Details

analyze197.0ms (5.7%)

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)

sample1.4s (39.5%)

Results

1.3s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify58.0ms (1.7%)

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 → 2

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

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 (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)

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 (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)

Compiler

Compiled 172 to 108 computations (37.2% 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	(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))

series58.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

35.0ms	(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))
12.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(fma.f64 a -3 1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

4.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(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))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a -3 1)

simplify101.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune149.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	124	3	127

Error

0.0b

Counts

127 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -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)
✓	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)

Compiler

Compiled 3620 to 2039 computations (43.7% saved)

localize23.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 a 2))
✓	0.2b	(.f64 12 (.f64 a (pow.f64 b 2)))
✓	0.5b	(*.f64 a (pow.f64 b 2))
✓	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series37.0ms (1.1%)

Counts

4 → 0

Calls

4 calls:

16.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
8.0ms	(*.f64 a (pow.f64 b 2))
2.0ms	(*.f64 4 (pow.f64 a 2))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`add-exp-log_binary64`
25×	`associate-r_binary64`
24×	`unswap-sqr_binary64`
22×	`unpow-prod-down_binary64`

Counts

4 → 132

Calls

4 calls:

6.0ms	(*.f64 4 (pow.f64 a 2))
5.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
4.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
4.0ms	(*.f64 a (pow.f64 b 2))

simplify109.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-def_binary64`
376×	`*-commutative_binary64`
327×	`sqr-pow_binary64`
307×	`log-prod_binary64`
261×	`exp-prod_binary64`

Counts

132 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	1426
1	300	1231
2	899	1195
3	1646	1138
4	2836	1138
5	4603	1138
6	4910	1138
7	4929	1138

prune306.0ms (8.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Error

0.0b

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -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)
✓	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)

Compiler

Compiled 9547 to 7371 computations (22.8% saved)

localize17.0ms (0.5%)

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 1 (.f64 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.5b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series46.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

20.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 107

Calls

4 calls:

9.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
6.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))
3.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify106.0ms (3%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-neg_binary64`
393×	`associate-l_binary64`
327×	`associate-r_binary64`
279×	`associate-+l+_binary64`
274×	`associate-+r+_binary64`

Counts

191 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3558
1	659	3149
2	2503	3093
3	4569	3093
4	5073	3093

prune292.0ms (8.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	198	3	201

Error

0.0b

Counts

201 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -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)
✓	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)

Compiler

Compiled 7787 to 4431 computations (43.1% saved)

regimes390.0ms (11.2%)

Accuracy

Total 0.0b remaining (42.5%)

Threshold costs 0.0b (42.5%)

Counts

55 → 1

Compiler

Compiled 7331 to 5098 computations (30.5% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

8×	`+-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	24	56
1	45	56
2	52	56
3	56	56
4	59	56
5	60	56
6	57	56

end126.0ms (3.6%)

Compiler: Compiled 185 to 129 computations (30.3% saved)

Details

analyze197.0ms (5.7%)

sample1.4s (39.5%)

simplify58.0ms (1.7%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series58.0ms (1.7%)

rewrite7.0ms (0.2%)

simplify101.0ms (2.9%)

prune149.0ms (4.3%)

localize23.0ms (0.7%)

series37.0ms (1.1%)

rewrite24.0ms (0.7%)

simplify109.0ms (3.1%)

prune306.0ms (8.8%)

localize17.0ms (0.5%)

series46.0ms (1.3%)

rewrite31.0ms (0.9%)

simplify106.0ms (3%)

prune292.0ms (8.4%)

regimes390.0ms (11.2%)

simplify9.0ms (0.3%)

end126.0ms (3.6%)

Profiling