Details

analyze1.4s (27%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (24.5%)

Results

1.1s	8255×	body	128	valid
88.0ms	685×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series61.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
22.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune125.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
	2.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
▶	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 3359 to 1128 computations (66.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series84.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
21.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
21.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
8.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify185.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune239.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	337	5	342

Error

Counts

342 → 5

Alt Table

Status	Error	Program
	2.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 8636 to 2766 computations (68% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series72.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

41.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
22.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
9.0ms	(/.f64 1 (-.f64 a t))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

12.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify136.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
675×	`times-frac_binary64`
380×	`fma-neg_binary64`
354×	`sub-neg_binary64`
192×	`+-commutative_binary64`

Counts

225 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4903
1	792	4646
2	2764	4604
3	4923	4603
4	5113	4603

prune153.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	227	5	232

Error

Counts

232 → 5

Alt Table

Status	Error	Program
▶	2.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 5271 to 1945 computations (63.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	9.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series110.0ms (2.2%)

Counts

3 → 132

Calls

3 calls:

57.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
35.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
16.0ms	(/.f64 y (-.f64 a t))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

10.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
4.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms	(/.f64 y (-.f64 a t))

simplify209.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune208.0ms (4.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	308	5	313

Error

Counts

313 → 5

Alt Table

Status	Error	Program
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	2.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 7969 to 2034 computations (74.5% saved)

regimes404.0ms (8.1%)

Accuracy

Total 1.3b remaining (99%)

Threshold costs 0b (0%)

Counts

66 → 1

Compiler

Compiled 7989 to 4832 computations (39.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	19	14
3	21	14
4	22	14
5	22	14

end68.0ms (1.4%)

Compiler: Compiled 111 to 69 computations (37.8% saved)

Details

analyze1.4s (27%)

sample1.2s (24.5%)

simplify115.0ms (2.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series61.0ms (1.2%)

rewrite11.0ms (0.2%)

simplify114.0ms (2.3%)

prune125.0ms (2.5%)

localize9.0ms (0.2%)

series84.0ms (1.7%)

rewrite43.0ms (0.9%)

simplify185.0ms (3.7%)

prune239.0ms (4.8%)

localize8.0ms (0.2%)

series72.0ms (1.4%)

rewrite23.0ms (0.5%)

simplify136.0ms (2.7%)

prune153.0ms (3.1%)

localize8.0ms (0.2%)

series110.0ms (2.2%)

rewrite33.0ms (0.7%)

simplify209.0ms (4.2%)

prune208.0ms (4.2%)

regimes404.0ms (8.1%)

simplify2.0ms (0%)

end68.0ms (1.4%)

Profiling