Details

analyze119.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 20 to 11 computations (45% saved)

sample32.0ms (1.2%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	6×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify61.0ms (2.3%)

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 → 1

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

1 alts after pruning (1 fresh and 0 done)

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

Error

14.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.8b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
14.8b	(/.f64 b (*.f64 a a))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

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:

4.0ms	(/.f64 b (*.f64 a a))
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 690 to 327 computations (52.6% saved)

series34.0ms (1.3%)

Error

14.8b

Counts

2 → 12

Calls

2 calls:

20.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
13.0ms	(/.f64 b (*.f64 a a))

Compiler

Compiled 300 to 225 computations (25% saved)

simplify88.0ms (3.3%)

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

56 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	794
1	131	722
2	258	722
3	623	722
4	1939	722
5	2527	722
6	4267	722
7	5200	722

prune11.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
	14.8b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))

Compiler

Compiled 219 to 127 computations (42% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
0.3b	(/.f64 a (/.f64 b a))
0.3b	(/.f64 1 (/.f64 a (/.f64 b a)))

rewrite243.0ms (9.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

471×	`times-frac_binary64`
236×	`add-sqr-sqrt_binary64`
232×	`*-un-lft-identity_binary64`
232×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

3 → 299

Calls

3 calls:

11.0ms	(/.f64 1 (/.f64 a (/.f64 b a)))
5.0ms	(/.f64 a (/.f64 b a))
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))

Compiler

Compiled 7080 to 3330 computations (53% saved)

series37.0ms (1.4%)

Error

Counts

3 → 18

Calls

3 calls:

13.0ms	(/.f64 1 (/.f64 a (/.f64 b a)))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))
11.0ms	(/.f64 a (/.f64 b a))

Compiler

Compiled 480 to 366 computations (23.8% saved)

simplify401.0ms (15%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-neg_binary64`
304×	`*-commutative_binary64`
295×	`associate-/r/_binary64`
275×	`div-sub_binary64`
262×	`sub-neg_binary64`

Counts

317 → 299

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	277	6706
1	517	5608
2	1513	5197
3	1771	5149
4	2368	5134
5	3695	4926
6	4327	4824
7	4690	4824
8	4878	4824

prune95.0ms (3.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	299	2	301

Error

Counts

301 → 2

Alt Table

Status	Error	Program
▶	14.8b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))

Compiler

Compiled 2695 to 1264 computations (53.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
0.0b	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3)
14.8b	(/.f64 b (*.f64 a a))

rewrite84.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`sqrt-prod_binary64`
30×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 123

Calls

4 calls:

5.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
3.0ms	(/.f64 b (*.f64 a a))
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3)
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 2112 to 1197 computations (43.3% saved)

series63.0ms (2.4%)

Error

Counts

4 → 24

Calls

4 calls:

24.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3)
13.0ms	(/.f64 b (*.f64 a a))
12.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 722 to 569 computations (21.2% saved)

simplify128.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
448×	`associate-/l*_binary64`
432×	`associate-l_binary64`
372×	`associate-/l/_binary64`
308×	`log-prod_binary64`

Counts

147 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	2891
1	241	2754
2	562	2662
3	1769	2648
4	4312	2648
5	4935	2648

prune24.0ms (0.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
	14.8b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1))) 3))
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 1 (/.f64 a (/.f64 b a))) -1)))

Compiler

Compiled 697 to 379 computations (45.6% saved)

regimes103.0ms (3.9%)

Accuracy

Total 0.0b remaining (24.4%)

Threshold costs 0.0b (24.4%)

Compiler

Compiled 1890 to 1252 computations (33.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
2	12	18

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample1.1s (40.2%)

Algorithm

1×

intervals

Results

425.0ms	8000×	body	128	valid
199.0ms	8000×	pre	128	true
3.0ms	122×	pre	128	false

Compiler

Compiled 65 to 44 computations (32.3% saved)

Details

analyze119.0ms (4.5%)

sample32.0ms (1.2%)

simplify61.0ms (2.3%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite36.0ms (1.3%)

series34.0ms (1.3%)

simplify88.0ms (3.3%)

prune11.0ms (0.4%)

localize12.0ms (0.4%)

rewrite243.0ms (9.1%)

series37.0ms (1.4%)

simplify401.0ms (15%)

prune95.0ms (3.6%)

localize9.0ms (0.3%)

rewrite84.0ms (3.2%)

series63.0ms (2.4%)

simplify128.0ms (4.8%)

prune24.0ms (0.9%)

regimes103.0ms (3.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (40.2%)

Profiling