Details

analyze110.0ms (5.1%)

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)

sample31.0ms (1.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	5×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify55.0ms (2.6%)

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

17.3b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
17.4b	(/.f64 b (*.f64 a a))

rewrite91.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
12×	`pow1_binary64`

Counts

3 → 114

Calls

3 calls:

15.0ms	(/.f64 b (*.f64 a a))
11.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
10.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)

Compiler

Compiled 1495 to 675 computations (54.8% saved)

series56.0ms (2.6%)

Error

0.7b

Counts

3 → 24

Calls

3 calls:

27.0ms	(fma.f64 b (/.f64 b (*.f64 a a)) -1)
15.0ms	(/.f64 b (*.f64 a a))
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 527 to 418 computations (20.7% saved)

simplify107.0ms (5%)

Algorithm

1×	egg-herbie

Rules

603×	`times-frac_binary64`
544×	`fma-neg_binary64`
386×	`associate-l_binary64`
314×	`associate-r_binary64`
293×	`associate-/l*_binary64`

Counts

138 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1416
1	216	1304
2	591	1300
3	3418	1276
4	4692	1275
5	4948	1275

prune21.0ms (1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	1	54

Error

0.0b

Counts

54 → 1

Alt Table

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

Compiler

Compiled 405 to 216 computations (46.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a))) -1)))
0.3b	(/.f64 (sqrt.f64 b) a)
0.3b	(/.f64 (sqrt.f64 b) a)
0.5b	(*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a)))

rewrite157.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-cube-cbrt_binary64`
28×	`pow1_binary64`
22×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`

Counts

4 → 183

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 b) a)
15.0ms	(*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a)))
13.0ms	(/.f64 (sqrt.f64 b) a)
10.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a))) -1)))

Compiler

Compiled 3296 to 1059 computations (67.9% saved)

series57.0ms (2.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

15.0ms	(*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a)))
13.0ms	(/.f64 (sqrt.f64 b) a)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (fabs.f64 (/.f64 (sqrt.f64 b) a)) (fabs.f64 (/.f64 (sqrt.f64 b) a))) -1)))
13.0ms	(/.f64 (sqrt.f64 b) a)

Compiler

Compiled 940 to 707 computations (24.8% saved)

simplify126.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

422×	`associate-/l*_binary64`
361×	`log-div_binary64`
339×	`associate-/r*_binary64`
315×	`cube-div_binary64`
283×	`fma-neg_binary64`

Counts

207 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	2188
1	244	1661
2	692	1600
3	2943	1590
4	4978	1590
5	5195	1590

prune47.0ms (2.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	1	108

Error

0.0b

Counts

108 → 1

Alt Table

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

Compiler

Compiled 1106 to 444 computations (59.9% saved)

regimes336.0ms (15.6%)

Accuracy

Total 0.0b remaining (55.6%)

Threshold costs 0.0b (55.6%)

Compiler

Compiled 5636 to 3976 computations (29.5% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`sqr-abs_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	17	26
2	17	26

end1.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

sample930.0ms (43.3%)

Algorithm

1×

intervals

Results

381.0ms	8000×	body	128	valid
181.0ms	8000×	pre	128	true
3.0ms	129×	pre	128	false

Compiler

Compiled 58 to 34 computations (41.4% saved)

Details

analyze110.0ms (5.1%)

sample31.0ms (1.5%)

simplify55.0ms (2.6%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

rewrite91.0ms (4.2%)

series56.0ms (2.6%)

simplify107.0ms (5%)

prune21.0ms (1%)

localize9.0ms (0.4%)

rewrite157.0ms (7.3%)

series57.0ms (2.7%)

simplify126.0ms (5.9%)

prune47.0ms (2.2%)

regimes336.0ms (15.6%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample930.0ms (43.3%)

Profiling