Details

analyze269.0ms (6.3%)

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%	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)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -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 141 to 90 computations (36.2% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (hypot.f64 a b) 4)
0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.5b	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite219.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`fma-udef_binary64`
16×	`pow1_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 147

Calls

4 calls:

52.0ms	(pow.f64 (hypot.f64 a b) 4)
16.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

Compiler

Compiled 3804 to 1933 computations (49.2% saved)

series218.0ms (5.1%)

Error

0.0b

Counts

4 → 58

Calls

4 calls:

70.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
66.0ms	(pow.f64 (hypot.f64 a b) 4)
26.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
21.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

Compiler

Compiled 2878 to 2121 computations (26.3% saved)

simplify113.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

536×	`cancel-sign-sub-inv_binary64`
511×	`distribute-rgt-in_binary64`
306×	`fma-neg_binary64`
274×	`unswap-sqr_binary64`
216×	`distribute-rgt-neg-in_binary64`

Counts

205 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3497
1	552	3279
2	2022	3145
3	5178	3145

prune90.0ms (2.1%)

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 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
	12.4b	(+.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
	13.2b	(+.f64 (.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12)))) -1)

Compiler

Compiled 2454 to 1317 computations (46.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.5b	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite187.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-cube-cbrt_binary64`
18×	`fma-udef_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 150

Calls

4 calls:

15.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
15.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
9.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

Compiler

Compiled 4477 to 1949 computations (56.5% saved)

series171.0ms (4%)

Error

Counts

4 → 58

Calls

4 calls:

54.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
43.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
25.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
18.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

Compiler

Compiled 3038 to 2184 computations (28.1% saved)

simplify138.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-neg_binary64`
542×	`cancel-sign-sub-inv_binary64`
337×	`unswap-sqr_binary64`
232×	`associate-r_binary64`
228×	`associate-l_binary64`

Counts

208 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	3763
1	567	3539
2	2115	3456
3	4497	3440
4	4955	3440

prune102.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	130	4	134

Error

Counts

134 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
▶	12.4b	(+.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
	13.2b	(+.f64 (.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12)))) -1)

Compiler

Compiled 2996 to 1438 computations (52% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 b b))
0.0b	(+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b)))))
0.1b	(*.f64 (pow.f64 a 3) (+.f64 4 a))
1.3b	(.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b))))

rewrite263.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-sqr-sqrt_binary64`
23×	`flip3-+_binary64`
22×	`add-exp-log_binary64`
20×	`associate-*r/_binary64`
19×	`pow1_binary64`

Counts

4 → 176

Calls

4 calls:

27.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b)))))
21.0ms	(.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b))))
19.0ms	(*.f64 (pow.f64 a 3) (+.f64 4 a))
16.0ms	(.f64 2 (.f64 b b))

Compiler

Compiled 4874 to 3146 computations (35.5% saved)

series103.0ms (2.4%)

Error

Counts

4 → 33

Calls

4 calls:

49.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b)))))
25.0ms	(.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b))))
10.0ms	(*.f64 (pow.f64 a 3) (+.f64 4 a))
6.0ms	(.f64 2 (.f64 b b))

Compiler

Compiled 1448 to 1162 computations (19.8% saved)

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
484×	`associate-l_binary64`
436×	`associate-r_binary64`
241×	`fma-def_binary64`
224×	`cube-prod_binary64`

Counts

209 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3673
1	721	3173
2	3652	3167
3	5127	3167

prune104.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	133	4	137

Error

Counts

137 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	12.4b	(+.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
▶	13.2b	(+.f64 (.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12)))) -1)

Compiler

Compiled 2765 to 1802 computations (34.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(fma.f64 b b (*.f64 a -12))
0.0b	(+.f64 4 (fma.f64 b b (*.f64 a -12)))
0.6b	(.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12))))

rewrite137.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64`
11×	`flip3-+_binary64`

Counts

3 → 124

Calls

3 calls:

15.0ms	(+.f64 4 (fma.f64 b b (*.f64 a -12)))
15.0ms	(.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12))))
10.0ms	(fma.f64 b b (*.f64 a -12))

Compiler

Compiled 2419 to 1505 computations (37.8% saved)

series78.0ms (1.8%)

Error

Counts

3 → 36

Calls

3 calls:

27.0ms	(.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12))))
19.0ms	(+.f64 4 (fma.f64 b b (*.f64 a -12)))
16.0ms	(fma.f64 b b (*.f64 a -12))

Compiler

Compiled 1008 to 778 computations (22.8% saved)

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-neg_binary64`
809×	`fma-def_binary64`
311×	`cancel-sign-sub-inv_binary64`
293×	`unswap-sqr_binary64`
194×	`distribute-rgt-neg-in_binary64`

Counts

160 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	2216
1	410	1997
2	1644	1836
3	4623	1836
4	5245	1836

prune77.0ms (1.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	109	4	113

Error

Counts

113 → 4

Alt Table

Status	Error	Program
	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
	12.4b	(+.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (.f64 (.f64 a a) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
	13.2b	(+.f64 (.f64 (.f64 b b) (+.f64 4 (fma.f64 b b (*.f64 a -12)))) -1)

Compiler

Compiled 1544 to 928 computations (39.9% saved)

regimes521.0ms (12.2%)

Accuracy

Total 0.0b remaining (79.7%)

Threshold costs 0.0b (79.7%)

Compiler

Compiled 10757 to 7474 computations (30.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25
2	13	25

end1.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

sample1.1s (25.9%)

Algorithm

1×

intervals

Results

719.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 149 to 97 computations (34.9% saved)

Details

analyze269.0ms (6.3%)

sample30.0ms (0.7%)

simplify67.0ms (1.6%)

prune4.0ms (0.1%)

localize15.0ms (0.4%)

rewrite219.0ms (5.1%)

series218.0ms (5.1%)

simplify113.0ms (2.6%)

prune90.0ms (2.1%)

localize15.0ms (0.4%)

rewrite187.0ms (4.4%)

series171.0ms (4%)

simplify138.0ms (3.2%)

prune102.0ms (2.4%)

localize13.0ms (0.3%)

rewrite263.0ms (6.1%)

series103.0ms (2.4%)

simplify119.0ms (2.8%)

prune104.0ms (2.4%)

localize8.0ms (0.2%)

rewrite137.0ms (3.2%)

series78.0ms (1.8%)

simplify104.0ms (2.4%)

prune77.0ms (1.8%)

regimes521.0ms (12.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (25.9%)

Profiling