Details

analyze94.0ms (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)

sample82.0ms (3.8%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify43.0ms (2%)

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)

localize7.0ms (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))

series72.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
34.0ms	(pow.f64 (hypot.f64 a b) 4)

rewrite9.0ms (0.4%)

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:

6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify60.0ms (2.8%)

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

prune69.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	0	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))
	16.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))
▶	11.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

Compiler

Compiled 1503 to 927 computations (38.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 b (fma.f64 b b 4))
✓	0.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
3.0ms	(*.f64 b (fma.f64 b b 4))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 b (fma.f64 b b 4))
0.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

simplify80.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
764×	`fma-def_binary64`
404×	`associate-+l+_binary64`
395×	`unswap-sqr_binary64`
359×	`associate-+r+_binary64`

Counts

56 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	650
1	111	579
2	299	579
3	963	579
4	2087	579
5	3910	579
6	4990	579
7	4818	579

prune49.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	16.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))
✓	11.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

Compiler

Compiled 895 to 579 computations (35.3% saved)

localize10.0ms (0.5%)

Local error

Found 4 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 4 (*.f64 b b) -1))
✓	0.1b	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3)
✓	15.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))

series184.0ms (8.5%)

Counts

3 → 72

Calls

3 calls:

102.0ms

(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3)

42.0ms

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

40.0ms

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

rewrite20.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`unpow-prod-down_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

7.0ms

(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3)

5.0ms

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

4.0ms

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

simplify192.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

439×	`unswap-sqr_binary64`
436×	`fma-def_binary64`
419×	`associate-+r+_binary64`
271×	`associate-+l+_binary64`
249×	`+-commutative_binary64`

Counts

150 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	4846
1	851	4487
2	3470	4467
3	4627	4467
4	4967	4467
5	4965	4467

prune153.0ms (7.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	153	3	156

Error

Counts

156 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	16.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))
✓	11.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

Compiler

Compiled 4983 to 3317 computations (33.4% saved)

regimes298.0ms (13.8%)

Accuracy

Total 0.0b remaining (29.1%)

Threshold costs 0.0b (29.1%)

Counts

34 → 1

Compiler

Compiled 2898 to 2185 computations (24.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	11	17
2	11	17

end1.0ms (0%)

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

sample712.0ms (33%)

Algorithm

1×

intervals

Results

442.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 78 to 55 computations (29.5% saved)

Details

analyze94.0ms (4.3%)

sample82.0ms (3.8%)

simplify43.0ms (2%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

series72.0ms (3.3%)

rewrite9.0ms (0.4%)

simplify60.0ms (2.8%)

prune69.0ms (3.2%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify80.0ms (3.7%)

prune49.0ms (2.2%)

localize10.0ms (0.5%)

series184.0ms (8.5%)

rewrite20.0ms (0.9%)

simplify192.0ms (8.9%)

prune153.0ms (7.1%)

regimes298.0ms (13.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample712.0ms (33%)

Profiling