Details

analyze26.0ms (0.8%)

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)

sample21.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	57×	body	512	valid
5.0ms	151×	body	128	valid
2.0ms	36×	body	256	valid
1.0ms	12×	body	1024	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify41.0ms (1.3%)

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

13.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.1b	(-.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))
✓	3.6b	(-.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))
3.0ms	(/.f64 1 (+.f64 x 1))

rewrite79.0ms (2.5%)

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:

25.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify339.0ms (10.7%)

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

prune370.0ms (11.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

0.2b

Counts

325 → 2

Alt Table

Status	Error	Program
✓	13.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
▶	0.2b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11272 to 8581 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.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))

simplify80.0ms (2.5%)

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

prune31.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	50	4	54

Error

0.0b

Counts

54 → 4

Alt Table

Status	Error	Program
✓	13.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	32.6b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
▶	15.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 718 to 384 computations (46.5% 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)))
✓	0.1b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	16.6b	(sqrt.f64 (fma.f64 x x x))

series18.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

7.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
6.0ms	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
5.0ms	(sqrt.f64 (fma.f64 x x x))

rewrite44.0ms (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)))
4.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
1.0ms	(sqrt.f64 (fma.f64 x x x))

simplify300.0ms (9.4%)

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

prune214.0ms (6.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	376	5	381

Error

Counts

381 → 5

Alt Table

Status	Error	Program
✓	13.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	32.5b	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
▶	15.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))) (/.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 x x x)))))
✓	15.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 8903 to 3130 computations (64.8% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
✓	9.9b	(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
	16.6b	(sqrt.f64 (fma.f64 x x x))
✓	17.4b	(cbrt.f64 (fma.f64 x x x))

series37.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

24.0ms	(cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
7.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
6.0ms	(cbrt.f64 (fma.f64 x x x))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

3.0ms	(sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
2.0ms	(cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
2.0ms	(cbrt.f64 (fma.f64 x x x))

simplify134.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

769×	`fma-neg_binary64`
370×	`fma-def_binary64`
243×	`cancel-sign-sub-inv_binary64`
242×	`distribute-rgt-neg-in_binary64`
230×	`distribute-lft-neg-in_binary64`

Counts

103 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	2041
1	420	1990
2	969	1881
3	2495	1857
4	4736	1857
5	4941	1857
6	4985	1857
7	4928	1857

prune370.0ms (11.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	461	0	461
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	461	5	466

Error

Counts

466 → 5

Alt Table

Status	Error	Program
✓	13.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	32.5b	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
✓	15.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))) (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))) (/.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 x x x)))))
✓	15.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 25088 to 9285 computations (63% saved)

regimes298.0ms (9.4%)

Accuracy

Total 0.2b remaining (60.4%)

Threshold costs 0.2b (60.4%)

Counts

129 → 1

Compiler

Compiled 7312 to 3832 computations (47.6% 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)

sample715.0ms (22.5%)

Algorithm

1×

intervals

Results

185.0ms	1940×	body	512	valid
160.0ms	4638×	body	128	valid
64.0ms	999×	body	256	valid
54.0ms	423×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 110 to 59 computations (46.4% 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

analyze26.0ms (0.8%)

sample21.0ms (0.7%)

simplify41.0ms (1.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite79.0ms (2.5%)

simplify339.0ms (10.7%)

prune370.0ms (11.7%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify80.0ms (2.5%)

prune31.0ms (1%)

localize6.0ms (0.2%)

series18.0ms (0.6%)

rewrite44.0ms (1.4%)

simplify300.0ms (9.4%)

prune214.0ms (6.7%)

localize14.0ms (0.5%)

series37.0ms (1.2%)

rewrite11.0ms (0.3%)

simplify134.0ms (4.2%)

prune370.0ms (11.7%)

regimes298.0ms (9.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample715.0ms (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