Details

analyze167.0ms (4.5%)

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)

sample87.0ms (2.3%)

Algorithm

1×

intervals

Results

25.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify62.0ms (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)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series98.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(pow.f64 (hypot.f64 a b) 4)
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)))
11.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

simplify122.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
417×	`fma-neg_binary64`
408×	`associate-+l+_binary64`
315×	`cancel-sign-sub-inv_binary64`
250×	`exp-prod_binary64`

Counts

159 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	3218
1	364	2814
2	1065	2628
3	3367	2622
4	4754	2618
5	4990	2618

prune174.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	139	3	142

Error

0.0b

Counts

142 → 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)
	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -1)

Compiler

Compiled 4104 to 2268 computations (44.7% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 2)
	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.1b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

series92.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

49.0ms	(pow.f64 (hypot.f64 a b) 2)
43.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
1.0ms	(pow.f64 (hypot.f64 a b) 2)

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
456×	`associate-/l/_binary64`
413×	`sqr-pow_binary64`
353×	`*-commutative_binary64`
334×	`log-prod_binary64`

Counts

98 → 78

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	1237
1	141	1046
2	302	1013
3	892	1010
4	1517	1007
5	3029	1007
6	4733	1007
7	4757	1007

prune174.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	144	3	147

Error

0.0b

Counts

147 → 3

Alt Table

Status	Error	Program
▶	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 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))) -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)
	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)

Compiler

Compiled 4564 to 2607 computations (42.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4)))
	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.1b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.3b	(pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))

series43.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4)))
15.0ms	(pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow-unpow_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4)))

simplify110.0ms (3%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-def_binary64`
592×	`unswap-sqr_binary64`
490×	`cancel-sign-sub-inv_binary64`
402×	`associate-+l+_binary64`
308×	`fma-neg_binary64`

Counts

80 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1997
1	244	1804
2	673	1554
3	2699	1550
4	4586	1550
5	5000	1550
6	4956	1550

prune165.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	147	3	150

Error

0.0b

Counts

150 → 3

Alt Table

Status	Error	Program
✓	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 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))) -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)
▶	12.2b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)

Compiler

Compiled 4738 to 2476 computations (47.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))
✓	0.0b	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))))
✓	0.0b	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	2.7b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series86.0ms (2.3%)

Counts

4 → 15

Calls

4 calls:

30.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))))
21.0ms	(+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))
18.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
17.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
27×	`add-sqr-sqrt_binary64`
17×	`unpow-prod-down_binary64`
16×	`unswap-sqr_binary64`

Counts

4 → 117

Calls

4 calls:

12.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))))
6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
6.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
5.0ms	(+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
572×	`distribute-rgt-in_binary64`
533×	`distribute-lft-in_binary64`
224×	`cancel-sign-sub-inv_binary64`
188×	`associate-r_binary64`

Counts

132 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2260
1	417	1953
2	1510	1899
3	5170	1899

prune332.0ms (9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	168	3	171

Error

Counts

171 → 3

Alt Table

Status	Error	Program
✓	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 (fma.f64 b b (*.f64 a a)) (sqrt.f64 4))) -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)
	35.1b	(+.f64 (/.f64 (-.f64 (.f64 (.f64 4 (pow.f64 a 2)) (.f64 4 (pow.f64 a 2))) (.f64 (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))))) (-.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))))) -1)

Compiler

Compiled 5829 to 4406 computations (24.4% saved)

regimes613.0ms (16.6%)

Accuracy

Total 0.0b remaining (37.4%)

Threshold costs 0.0b (37.4%)

Counts

100 → 1

Compiler

Compiled 14560 to 10499 computations (27.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	31	50
2	30	50

end1.0ms (0%)

Compiler: Compiled 37 to 26 computations (29.7% saved)

sample1.1s (29.1%)

Algorithm

1×

intervals

Results

693.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 208 to 150 computations (27.9% saved)

Details

analyze167.0ms (4.5%)

sample87.0ms (2.3%)

simplify62.0ms (1.7%)

prune5.0ms (0.1%)

localize16.0ms (0.4%)

series98.0ms (2.6%)

rewrite10.0ms (0.3%)

simplify122.0ms (3.3%)

prune174.0ms (4.7%)

localize18.0ms (0.5%)

series92.0ms (2.5%)

rewrite7.0ms (0.2%)

simplify93.0ms (2.5%)

prune174.0ms (4.7%)

localize17.0ms (0.4%)

series43.0ms (1.2%)

rewrite4.0ms (0.1%)

simplify110.0ms (3%)

prune165.0ms (4.5%)

localize15.0ms (0.4%)

series86.0ms (2.3%)

rewrite36.0ms (1%)

simplify66.0ms (1.8%)

prune332.0ms (9%)

regimes613.0ms (16.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (29.1%)

Profiling