Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample53.0ms (1.8%)

Algorithm

1×

intervals

Results

5.0ms	64×	body	512	valid
4.0ms	137×	body	128	valid
2.0ms	41×	body	256	valid
2.0ms	14×	body	1024	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

15.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	2.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite79.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

377×	`*-un-lft-identity_binary64`
375×	`times-frac_binary64`
284×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
234×	`prod-diff_binary64`

Counts

2 → 337

Calls

2 calls:

21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify396.0ms (13.4%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
395×	`sub-neg_binary64`
340×	`times-frac_binary64`
306×	`div-sub_binary64`
297×	`associate-l_binary64`

Counts

361 → 324

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	183	11806
1	380	6831
2	1040	5351
3	3726	5350
4	4176	5350
5	4425	5342
6	4803	5342

prune365.0ms (12.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	2	325

Error

0.3b

Counts

325 → 2

Alt Table

Status	Error	Program
	15.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 x))
▶	0.3b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11282 to 8589 computations (23.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -1 (fma.f64 x x x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 -1 (fma.f64 x x x))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

(/.f64 -1 (fma.f64 x x x))

simplify78.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
327×	`distribute-rgt-out_binary64`
306×	`unswap-sqr_binary64`
201×	`sub-neg_binary64`
188×	`cancel-sign-sub-inv_binary64`

Counts

41 → 52

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	78	654
1	148	618
2	308	611
3	680	611
4	2297	611
5	4211	603
6	4978	603
7	4914	603

prune38.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Error

0.2b

Counts

54 → 5

Alt Table

Status	Error	Program
	15.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 x))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
	13.8b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
▶	1.2b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
	30.4b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))

Compiler

Compiled 768 to 406 computations (47.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.3b	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
✓	15.8b	(cbrt.f64 (fma.f64 x x x))

series29.0ms (1%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
8.0ms	(cbrt.f64 (fma.f64 x x x))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
3.0ms	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

7.0ms	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
4.0ms	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
1.0ms	(cbrt.f64 (fma.f64 x x x))

simplify154.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
574×	`times-frac_binary64`
403×	`associate-l_binary64`
354×	`associate-/l/_binary64`
292×	`associate-/r/_binary64`

Counts

200 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5328
1	613	4956
2	1628	4414
3	4604	4414
4	5054	4414

prune204.0ms (6.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	361	1	362
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	361	6	367

Error

0.2b

Counts

367 → 6

Alt Table

Status	Error	Program
✓	1.2b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
	14.3b	(/.f64 (/.f64 -1 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))))) (cbrt.f64 (fma.f64 x x x)))
	15.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 x))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
▶	13.8b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	30.4b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))

Compiler

Compiled 9847 to 3362 computations (65.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
✓	0.2b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	15.0b	(sqrt.f64 (fma.f64 x x x))

series16.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

7.0ms	(sqrt.f64 (fma.f64 x x x))
6.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
3.0ms	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))

rewrite42.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 233

Calls

3 calls:

8.0ms	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
3.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
1.0ms	(sqrt.f64 (fma.f64 x x x))

simplify267.0ms (9%)

Algorithm

1×	egg-herbie

Rules

462×	`associate-/l/_binary64`
429×	`fma-def_binary64`
311×	`times-frac_binary64`
294×	`associate-/r*_binary64`
230×	`fma-neg_binary64`

Counts

261 → 339

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	264	8068
1	590	7401
2	1163	6523
3	2859	6418
4	4696	6408
5	4997	6408
6	4907	6408

prune227.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	378	5	383

Error

0.2b

Counts

383 → 5

Alt Table

Status	Error	Program
	15.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 x))
	30.3b	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
	14.0b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (/.f64 (sqrt.f64 (fma.f64 x x x)) (/.f64 -1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
✓	1.2b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))

Compiler

Compiled 8826 to 3094 computations (64.9% saved)

regimes267.0ms (9%)

Accuracy

Total 0.2b remaining (52.6%)

Threshold costs 0.2b (52.6%)

Counts

133 → 1

Compiler

Compiled 4724 to 3266 computations (30.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

sample667.0ms (22.5%)

Algorithm

1×

intervals

Results

175.0ms	1986×	body	512	valid
152.0ms	4622×	body	128	valid
63.0ms	984×	body	256	valid
50.0ms	408×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 93 to 50 computations (46.2% saved)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Details

analyze5.0ms (0.2%)

sample53.0ms (1.8%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite79.0ms (2.7%)

simplify396.0ms (13.4%)

prune365.0ms (12.3%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify78.0ms (2.6%)

prune38.0ms (1.3%)

localize7.0ms (0.2%)

series29.0ms (1%)

rewrite29.0ms (1%)

simplify154.0ms (5.2%)

prune204.0ms (6.9%)

localize6.0ms (0.2%)

series16.0ms (0.6%)

rewrite42.0ms (1.4%)

simplify267.0ms (9%)

prune227.0ms (7.7%)

regimes267.0ms (9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample667.0ms (22.5%)

Profiling

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13