Details

analyze32.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample75.0ms (2.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	13×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify44.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

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

17.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
	17.4b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 79 to 45 computations (43% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	17.0b	(/.f64 b (*.f64 a a))

series41.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 b (*.f64 a a))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 44

Calls

2 calls:

3.0ms	(/.f64 b (*.f64 a a))
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

simplify84.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

553×	`div-sub_binary64`
385×	`associate-/l*_binary64`
361×	`associate-/l/_binary64`
322×	`*-commutative_binary64`
270×	`fma-def_binary64`

Counts

92 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1190
1	131	1118
2	258	1118
3	623	1118
4	1939	1118
5	2527	1118
6	4267	1118
7	5200	1118

prune43.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Error

0.0b

Counts

55 → 4

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a)) -1)))
✓	17.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
	17.4b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
	17.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))

Compiler

Compiled 954 to 471 computations (50.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 b) a)
✓	0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a))
✓	0.5b	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
✓	0.6b	(cbrt.f64 b)

series374.0ms (12.7%)

Counts

4 → 72

Calls

4 calls:

260.0ms	(/.f64 (cbrt.f64 b) a)
39.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a))
38.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
37.0ms	(cbrt.f64 b)

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
42×	`cbrt-prod_binary64`

Counts

4 → 157

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a))
4.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
3.0ms	(/.f64 (cbrt.f64 b) a)
1.0ms	(cbrt.f64 b)

simplify121.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

626×	`unswap-sqr_binary64`
450×	`associate-/r*_binary64`
435×	`*-commutative_binary64`
409×	`associate-/r/_binary64`
382×	`log-prod_binary64`

Counts

229 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2761
1	410	2374
2	1582	2286
3	2925	2218
4	4559	2218
5	5085	2218

prune221.0ms (7.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	268	4	272

Error

0.0b

Counts

272 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a)) -1)))
✓	17.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
	17.4b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.1b	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a)) -1)))

Compiler

Compiled 6191 to 2280 computations (63.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 (cbrt.f64 b) a)
✓	0.4b	(*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a))
	0.6b	(cbrt.f64 b)
✓	6.8b	(pow.f64 b 2/3)

series60.0ms (2%)

Counts

2 → 36

Calls

2 calls:

35.0ms	(*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a))
25.0ms	(pow.f64 b 2/3)

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`

Counts

2 → 104

Calls

2 calls:

16.0ms	(*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a))
1.0ms	(pow.f64 b 2/3)

simplify100.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
417×	`*-commutative_binary64`
373×	`associate-/l/_binary64`
361×	`log-prod_binary64`
324×	`associate-/r*_binary64`

Counts

140 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2269
1	501	1771
2	1466	1581
3	3706	1509
4	4670	1509
5	5066	1509

prune211.0ms (7.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	238	4	242

Error

0.0b

Counts

242 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a)) -1)))
✓	17.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
▶	17.4b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	0.1b	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a)) -1)))

Compiler

Compiled 5334 to 2788 computations (47.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	16.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series55.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
24.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
7.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify104.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

147 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2391
1	285	2222
2	879	2113
3	3871	2101
4	4888	2101
5	4981	2101

prune88.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	126	3	129

Error

Counts

129 → 3

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) a) (/.f64 (cbrt.f64 b) a)) -1)))
✓	0.1b	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (pow.f64 b 2/3) a) (/.f64 (cbrt.f64 b) a)) -1)))

Compiler

Compiled 2451 to 683 computations (72.1% saved)

regimes248.0ms (8.5%)

Accuracy

Total 0.0b remaining (47.8%)

Threshold costs 0.0b (47.8%)

Counts

43 → 1

Compiler

Compiled 5017 to 3235 computations (35.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	18	17
2	30	17
3	39	17
4	46	17
5	49	17
6	50	17
7	50	17

end0.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample910.0ms (31%)

Algorithm

1×

intervals

Results

359.0ms	8000×	body	128	valid
200.0ms	8000×	pre	128	true
9.0ms	418×	pre	128	false

Compiler

Compiled 90 to 56 computations (37.8% saved)

Details

analyze32.0ms (1.1%)

sample75.0ms (2.5%)

simplify44.0ms (1.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series41.0ms (1.4%)

rewrite7.0ms (0.2%)

simplify84.0ms (2.9%)

prune43.0ms (1.5%)

localize11.0ms (0.4%)

series374.0ms (12.7%)

rewrite30.0ms (1%)

simplify121.0ms (4.1%)

prune221.0ms (7.5%)

localize12.0ms (0.4%)

series60.0ms (2%)

rewrite26.0ms (0.9%)

simplify100.0ms (3.4%)

prune211.0ms (7.2%)

localize8.0ms (0.3%)

series55.0ms (1.9%)

rewrite18.0ms (0.6%)

simplify104.0ms (3.6%)

prune88.0ms (3%)

regimes248.0ms (8.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample910.0ms (31%)

Profiling