Details

analyze105.0ms (3.6%)

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)

sample1.3s (44.3%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify42.0ms (1.5%)

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 (0.1%)

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

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)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series44.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
3×	`pow1_binary64`

Counts

2 → 30

Calls

2 calls:

1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify130.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
313×	`unswap-sqr_binary64`
224×	`distribute-neg-frac_binary64`
212×	`distribute-rgt-neg-in_binary64`

Counts

78 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	1171
1	236	1129
2	645	1086
3	2573	1086
4	4782	1086
5	5025	1086

prune78.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	77	2	79

Error

0.0b

Counts

79 → 2

Alt Table

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

Status

Error

Program

0.2b

(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))

▶

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1614 to 1047 computations (35.1% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))
✓	0.0b	(+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))
✓	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series49.0ms (1.7%)

Counts

3 → 18

Calls

3 calls:

19.0ms	(+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))
18.0ms	(+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))
11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
17×	`unpow-prod-down_binary64`
16×	`unswap-sqr_binary64`
15×	`add-exp-log_binary64`
11×	`sqr-pow_binary64`

Counts

3 → 90

Calls

3 calls:

10.0ms	(+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))
7.0ms	(+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))
5.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

simplify88.0ms (3%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
441×	`fma-def_binary64`
347×	`distribute-rgt-neg-in_binary64`
314×	`distribute-lft-neg-in_binary64`
309×	`*-commutative_binary64`

Counts

108 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1585
1	309	1463
2	1009	1423
3	3142	1383
4	4792	1383
5	5075	1383

prune155.0ms (5.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	134	2	136

Error

Counts

136 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Status

Error

Program

▶

0.1b

(+.f64 (fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

✓

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 4281 to 2986 computations (30.2% saved)

localize17.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))
	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
✓	10.8b	(sqrt.f64 (pow.f64 a 4))

series21.0ms (0.7%)

Counts

2 → 36

Calls

2 calls:

19.0ms	(fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))
2.0ms	(sqrt.f64 (pow.f64 a 4))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(sqrt.f64 (pow.f64 a 4))
0.0ms	(fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4)))

simplify68.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

842×	`associate-l_binary64`
699×	`associate-r_binary64`
592×	`distribute-rgt-in_binary64`
584×	`distribute-lft-in_binary64`
470×	`exp-prod_binary64`

Counts

67 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	942
1	81	881
2	191	761
3	633	758
4	4822	758
5	5470	758

prune250.0ms (8.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	183	2	185

Error

Counts

185 → 2

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Status

Error

Program

✓

0.1b

(+.f64 (fma.f64 (sqrt.f64 (pow.f64 a 4)) (sqrt.f64 (pow.f64 a 4)) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

✓

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 6316 to 4526 computations (28.3% saved)

regimes426.0ms (14.7%)

Accuracy

Total 0.0b remaining (5%)

Threshold costs 0.0b (5%)

Counts

70 → 1

Compiler

Compiled 8918 to 6413 computations (28.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	20	33
2	20	33

end81.0ms (2.8%)

Compiler: Compiled 107 to 82 computations (23.4% saved)

Details

analyze105.0ms (3.6%)

sample1.3s (44.3%)

simplify42.0ms (1.5%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

series44.0ms (1.5%)

rewrite3.0ms (0.1%)

simplify130.0ms (4.5%)

prune78.0ms (2.7%)

localize13.0ms (0.5%)

series49.0ms (1.7%)

rewrite26.0ms (0.9%)

simplify88.0ms (3%)

prune155.0ms (5.4%)

localize17.0ms (0.6%)

series21.0ms (0.7%)

rewrite5.0ms (0.2%)

simplify68.0ms (2.4%)

prune250.0ms (8.6%)

regimes426.0ms (14.7%)

simplify2.0ms (0.1%)

end81.0ms (2.8%)

Profiling