Details

analyze104.0ms (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)

sample1.1s (36.8%)

Results

995.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify41.0ms (1.4%)

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 3 expressions with local error:

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

series81.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

36.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
33.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 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)
0.0ms	(hypot.f64 a b)

simplify99.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
280×	`associate-r_binary64`
276×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2123
1	343	2010
2	979	1901
3	4070	1899
4	4922	1899
5	4944	1899

prune106.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Error

Counts

116 → 4

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
	11.7b	(+.f64 (fma.f64 2 (.f64 (.f64 a a) (.f64 b b)) (pow.f64 b 4)) (fma.f64 b (.f64 b 4) -1))
	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 2412 to 1545 computations (35.9% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series42.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
6.0ms	(+.f64 (.f64 a a) (.f64 b b))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`fma-def_binary64`
9×	`*-un-lft-identity_binary64`
7×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 57

Calls

3 calls:

7.0ms	(+.f64 (.f64 a a) (.f64 b b))
6.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify124.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
541×	`fma-neg_binary64`
450×	`associate-l_binary64`
400×	`associate-r_binary64`
310×	`distribute-rgt-in_binary64`

Counts

129 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2036
1	286	1858
2	879	1687
3	4101	1685
4	4964	1685
5	4990	1685
6	4935	1685

prune96.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

Counts

117 → 4

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
▶	8.0b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2) (fma.f64 b (*.f64 b 4) -1))
	11.7b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)

Compiler

Compiled 2549 to 1372 computations (46.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 b a) 2)
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)
✓	0.3b	(pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2)
✓	24.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3))

series161.0ms (5.6%)

Counts

4 → 96

Calls

4 calls:

53.0ms	(pow.f64 (hypot.f64 b a) 2)
46.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3))
34.0ms	(pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2)
28.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`unpow-prod-down_binary64`
44×	`cbrt-prod_binary64`
24×	`cube-prod_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`

Counts

4 → 134

Calls

4 calls:

5.0ms	(pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2)
3.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3))
3.0ms	(pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)
1.0ms	(pow.f64 (hypot.f64 b a) 2)

simplify178.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

521×	`distribute-rgt-in_binary64`
443×	`fma-def_binary64`
412×	`sqr-pow_binary64`
399×	`distribute-lft-in_binary64`
393×	`exp-prod_binary64`

Counts

230 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	3030
1	271	2659
2	719	2578
3	1169	2539
4	2272	2539
5	4115	2539
6	4619	2539
7	4986	2539
8	4822	2539

prune149.0ms (5.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	160	4	164

Error

Counts

164 → 4

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	8.0b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2) (fma.f64 b (*.f64 b 4) -1))
▶	11.7b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)

Compiler

Compiled 3753 to 2605 computations (30.6% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)
✓	0.8b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series46.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))
21.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify80.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

537×	`sub-neg_binary64`
425×	`unsub-neg_binary64`
360×	`*-commutative_binary64`
285×	`exp-prod_binary64`
273×	`cancel-sign-sub-inv_binary64`

Counts

77 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1758
1	135	1492
2	323	1471
3	1561	1469
4	3616	1469
5	5205	1469

prune60.0ms (2.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	63	4	67

Error

Counts

67 → 4

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 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	8.0b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 3)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	11.7b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1)

Compiler

Compiled 1512 to 899 computations (40.5% saved)

regimes261.0ms (9%)

Accuracy

Total 0.0b remaining (64.8%)

Threshold costs 0.0b (64.8%)

Counts

31 → 1

Compiler

Compiled 3388 to 2449 computations (27.7% 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

end106.0ms (3.7%)

Compiler: Compiled 96 to 69 computations (28.1% saved)

Details

analyze104.0ms (3.6%)

sample1.1s (36.8%)

simplify41.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

series81.0ms (2.8%)

rewrite9.0ms (0.3%)

simplify99.0ms (3.4%)

prune106.0ms (3.7%)

localize9.0ms (0.3%)

series42.0ms (1.4%)

rewrite19.0ms (0.7%)

simplify124.0ms (4.3%)

prune96.0ms (3.3%)

localize11.0ms (0.4%)

series161.0ms (5.6%)

rewrite18.0ms (0.6%)

simplify178.0ms (6.2%)

prune149.0ms (5.2%)

localize9.0ms (0.3%)

series46.0ms (1.6%)

rewrite4.0ms (0.1%)

simplify80.0ms (2.8%)

prune60.0ms (2.1%)

regimes261.0ms (9%)

simplify2.0ms (0.1%)

end106.0ms (3.7%)

Profiling