Details

analyze29.0ms (0.9%)

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)

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms	72×	body	512	valid
5.0ms	140×	body	128	valid
2.0ms	16×	body	1024	valid
2.0ms	28×	body	256	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify14.0ms (0.5%)

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

13.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.9b	(-.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))
✓	2.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

rewrite69.0ms (2.3%)

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:

26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

series5.0ms (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))

simplify348.0ms (11.4%)

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 → 703

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

prune334.0ms (11%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	701	2	703
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	702	2	704

Error

0.5b

Counts

704 → 2

Alt Table

Status	Error	Program
	26.2b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 1 x))
▶	0.5b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11299 to 8603 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 -1 (fma.f64 x x x))

rewrite4.0ms (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))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

simplify93.0ms (3.1%)

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 → 64

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

prune34.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

0.2b

Counts

66 → 5

Alt Table

Status	Error	Program
	14.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
▶	1.3b	(/.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)))
	31.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
	26.2b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 1 x))
✓	0.5b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 790 to 424 computations (46.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
	17.6b	(cbrt.f64 (fma.f64 x x x))
	17.6b	(cbrt.f64 (fma.f64 x x x))
✓	17.6b	(cbrt.f64 (fma.f64 x x x))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

2 → 36

Calls

2 calls:

7.0ms	(/.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))

series16.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
6.0ms	(cbrt.f64 (fma.f64 x x x))

simplify123.0ms (4%)

Algorithm

1×	egg-herbie

Rules

569×	`div-sub_binary64`
497×	`associate-l_binary64`
415×	`associate-r_binary64`
309×	`unswap-sqr_binary64`
292×	`cancel-sign-sub-inv_binary64`

Counts

60 → 105

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	120	1329
1	284	1202
2	654	1155
3	1582	1155
4	3860	1065
5	4680	1065
6	4834	1062
7	5376	1062

prune97.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	228	5	233

Error

0.2b

Counts

233 → 5

Alt Table

Status	Error	Program
▶	14.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	31.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
	26.2b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 1 x))
	15.1b	(/.f64 (/.f64 -1 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 3892 to 1558 computations (60% saved)

localize6.0ms (0.2%)

Local error

Found 4 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)))
	16.9b	(sqrt.f64 (fma.f64 x x x))
✓	16.9b	(sqrt.f64 (fma.f64 x x x))

rewrite34.0ms (1.1%)

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:

9.0ms	(/.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))

series15.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

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

simplify318.0ms (10.5%)

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 → 510

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

prune230.0ms (7.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	549	2	551
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	550	6	556

Error

0.2b

Counts

556 → 6

Alt Table

Status	Error	Program
✓	14.7b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	31.3b	(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
	14.8b	(/.f64 (/.f64 -1 (*.f64 (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)))
	26.2b	(-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 1 x))
	15.1b	(/.f64 (/.f64 -1 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 8857 to 3110 computations (64.9% saved)

regimes468.0ms (15.4%)

Accuracy

Total 0.2b remaining (62.6%)

Threshold costs 0.2b (62.6%)

Compiler

Compiled 9068 to 6580 computations (27.4% saved)

simplify3.0ms (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)

sample753.0ms (24.7%)

Algorithm

1×

intervals

Results

204.0ms	1962×	body	512	valid
159.0ms	4594×	body	128	valid
69.0ms	1049×	body	256	valid
46.0ms	395×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 124 to 66 computations (46.8% 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

analyze29.0ms (0.9%)

sample23.0ms (0.8%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite69.0ms (2.3%)

series5.0ms (0.2%)

simplify348.0ms (11.4%)

prune334.0ms (11%)

localize3.0ms (0.1%)

rewrite4.0ms (0.1%)

series4.0ms (0.1%)

simplify93.0ms (3.1%)

prune34.0ms (1.1%)

localize7.0ms (0.2%)

rewrite9.0ms (0.3%)

series16.0ms (0.5%)

simplify123.0ms (4%)

prune97.0ms (3.2%)

localize6.0ms (0.2%)

rewrite34.0ms (1.1%)

series15.0ms (0.5%)

simplify318.0ms (10.5%)

prune230.0ms (7.5%)

regimes468.0ms (15.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample753.0ms (24.7%)

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