Details

analyze64.0ms (2.3%)

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)

sample148.0ms (5.2%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
11.0ms	256×	pre	128	true
1.0ms	14×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify57.0ms (2%)

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

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

14.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.6b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize13.0ms (0.5%)

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)))
✓	14.4b	(/.f64 b (*.f64 a a))

series69.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(/.f64 b (*.f64 a a))
21.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite18.0ms (0.6%)

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:

11.0ms	(/.f64 b (*.f64 a a))
3.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

simplify137.0ms (4.8%)

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

prune62.0ms (2.2%)

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 (/.f64 1 a) (/.f64 b a)) -1)))

Compiler

Compiled 872 to 423 computations (51.5% saved)

localize19.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 1 a) (/.f64 b a)) -1)))
✓	0.4b	(*.f64 (/.f64 1 a) (/.f64 b a))

series75.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(*.f64 (/.f64 1 a) (/.f64 b a))
23.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 1 a) (/.f64 b a)) -1)))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 79

Calls

2 calls:

17.0ms	(*.f64 (/.f64 1 a) (/.f64 b a))
3.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 1 a) (/.f64 b a)) -1)))

simplify217.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
444×	`times-frac_binary64`
349×	`associate-/l*_binary64`
344×	`fma-def_binary64`
235×	`*-commutative_binary64`

Counts

127 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1691
1	275	1541
2	745	1506
3	1840	1494
4	2313	1494
5	3319	1494
6	4349	1494
7	4726	1494
8	4940	1494

prune133.0ms (4.7%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	1	125

Error

0.0b

Counts

125 → 1

Alt Table

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

Compiler

Compiled 2339 to 1280 computations (45.3% saved)

regimes136.0ms (4.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

10 → 1

Compiler

Compiled 1173 to 746 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	14	18
2	13	18

end1.0ms (0%)

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

sample1.6s (57.8%)

Algorithm

1×

intervals

Results

689.0ms	8000×	body	128	valid
338.0ms	8000×	pre	128	true
24.0ms	406×	pre	128	false

Compiler

Compiled 56 to 37 computations (33.9% saved)

Details

analyze64.0ms (2.3%)

sample148.0ms (5.2%)

simplify57.0ms (2%)

prune5.0ms (0.2%)

localize13.0ms (0.5%)

series69.0ms (2.4%)

rewrite18.0ms (0.6%)

simplify137.0ms (4.8%)

prune62.0ms (2.2%)

localize19.0ms (0.7%)

series75.0ms (2.7%)

rewrite32.0ms (1.1%)

simplify217.0ms (7.7%)

prune133.0ms (4.7%)

regimes136.0ms (4.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (57.8%)

Profiling