Details

analyze534.0ms (17.6%)

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)

sample975.0ms (32.3%)

Results

818.0ms	8256×	body	128	valid
110.0ms	1101×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
407×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`
251×	`times-frac_binary64`
245×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	56	11
3	175	11
4	443	11
5	1025	11
6	2797	11

Stop Event

1×	node limit

Counts

1 → 2

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

3.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
	9.6b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
✓	2.9b	(/.f64 (fma.f64 x y x) z)

series28.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)
12.0ms	(/.f64 (fma.f64 x y x) z)

rewrite57.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`expm1-log1p-u_binary64`
664×	`prod-diff_binary64`
137×	`egg-rr`
83×	`add-sqr-sqrt_binary64`
79×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	156	19
2	2253	19

Stop Event

1×	node limit

Counts

2 → 137

Calls

2 calls:

54.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)
54.0ms	(/.f64 (fma.f64 x y x) z)

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
574×	`fma-neg_binary64`
201×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`
128×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	797
1	63	797
2	127	797
3	388	647
4	1148	647
5	2040	647
6	3179	647
7	3669	647
8	3702	647
9	3710	647
10	3710	647

Stop Event

1×

saturated

Counts

209 → 151

prune85.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
	3.8b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
▶	3.2b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
	4.1b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	15.7b	(-.f64 (*.f64 y (/.f64 x z)) x)
	9.6b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
	33.7b	(+.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 z) 2)) (/.f64 (fma.f64 x y x) (cbrt.f64 z)) (neg.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))

Compiler

Compiled 3001 to 927 computations (69.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
✓	3.0b	(*.f64 (fma.f64 x y x) (/.f64 1 z))

series28.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
12.0ms	(*.f64 (fma.f64 x y x) (/.f64 1 z))

rewrite58.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`prod-diff_binary64`
282×	`fma-def_binary64`
174×	`fma-neg_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	193	19
2	2550	19

Stop Event

1×	node limit

Counts

2 → 155

Calls

2 calls:

54.0ms	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
54.0ms	(*.f64 (fma.f64 x y x) (/.f64 1 z))

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
574×	`fma-neg_binary64`
201×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`
128×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	797
1	63	797
2	127	797
3	388	647
4	1148	647
5	2040	647
6	3179	647
7	3669	647
8	3702	647
9	3710	647
10	3710	647

Stop Event

1×

saturated

Counts

227 → 168

prune86.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	168	6	174

Error

0.0b

Counts

174 → 6

Alt Table

Status	Error	Program
▶	3.1b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
	3.8b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
✓	3.2b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
	4.1b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	15.7b	(-.f64 (*.f64 y (/.f64 x z)) x)
	33.7b	(+.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 z) 2)) (/.f64 (fma.f64 x y x) (cbrt.f64 z)) (neg.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))

Compiler

Compiled 2908 to 867 computations (70.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y x) x)
✓	0.0b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
✓	2.9b	(/.f64 (+.f64 (*.f64 y x) x) z)

series39.0ms (1.3%)

Counts

3 → 75

Calls

3 calls:

18.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
16.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)
3.0ms	(+.f64 (*.f64 y x) x)

rewrite69.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

531×	`log-prod_binary64`
432×	`fma-def_binary64`
252×	`fma-neg_binary64`
220×	`egg-rr`
182×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	187	24
2	2880	24

Stop Event

1×	node limit

Counts

3 → 220

Calls

3 calls:

65.0ms	(+.f64 (*.f64 y x) x)
65.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
65.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)

simplify70.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
568×	`fma-neg_binary64`
196×	`distribute-rgt-in_binary64`
171×	`distribute-lft-in_binary64`
128×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	880
1	63	880
2	127	776
3	388	620
4	1149	620
5	2042	620
6	3158	620
7	3644	620
8	3678	620
9	3686	620
10	3686	620

Stop Event

1×

saturated

Counts

295 → 238

prune135.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	237	7	244

Error

Counts

244 → 7

Alt Table

Status	Error	Program
	17.8b	(-.f64 (/.f64 x (/.f64 z y)) x)
✓	3.1b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
▶	3.8b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
✓	3.2b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
	4.1b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
	15.7b	(-.f64 (*.f64 y (/.f64 x z)) x)
	33.7b	(+.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 z) 2)) (/.f64 (fma.f64 x y x) (cbrt.f64 z)) (neg.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))

Compiler

Compiled 3924 to 1246 computations (68.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3)
	2.9b	(/.f64 (fma.f64 x y x) z)
✓	6.9b	(cbrt.f64 (/.f64 (fma.f64 x y x) z))

series120.0ms (4%)

Counts

3 → 44

Calls

3 calls:

61.0ms	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3)
35.0ms	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
23.0ms	(cbrt.f64 (/.f64 (fma.f64 x y x) z))

rewrite62.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

802×	`prod-diff_binary64`
283×	`fma-def_binary64`
190×	`egg-rr`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	218	29
2	2772	29

Stop Event

1×	node limit

Counts

3 → 190

Calls

3 calls:

59.0ms	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
59.0ms	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3)
59.0ms	(cbrt.f64 (/.f64 (fma.f64 x y x) z))

simplify42.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

366×	`unswap-sqr_binary64`
341×	`cancel-sign-sub-inv_binary64`
260×	`associate-r_binary64`
250×	`associate-l_binary64`
216×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	934
1	232	930
2	641	888
3	2386	888

Stop Event

1×	node limit

Counts

234 → 216

prune150.0ms (5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	255	7	262

Error

Counts

262 → 7

Alt Table

Status	Error	Program
	17.8b	(-.f64 (/.f64 x (/.f64 z y)) x)
✓	3.1b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
✓	3.8b	(-.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 3) x)
✓	3.2b	(-.f64 (*.f64 (fma.f64 x y x) (/.f64 1 z)) x)
	15.7b	(-.f64 (*.f64 y (/.f64 x z)) x)
	4.1b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	33.7b	(+.f64 (fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 z) 2)) (/.f64 (fma.f64 x y x) (cbrt.f64 z)) (neg.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))

Compiler

Compiled 4758 to 1722 computations (63.8% saved)

regimes162.0ms (5.4%)

Accuracy

Total 0.1b remaining (89.5%)

Threshold costs 0.1b (89.5%)

Counts

26 → 3

Compiler

Compiled 1264 to 778 computations (38.4% saved)

bsearch32.0ms (1.1%)

Steps

Iters	Range		Point
7	4.387237168915427e-22	7.97254470315435e-21	4.689163988824187e-21
8	-2.919278774921322e-21	-1.4670149496801775e-24	-2.8830491714104415e-21

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	31	50
2	35	50
3	37	50
4	38	50

Stop Event

1×

saturated

end90.0ms (3%)

Compiler: Compiled 175 to 101 computations (42.3% saved)

Details

analyze534.0ms (17.6%)

sample975.0ms (32.3%)

simplify27.0ms (0.9%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series28.0ms (0.9%)

rewrite57.0ms (1.9%)

simplify70.0ms (2.3%)

prune85.0ms (2.8%)

localize6.0ms (0.2%)

series28.0ms (0.9%)

rewrite58.0ms (1.9%)

simplify70.0ms (2.3%)

prune86.0ms (2.9%)

localize6.0ms (0.2%)

series39.0ms (1.3%)

rewrite69.0ms (2.3%)

simplify70.0ms (2.3%)

prune135.0ms (4.5%)

localize8.0ms (0.3%)

series120.0ms (4%)

rewrite62.0ms (2.1%)

simplify42.0ms (1.4%)

prune150.0ms (5%)

regimes162.0ms (5.4%)

bsearch32.0ms (1.1%)

simplify7.0ms (0.2%)

end90.0ms (3%)

Profiling