Details

analyze192.0ms (5.1%)

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 (34.9%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify60.0ms (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 → 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)

localize13.0ms (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)))
✓	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series64.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

38.0ms	(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))
15.0ms	(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)

rewrite8.0ms (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 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)))

simplify105.0ms (2.8%)

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

prune156.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Error

0.0b

Counts

127 → 4

Alt Table

Status	Error	Program
	11.2b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -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)
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4)) -1)

Compiler

Compiled 3630 to 2035 computations (43.9% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a a (pow.f64 a 3))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
✓	0.0b	(*.f64 a (fma.f64 a 2 -12))
✓	1.1b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))

series51.0ms (1.4%)

Counts

4 → 72

Calls

4 calls:

25.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
19.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
4.0ms	(*.f64 a (fma.f64 a 2 -12))
3.0ms	(fma.f64 a a (pow.f64 a 3))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
3.0ms	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
3.0ms	(*.f64 a (fma.f64 a 2 -12))
0.0ms	(fma.f64 a a (pow.f64 a 3))

simplify118.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
571×	`associate-+l+_binary64`
397×	`*-commutative_binary64`
380×	`associate-+r+_binary64`
317×	`exp-sum_binary64`

Counts

147 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	3705
1	468	2785
2	1669	2717
3	3700	2717
4	4999	2717
5	4926	2717

prune219.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	156	4	160

Error

Counts

160 → 4

Alt Table

Status	Error	Program
	11.2b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -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)
▶	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4)) -1)

Compiler

Compiled 5907 to 3840 computations (35% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a a (pow.f64 a 3))
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))
✓	0.1b	(.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
✓	0.1b	(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

series70.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

27.0ms

(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))

22.0ms

(*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))

21.0ms

(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

3 → 64

Calls

3 calls:

4.0ms

(*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))

3.0ms

(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))

3.0ms

(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

simplify103.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

462×	`associate-+l+_binary64`
433×	`distribute-rgt-in_binary64`
416×	`distribute-lft-in_binary64`
414×	`fma-neg_binary64`
272×	`associate-+r+_binary64`

Counts

136 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	4085
1	413	3508
2	1332	2889
3	4664	2889
4	4970	2889

prune193.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
	11.2b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -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)
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4)) -1)

Compiler

Compiled 5177 to 3390 computations (34.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.2b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series58.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

30.0ms	(+.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))))))
13.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
12.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`

Counts

4 → 102

Calls

4 calls:

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

simplify91.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

870×	`distribute-rgt-in_binary64`
807×	`distribute-lft-in_binary64`
278×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
213×	`associate-r_binary64`

Counts

186 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3661
1	577	3211
2	1997	3007
3	5819	3007

prune250.0ms (6.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
	11.2b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -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)
✓	0.1b	(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4)) -1)

Compiler

Compiled 7326 to 4164 computations (43.2% saved)

regimes473.0ms (12.6%)

Accuracy

Total 0.0b remaining (83.9%)

Threshold costs 0.0b (83.9%)

Counts

75 → 1

Compiler

Compiled 9237 to 6487 computations (29.8% saved)

simplify2.0ms (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

end105.0ms (2.8%)

Compiler: Compiled 149 to 96 computations (35.6% saved)

Details

analyze192.0ms (5.1%)

sample1.3s (34.9%)

simplify60.0ms (1.6%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series64.0ms (1.7%)

rewrite8.0ms (0.2%)

simplify105.0ms (2.8%)

prune156.0ms (4.1%)

localize18.0ms (0.5%)

series51.0ms (1.4%)

rewrite18.0ms (0.5%)

simplify118.0ms (3.1%)

prune219.0ms (5.8%)

localize16.0ms (0.4%)

series70.0ms (1.9%)

rewrite13.0ms (0.4%)

simplify103.0ms (2.7%)

prune193.0ms (5.1%)

localize16.0ms (0.4%)

series58.0ms (1.5%)

rewrite31.0ms (0.8%)

simplify91.0ms (2.4%)

prune250.0ms (6.6%)

regimes473.0ms (12.6%)

simplify2.0ms (0.1%)

end105.0ms (2.8%)

Profiling