Details

analyze1.3s (27.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.2s (25.4%)

Results

438.0ms	2011×	body	512	valid
429.0ms	4814×	body	128	valid
145.0ms	1006×	body	256	valid
119.0ms	425×	body	1024	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 21 to 17 computations (19% saved)

simplify10.0ms (0.2%)

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%)

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

17.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	3.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite71.0ms (1.6%)

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:

18.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify318.0ms (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

prune327.0ms (7.2%)

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

0.1b

Counts

325 → 2

Alt Table

Status	Error	Program
	17.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 x))
▶	0.1b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11282 to 8589 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(/.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))

simplify86.0ms (1.9%)

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

prune29.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Error

0.0b

Counts

54 → 4

Alt Table

Status	Error	Program
	12.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
▶	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	32.5b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 x x x)) 3))

Compiler

Compiled 744 to 392 computations (47.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
✓	13.8b	(cbrt.f64 (fma.f64 x x x))

series28.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
7.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
6.0ms	(cbrt.f64 (fma.f64 x x x))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

15.0ms	(*.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))))
3.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
1.0ms	(cbrt.f64 (fma.f64 x x x))

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-neg_binary64`
425×	`times-frac_binary64`
417×	`fma-def_binary64`
319×	`associate-l_binary64`
275×	`associate-r_binary64`

Counts

181 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	3541
1	538	3241
2	1337	2998
3	4033	2987
4	4905	2987

prune184.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	301	6	307

Error

0.0b

Counts

307 → 6

Alt Table

Status	Error	Program
▶	12.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
✓	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	39.7b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	32.5b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 x x x)) 3))
	13.3b	(.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))))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))

Compiler

Compiled 8626 to 3406 computations (60.5% saved)

localize5.0ms (0.1%)

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)))
✓	12.9b	(sqrt.f64 (fma.f64 x x x))

series16.0ms (0.3%)

Counts

3 → 28

Calls

3 calls:

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

rewrite41.0ms (0.9%)

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:

7.0ms	(/.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))

simplify264.0ms (5.8%)

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

prune222.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	373	4	377
Fresh	3	0	3
Picked	0	1	1
Done	1	1	2
Total	377	6	383

Error

Counts

383 → 6

Alt Table

Status	Error	Program
	12.9b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))))
	33.0b	(+.f64 1 (/.f64 -1 x))
✓	12.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
	12.8b	(/.f64 (/.f64 (/.f64 -1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x x x)))
	13.1b	(/.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (cbrt.f64 (fma.f64 x x x))))) (sqrt.f64 (fma.f64 x x x)))

Compiler

Compiled 8848 to 3102 computations (64.9% saved)

regimes305.0ms (6.7%)

Accuracy

Total 0.1b remaining (15.6%)

Threshold costs 0.1b (15.6%)

Counts

145 → 1

Compiler

Compiled 6431 to 4357 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end70.0ms (1.5%)

Compiler: Compiled 110 to 52 computations (52.7% 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

analyze1.3s (27.4%)

sample1.2s (25.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series5.0ms (0.1%)

rewrite71.0ms (1.6%)

simplify318.0ms (7%)

prune327.0ms (7.2%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify86.0ms (1.9%)

prune29.0ms (0.6%)

localize9.0ms (0.2%)

series28.0ms (0.6%)

rewrite29.0ms (0.6%)

simplify109.0ms (2.4%)

prune184.0ms (4%)

localize5.0ms (0.1%)

series16.0ms (0.3%)

rewrite41.0ms (0.9%)

simplify264.0ms (5.8%)

prune222.0ms (4.9%)

regimes305.0ms (6.7%)

simplify2.0ms (0%)

end70.0ms (1.5%)

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