 139

Calls

4 calls:

10.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z)))
9.0ms	(/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify120.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-neg_binary64`
495×	`associate-/r/_binary64`
433×	`*-commutative_binary64`
328×	`unswap-sqr_binary64`
168×	`fma-def_binary64`

Counts

223 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	3283
1	438	2349
2	1915	2292
3	2643	2238
4	4578	2238
5	4915	2238

prune162.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	252	5	257

Error

Counts

257 → 5

Alt Table

Status	Error	Program
	11.2b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	2.8b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
▶	3.6b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	2.9b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z))))

Compiler

Compiled 6031 to 1461 computations (75.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 y) z)
✓	3.4b	(fma.f64 (/.f64 (-.f64 1 y) z) x y)

series21.0ms (0.6%)

Counts

2 → 52

Calls

2 calls:

16.0ms	(fma.f64 (/.f64 (-.f64 1 y) z) x y)
5.0ms	(/.f64 (-.f64 1 y) z)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

2 → 54

Calls

2 calls:

4.0ms	(/.f64 (-.f64 1 y) z)
0.0ms	(fma.f64 (/.f64 (-.f64 1 y) z) x y)

simplify76.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
429×	`neg-mul-1_binary64`
424×	`associate-/l/_binary64`
291×	`distribute-rgt-neg-out_binary64`
281×	`fma-neg_binary64`

Counts

106 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1312
1	225	1203
2	575	1199
3	1759	1199
4	4062	1199
5	5080	1199

prune65.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	81	5	86

Error

Counts

86 → 5

Alt Table

Status	Error	Program
	11.2b	(*.f64 (fma.f64 y (-.f64 z x) x) (/.f64 1 z))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
✓	2.8b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	3.6b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
✓	2.9b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 (/.f64 y (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 x (cbrt.f64 z))))

Compiler

Compiled 1341 to 812 computations (39.4% saved)

regimes157.0ms (4.3%)

Accuracy

Total 0.0b remaining (73.4%)

Threshold costs 0.0b (73.4%)

Counts

45 → 1

Compiler

Compiled 2608 to 1484 computations (43.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	14	11
2	18	11
3	20	11
4	21	11
5	20	11

end68.0ms (1.9%)

Compiler: Compiled 96 to 58 computations (39.6% saved)

Details

analyze615.0ms (17%)

sample1.1s (31.4%)

simplify112.0ms (3.1%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify90.0ms (2.5%)

prune44.0ms (1.2%)

localize6.0ms (0.2%)

series29.0ms (0.8%)

rewrite23.0ms (0.6%)

simplify147.0ms (4.1%)

prune76.0ms (2.1%)

localize10.0ms (0.3%)

series575.0ms (15.9%)

rewrite31.0ms (0.9%)

simplify120.0ms (3.3%)

prune162.0ms (4.5%)

localize6.0ms (0.2%)

series21.0ms (0.6%)

rewrite11.0ms (0.3%)

simplify76.0ms (2.1%)

prune65.0ms (1.8%)

regimes157.0ms (4.3%)

simplify5.0ms (0.1%)

end68.0ms (1.9%)

Profiling