Details

analyze399.0ms (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)

sample63.0ms (0.8%)

Algorithm

1×

intervals

Results

48.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify84.0ms (1.1%)

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

prune9.0ms (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)

localize28.0ms (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))
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite17.0ms (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:

10.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
1.0ms	(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))
1.0ms	(fma.f64 a -3 1)
1.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))

series203.0ms (2.6%)

Counts

4 → 84

Calls

4 calls:

86.0ms	(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))
57.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
51.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(fma.f64 a -3 1)

simplify211.0ms (2.7%)

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 → 250

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

prune272.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	249	3	252

Error

0.0b

Counts

252 → 3

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)
	10.8b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
▶	8.2b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 3583 to 2012 computations (43.8% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))
✓	0.0b	(+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))
✓	0.0b	(*.f64 a (fma.f64 a 2 -12))
✓	1.3b	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))

rewrite80.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

55.0ms	(+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))
11.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
5.0ms	(*.f64 a (fma.f64 a 2 -12))
1.0ms	(fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))

series249.0ms (3.2%)

Counts

4 → 84

Calls

4 calls:

74.0ms	(.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
69.0ms	(fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))
44.0ms	(+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))
17.0ms	(*.f64 a (fma.f64 a 2 -12))

simplify223.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-def_binary64`
644×	`fma-neg_binary64`
439×	`cancel-sign-sub-inv_binary64`
350×	`*-commutative_binary64`
226×	`unswap-sqr_binary64`

Counts

160 → 302

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	3684
1	387	2626
2	1365	2610
3	3123	2610
4	4993	2610
5	4990	2610

prune406.0ms (5.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	301	4	305

Error

Counts

305 → 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)
	10.8b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
▶	8.3b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))) -1)
✓	8.2b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 4881 to 3062 computations (37.3% saved)

localize68.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
✓	0.0b	(sqrt.f64 (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
✓	0.6b	(.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) (sqrt.f64 (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))
✓	0.7b	(.f64 (.f64 b b) (sqrt.f64 (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
16×	`sqrt-div_binary64`
12×	`associate-r_binary64`

Counts

3 → 78

Calls

3 calls:

20.0ms

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

13.0ms

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

4.0ms

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

series280.0ms (3.6%)

Counts

3 → 72

Calls

3 calls:

140.0ms

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

79.0ms

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

60.0ms

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

simplify278.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
439×	`fma-def_binary64`
394×	`associate-l_binary64`
358×	`associate-r_binary64`
228×	`associate-+l+_binary64`

Counts

150 → 285

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	6275
1	1329	5610
2	4936	5604
3	5316	5604

prune996.0ms (12.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	361	0	361
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	361	4	365

Error

Counts

365 → 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)
▶	10.8b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	8.3b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))) -1)
✓	8.2b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 16746 to 11540 computations (31.1% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))
✓	0.0b	(.f64 2 (.f64 b b))
✓	0.0b	(*.f64 a (+.f64 4 a))
✓	1.8b	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))

rewrite65.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

22.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
14.0ms	(+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))
9.0ms	(*.f64 a (+.f64 4 a))
8.0ms	(.f64 2 (.f64 b b))

series147.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

70.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
45.0ms	(+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))
19.0ms	(.f64 2 (.f64 b b))
13.0ms	(*.f64 a (+.f64 4 a))

simplify220.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-neg_binary64`
411×	`associate-+l+_binary64`
399×	`associate-+r+_binary64`
366×	`associate-l_binary64`
296×	`associate-r_binary64`

Counts

169 → 312

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	3345
1	611	2707
2	2491	2683
3	4893	2677
4	5420	2677

prune398.0ms (5.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	312	4	316

Error

Counts

316 → 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)
✓	10.8b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	8.3b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 (.f64 b b) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) (sqrt.f64 (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12)))))) -1)
✓	8.2b	(+.f64 (fma.f64 a (.f64 a 4) (.f64 (.f64 b b) (+.f64 (fma.f64 b b 4) (.f64 a (fma.f64 a 2 -12))))) -1)

Compiler

Compiled 5167 to 3208 computations (37.9% saved)

regimes1.1s (14.6%)

Accuracy

Total 0.0b remaining (48.7%)

Threshold costs 0.0b (48.7%)

Compiler

Compiled 12141 to 8564 computations (29.5% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
2	19	32

end1.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

sample1.9s (24.4%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 169 to 113 computations (33.1% saved)

Details

analyze399.0ms (5.1%)

sample63.0ms (0.8%)

simplify84.0ms (1.1%)

prune9.0ms (0.1%)

localize28.0ms (0.4%)

rewrite17.0ms (0.2%)

series203.0ms (2.6%)

simplify211.0ms (2.7%)

prune272.0ms (3.5%)

localize26.0ms (0.3%)

rewrite80.0ms (1%)

series249.0ms (3.2%)

simplify223.0ms (2.8%)

prune406.0ms (5.2%)

localize68.0ms (0.9%)

rewrite51.0ms (0.6%)

series280.0ms (3.6%)

simplify278.0ms (3.5%)

prune996.0ms (12.7%)

localize23.0ms (0.3%)

rewrite65.0ms (0.8%)

series147.0ms (1.9%)

simplify220.0ms (2.8%)

prune398.0ms (5.1%)

regimes1.1s (14.6%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample1.9s (24.4%)

Profiling