Details

analyze108.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.1s (41.5%)

Results

983.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify44.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 97 to 64 computations (34% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

series77.0ms (3%)

Counts

2 → 48

Calls

2 calls:

43.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
34.0ms	(pow.f64 (hypot.f64 a b) 4)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify62.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-+l+_binary64`
307×	`fma-def_binary64`
295×	`cancel-sign-sub-inv_binary64`
264×	`fma-neg_binary64`
253×	`unswap-sqr_binary64`

Counts

90 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1576
1	194	1474
2	523	1381
3	2044	1379
4	5169	1379

prune64.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	18.1b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 1519 to 937 computations (38.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
✓	0.0b	(.f64 4 (.f64 b b))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series62.0ms (2.5%)

Counts

4 → 84

Calls

4 calls:

24.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
22.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
2.0ms	(.f64 4 (.f64 b b))

rewrite28.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 97

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
7.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
4.0ms	(.f64 4 (.f64 b b))
3.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify131.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
591×	`fma-def_binary64`
532×	`associate-l_binary64`
456×	`associate-r_binary64`
273×	`distribute-rgt-in_binary64`

Counts

181 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	3745
1	320	2999
2	929	2633
3	3956	2633
4	4890	2633
5	4924	2633

prune137.0ms (5.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	162	3	165

Error

Counts

165 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	18.1b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 4163 to 2185 computations (47.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
✓	0.2b	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
✓	27.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))

series108.0ms (4.3%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
36.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
35.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64`
39×	`unpow-prod-down_binary64`
23×	`fma-def_binary64`
21×	`cube-prod_binary64`
21×	`*-un-lft-identity_binary64`

Counts

3 → 104

Calls

3 calls:

9.0ms	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
3.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))
2.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

simplify112.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

797×	`distribute-rgt-in_binary64`
700×	`fma-def_binary64`
461×	`fma-neg_binary64`
310×	`*-commutative_binary64`
196×	`sqr-pow_binary64`

Counts

176 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2879
1	372	2725
2	1218	2519
3	2785	2452
4	4922	2452
5	5114	2452

prune149.0ms (5.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	18.1b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 3853 to 2593 computations (32.7% saved)

regimes274.0ms (10.8%)

Accuracy

Total 0.0b remaining (50.6%)

Threshold costs 0.0b (50.6%)

Counts

44 → 1

Compiler

Compiled 4329 to 3190 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end68.0ms (2.7%)

Compiler: Compiled 78 to 55 computations (29.5% saved)

Details

analyze108.0ms (4.3%)

sample1.1s (41.5%)

simplify44.0ms (1.7%)

prune4.0ms (0.2%)

localize8.0ms (0.3%)

series77.0ms (3%)

rewrite7.0ms (0.3%)

simplify62.0ms (2.5%)

prune64.0ms (2.5%)

localize9.0ms (0.3%)

series62.0ms (2.5%)

rewrite28.0ms (1.1%)

simplify131.0ms (5.2%)

prune137.0ms (5.4%)

localize10.0ms (0.4%)

series108.0ms (4.3%)

rewrite20.0ms (0.8%)

simplify112.0ms (4.4%)

prune149.0ms (5.9%)

regimes274.0ms (10.8%)

simplify2.0ms (0.1%)

end68.0ms (2.7%)

Profiling