Details

analyze177.0ms (4.9%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.3s (36.3%)

Results

1.2s	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (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
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

0.0b

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

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize15.0ms (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 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.8b	(.f64 (.f64 b b) (+.f64 a 3))

series95.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(pow.f64 (hypot.f64 a b) 4)
35.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
15.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune182.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Error

0.0b

Counts

164 → 3

Alt Table

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

Compiler

Compiled 4921 to 2870 computations (41.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.8b	(.f64 (.f64 b b) (+.f64 a 3))
✓	10.2b	(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

series99.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

51.0ms

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

47.0ms

(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite3.0ms (0.1%)

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 (hypot.f64 a b) 4))

0.0ms

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

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
567×	`fma-neg_binary64`
532×	`cancel-sign-sub-inv_binary64`
512×	`associate-+l+_binary64`
335×	`distribute-lft-out_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1708
1	248	1553
2	746	1322
3	3076	1301
4	4889	1301
5	5008	1301

prune249.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	189	4	193

Error

Counts

193 → 4

Alt Table

Status	Error	Program
	12.4b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 6496 to 3718 computations (42.8% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
✓	0.0b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.8b	(.f64 (.f64 b b) (+.f64 3 a))

series42.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

18.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
13.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`associate-*r/_binary64`

Counts

4 → 126

Calls

4 calls:

10.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
8.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify119.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-neg_binary64`
508×	`associate-l_binary64`
407×	`associate-r_binary64`
259×	`unswap-sqr_binary64`
217×	`*-commutative_binary64`

Counts

210 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	3630
1	678	3284
2	2879	3079
3	4664	3079
4	5008	3079

prune253.0ms (7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
▶	12.4b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 8270 to 4216 computations (49% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	0.0b	(*.f64 b (fma.f64 b b 12))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
3.0ms	(*.f64 b (fma.f64 b b 12))

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 12))
0.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)

simplify75.0ms (2.1%)

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	60	650
1	112	579
2	300	579
3	964	579
4	2086	579
5	3910	579
6	4988	579
7	4817	579

prune61.0ms (1.7%)

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
✓	12.4b	(fma.f64 b (*.f64 b (fma.f64 b b 12)) -1)
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 935 to 602 computations (35.6% saved)

regimes507.0ms (14%)

Accuracy

Total 0.0b remaining (61.4%)

Threshold costs 0.0b (61.4%)

Counts

104 → 1

Compiler

Compiled 12111 to 8285 computations (31.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	21	33
2	25	33
3	27	33
4	28	33
5	28	33

end92.0ms (2.5%)

Compiler: Compiled 149 to 98 computations (34.2% saved)

Details

analyze177.0ms (4.9%)

sample1.3s (36.3%)

simplify58.0ms (1.6%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series95.0ms (2.6%)

rewrite18.0ms (0.5%)

simplify81.0ms (2.2%)

prune182.0ms (5%)

localize16.0ms (0.4%)

series99.0ms (2.7%)

rewrite3.0ms (0.1%)

simplify87.0ms (2.4%)

prune249.0ms (6.9%)

localize14.0ms (0.4%)

series42.0ms (1.2%)

rewrite35.0ms (1%)

simplify119.0ms (3.3%)

prune253.0ms (7%)

localize5.0ms (0.1%)

series6.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify75.0ms (2.1%)

prune61.0ms (1.7%)

regimes507.0ms (14%)

simplify2.0ms (0.1%)

end92.0ms (2.5%)

Profiling