Details

analyze173.0ms (5%)

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%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.3s (38.5%)

Results

1.3s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`fma-neg_binary64`
232×	`associate-+l+_binary64`
211×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	193	36
3	742	36
4	2867	32
5	4882	32

Stop Event

1×	node limit

Counts

1 → 2

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 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -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 1 (*.f64 3 a)))))) 1)

▶

0.0b

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

Compiler

Compiled 172 to 109 computations (36.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(*.f64 b (fma.f64 a -3 1))
✓	0.0b	(.f64 b (.f64 b (fma.f64 a -3 1)))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))

series27.0ms (0.8%)

Counts

4 → 84

Calls

4 calls:

11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
8.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
6.0ms	(*.f64 b (fma.f64 a -3 1))
1.0ms	(fma.f64 a -3 1)

rewrite49.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
328×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	195	43
2	2243	43

Stop Event

1×	node limit

Counts

4 → 80

Calls

4 calls:

48.0ms	(fma.f64 a -3 1)
48.0ms	(*.f64 b (fma.f64 a -3 1))
48.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
48.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

571×	`cancel-sign-sub-inv_binary64`
533×	`fma-neg_binary64`
443×	`fma-def_binary64`
375×	`associate-l_binary64`
262×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1149
1	86	1002
2	240	838
3	692	834
4	2630	834

Stop Event

1×	node limit

Counts

164 → 107

prune103.0ms (3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Error

0.0b

Counts

109 → 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 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -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 1 (*.f64 3 a)))))) 1)

✓

0.0b

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

Compiler

Compiled 2862 to 1625 computations (43.2% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 3 a))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series24.0ms (0.7%)

Counts

4 → 63

Calls

4 calls:

10.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
2.0ms	(.f64 (.f64 a a) (+.f64 1 a))
1.0ms	(-.f64 1 (*.f64 3 a))

rewrite64.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	41
1	336	38
2	4290	38

Stop Event

1×	node limit

Counts

4 → 109

Calls

4 calls:

59.0ms	(-.f64 1 (*.f64 3 a))
59.0ms	(.f64 (.f64 a a) (+.f64 1 a))
59.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
59.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
551×	`unswap-sqr_binary64`
541×	`associate-l_binary64`
397×	`associate-r_binary64`
183×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	816
1	71	792
2	192	726
3	609	726
4	2589	726

Stop Event

1×	node limit

Counts

172 → 132

prune168.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
	18.5b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 4921 to 2850 computations (42.1% saved)

localize23.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 3 a))
	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
	0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	0.6b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series10.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

10.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite32.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
399×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
161×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	144	7
2	1607	7

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

32.0ms

(*.f64 (pow.f64 a 2) (pow.f64 b 2))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

18 → 18

prune172.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
▶	18.5b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 4901 to 3459 computations (29.4% saved)

localize23.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
	0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	0.2b	(*.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2))
✓	24.3b	(/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (*.f64 b b)))

series71.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

49.0ms	(/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (*.f64 b b)))
22.0ms	(*.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2))

rewrite59.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`log1p-udef_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
158×	`add-sqr-sqrt_binary64`
156×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	347	26
2	4704	26

Stop Event

1×	node limit

Counts

2 → 76

Calls

2 calls:

57.0ms	(*.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2))
57.0ms	(/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (*.f64 b b)))

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
449×	`fma-neg_binary64`
355×	`cancel-sign-sub-inv_binary64`
298×	`difference-of-squares_binary64`
196×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	888
1	84	858
2	239	834
3	1040	834
4	3968	834

Stop Event

1×	node limit

Counts

124 → 98

prune218.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	159	3	162

Error

Counts

162 → 3

Alt Table

Status	Error	Program
✓	18.5b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 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 1 (.f64 3 a)))))) 1)

Compiler

Compiled 7160 to 4099 computations (42.8% saved)

regimes599.0ms (17.4%)

Accuracy

Total 0.0b remaining (35.1%)

Threshold costs 0.0b (35.1%)

Counts

99 → 1

Compiler

Compiled 16924 to 11814 computations (30.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	47	55
2	56	55
3	60	55
4	63	55
5	64	55

Stop Event

1×

saturated

end110.0ms (3.2%)

Compiler: Compiled 197 to 139 computations (29.4% saved)

Details

analyze173.0ms (5%)

sample1.3s (38.5%)

simplify33.0ms (0.9%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series27.0ms (0.8%)

rewrite49.0ms (1.4%)

simplify39.0ms (1.1%)

prune103.0ms (3%)

localize18.0ms (0.5%)

series24.0ms (0.7%)

rewrite64.0ms (1.9%)

simplify40.0ms (1.1%)

prune168.0ms (4.9%)

localize23.0ms (0.7%)

series10.0ms (0.3%)

rewrite32.0ms (0.9%)

simplify6.0ms (0.2%)

prune172.0ms (5%)

localize23.0ms (0.7%)

series71.0ms (2.1%)

rewrite59.0ms (1.7%)

simplify38.0ms (1.1%)

prune218.0ms (6.3%)

regimes599.0ms (17.4%)

simplify3.0ms (0.1%)

end110.0ms (3.2%)

Profiling