Details

analyze100.0ms (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 (39%)

Results

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

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify41.0ms (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

prune5.0ms (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
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series79.0ms (2.9%)

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)
11.0ms	(hypot.f64 a b)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 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)
0.0ms	(hypot.f64 a b)

simplify101.0ms (3.7%)

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 → 120

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

prune127.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Error

Counts

122 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	11.2b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2481 to 1574 computations (36.6% saved)

localize11.0ms (0.4%)

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)) (-.f64 (pow.f64 a 4) 1))
✓	1.0b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series52.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
24.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-+r+_binary64`
22×	`*-un-lft-identity_binary64`
21×	`prod-diff_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify114.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1022×	`fma-neg_binary64`
406×	`fma-def_binary64`
323×	`distribute-rgt-in_binary64`
316×	`distribute-lft-in_binary64`
218×	`associate-l_binary64`

Counts

104 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	2771
1	213	2370
2	569	2351
3	3145	2351
4	4559	2351
5	4958	2351

prune125.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Error

Counts

105 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	11.2b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 3082 to 2074 computations (32.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series131.0ms (4.7%)

Counts

3 → 72

Calls

3 calls:

54.0ms	(pow.f64 (hypot.f64 a b) 2)
39.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
38.0ms	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64`
12×	`fma-def_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

6.0ms	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
5.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
1.0ms	(pow.f64 (hypot.f64 a b) 2)

simplify147.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

444×	`log-prod_binary64`
413×	`exp-prod_binary64`
342×	`cancel-sign-sub-inv_binary64`
321×	`fma-def_binary64`
284×	`fma-neg_binary64`

Counts

149 → 127

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	111	2194
1	252	1935
2	640	1839
3	2392	1834
4	4109	1834
5	4473	1828
6	4971	1828
7	4924	1828

prune151.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
▶	11.2b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 3795 to 2581 computations (32% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.1b	(*.f64 b (fma.f64 b b 4))

series6.0ms (0.2%)

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 (0.1%)

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)

simplify79.0ms (2.9%)

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	2085	579
5	3908	579
6	4988	579
7	4818	579

prune52.0ms (1.9%)

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 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
✓	11.2b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 899 to 583 computations (35.2% saved)

regimes217.0ms (7.8%)

Accuracy

Total 0.0b remaining (53.6%)

Threshold costs 0.0b (53.6%)

Counts

29 → 1

Compiler

Compiled 2573 to 1924 computations (25.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	20	27
2	21	27
3	19	27

end88.0ms (3.2%)

Compiler: Compiled 105 to 75 computations (28.6% saved)

Details

analyze100.0ms (3.6%)

sample1.1s (39%)

simplify41.0ms (1.5%)

prune5.0ms (0.2%)

localize7.0ms (0.2%)

series79.0ms (2.9%)

rewrite7.0ms (0.3%)

simplify101.0ms (3.7%)

prune127.0ms (4.6%)

localize11.0ms (0.4%)

series52.0ms (1.9%)

rewrite13.0ms (0.5%)

simplify114.0ms (4.1%)

prune125.0ms (4.5%)

localize9.0ms (0.3%)

series131.0ms (4.7%)

rewrite16.0ms (0.6%)

simplify147.0ms (5.3%)

prune151.0ms (5.5%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify79.0ms (2.9%)

prune52.0ms (1.9%)

regimes217.0ms (7.8%)

simplify3.0ms (0.1%)

end88.0ms (3.2%)

Profiling