Details

analyze552.0ms (10%)

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)

sample169.0ms (3.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	40×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify119.0ms (2.2%)

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

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

9.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.1b	(/.f64 (fma.f64 y (-.f64 z x) x) z)
	9.1b	(/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

Compiler

Compiled 66 to 35 computations (47% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	8.5b	(/.f64 (fma.f64 y (-.f64 z x) x) z)

series19.0ms (0.3%)

Counts

2 → 72

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 y (-.f64 z x) x) z)
7.0ms	(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)

simplify95.0ms (1.7%)

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 (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Error

0.0b

Counts

67 → 5

Alt Table

Status	Error	Program
	5.2b	(*.f64 1 (fma.f64 (/.f64 (-.f64 1 y) z) x y))
▶	3.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
	10.2b	(/.f64 (/.f64 (fma.f64 y (-.f64 z x) x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
	9.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
	35.6b	(*.f64 (sqrt.f64 (fma.f64 y (-.f64 z x) x)) (/.f64 (sqrt.f64 (fma.f64 y (-.f64 z x) x)) z))

Compiler

Compiled 1001 to 266 computations (73.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 x z))
✓	0.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	5.4b	(/.f64 (*.f64 y x) z)

series38.0ms (0.7%)

Counts

3 → 18

Calls

3 calls:

19.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
12.0ms	(/.f64 (*.f64 y x) z)
7.0ms	(+.f64 y (/.f64 x z))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

9.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
4.0ms	(+.f64 y (/.f64 x z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
611×	`times-frac_binary64`
302×	`distribute-rgt-in_binary64`
248×	`fma-neg_binary64`
190×	`cancel-sign-sub-inv_binary64`

Counts

117 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2790
1	449	1800
2	1540	1496
3	4290	1496
4	4985	1496
5	4989	1496
6	4844	1496

prune86.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	143	5	148

Error

0.0b

Counts

148 → 5

Alt Table

Status	Error	Program
	9.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
	25.0b	(*.f64 y (-.f64 1 (/.f64 x z)))
	10.2b	(/.f64 (/.f64 (fma.f64 y (-.f64 z x) x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	3.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
▶	0.1b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 y (/.f64 z x)))

Compiler

Compiled 3250 to 710 computations (78.2% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series29.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

17.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 y (/.f64 z x)))
13.0ms	(/.f64 y (/.f64 z x))

rewrite81.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

408×	`times-frac_binary64`
359×	`*-un-lft-identity_binary64`
273×	`add-sqr-sqrt_binary64`
264×	`add-cube-cbrt_binary64`
176×	`prod-diff_binary64`

Counts

2 → 318

Calls

2 calls:

23.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 y (/.f64 z x)))
5.0ms	(/.f64 y (/.f64 z x))

simplify323.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

425×	`associate-*r/_binary64`
360×	`associate-*l/_binary64`
267×	`associate-/r/_binary64`
230×	`associate-l_binary64`
221×	`div-sub_binary64`

Counts

390 → 361

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	574	19164
1	1621	10234
2	4198	9775
3	4938	9775
4	5040	9775

prune251.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	384	2	386
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	385	6	391

Error

Counts

391 → 6

Alt Table

Status	Error	Program
	9.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
	25.0b	(*.f64 y (-.f64 1 (/.f64 x z)))
✓	3.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
▶	0.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 1 (/.f64 (/.f64 z x) y)))
	0.1b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 y (.f64 (/.f64 1 z) x)))
✓	0.1b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 y (/.f64 z x)))

Compiler

Compiled 13871 to 2642 computations (81% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 y (/.f64 x z))
✓	0.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 1 (/.f64 (/.f64 z x) y)))
✓	0.5b	(/.f64 1 (/.f64 (/.f64 z x) y))
✓	2.6b	(/.f64 (/.f64 z x) y)

series50.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

22.0ms	(/.f64 (/.f64 z x) y)
14.0ms	(/.f64 1 (/.f64 (/.f64 z x) y))
13.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 1 (/.f64 (/.f64 z x) y)))

rewrite294.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

2115×	`times-frac_binary64`
1390×	`*-un-lft-identity_binary64`
1132×	`add-sqr-sqrt_binary64`
1109×	`add-cube-cbrt_binary64`
536×	`prod-diff_binary64`

Counts

3 → 976

Calls

3 calls:

57.0ms	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 1 (/.f64 (/.f64 z x) y)))
9.0ms	(/.f64 1 (/.f64 (/.f64 z x) y))
6.0ms	(/.f64 (/.f64 z x) y)

simplify1.0s (18.9%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-/r/_binary64`
310×	`associate-*r/_binary64`
301×	`associate-*l/_binary64`
198×	`associate-/l/_binary64`
193×	`associate-/l*_binary64`

Counts

1084 → 1050

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	695	71349
1	1871	40983
2	4642	40929
3	5238	40929

prune1.3s (23.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1075	0	1075
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1075	6	1081

Error

Counts

1081 → 6

Alt Table

Status	Error	Program
	9.3b	(/.f64 1 (/.f64 z (fma.f64 y (-.f64 z x) x)))
	25.0b	(*.f64 y (-.f64 1 (/.f64 x z)))
✓	3.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))
✓	0.0b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 1 (/.f64 (/.f64 z x) y)))
	0.1b	(-.f64 (+.f64 y (/.f64 x z)) (.f64 y (.f64 (/.f64 1 z) x)))
✓	0.1b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 y (/.f64 z x)))

Compiler

Compiled 50953 to 17736 computations (65.2% saved)

regimes171.0ms (3.1%)

Accuracy

Total 0.1b remaining (88.2%)

Threshold costs 0.1b (88.2%)

Counts

43 → 1

Compiler

Compiled 2592 to 1432 computations (44.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	16	19
2	22	19
3	24	19
4	25	19
5	23	19

end1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample665.0ms (12%)

Algorithm

1×

intervals

Results

287.0ms	8000×	body	128	valid
36.0ms	1022×	body	128	invalid

Compiler

Compiled 115 to 72 computations (37.4% saved)

Details

analyze552.0ms (10%)

sample169.0ms (3.1%)

simplify119.0ms (2.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series19.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify95.0ms (1.7%)

prune44.0ms (0.8%)

localize7.0ms (0.1%)

series38.0ms (0.7%)

rewrite32.0ms (0.6%)

simplify121.0ms (2.2%)

prune86.0ms (1.6%)

localize13.0ms (0.2%)

series29.0ms (0.5%)

rewrite81.0ms (1.5%)

simplify323.0ms (5.8%)

prune251.0ms (4.5%)

localize8.0ms (0.1%)

series50.0ms (0.9%)

rewrite294.0ms (5.3%)

simplify1.0s (18.9%)

prune1.3s (23.6%)

regimes171.0ms (3.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample665.0ms (12%)

Profiling