Details

analyze331.0ms (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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample983.0ms (16.9%)

Symmetry

(sort x y)

Results

897.0ms	8256×	body	128	valid
44.0ms	453×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

7.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.6b	(*.f64 y (fma.f64 z z 1))
✓	5.3b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

series95.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

85.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms	(*.f64 y (fma.f64 z z 1))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

5.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms	(*.f64 y (fma.f64 z z 1))

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
453×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
297×	`associate-r_binary64`

Counts

134 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2203
1	330	1967
2	1107	1965
3	3956	1963
4	4482	1963
5	4806	1963
6	4938	1963

prune132.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

3.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	5.7b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	22.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	28.5b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	8.0b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))) (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x)))) (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))))
	7.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
▶	5.3b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	5.5b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	51.1b	(/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (fma.f64 y (.f64 z z) y) (sqrt.f64 x)))
	7.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	7.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))

Compiler

Compiled 2640 to 1510 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.9b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
✓	3.6b	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

series121.0ms (2.1%)

Counts

2 → 60

Calls

2 calls:

81.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
40.0ms	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`times-frac_binary64`
126×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
76×	`add-exp-log_binary64`

Counts

2 → 182

Calls

2 calls:

15.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
4.0ms	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

simplify132.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
687×	`times-frac_binary64`
610×	`associate-/l*_binary64`
504×	`fma-neg_binary64`
455×	`associate-/r*_binary64`

Counts

242 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	5183
1	573	4561
2	1638	4502
3	4092	4490
4	5107	4490

prune335.0ms (5.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	296	7	303
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	299	14	313

Error

0.7b

Counts

313 → 14

Alt Table

Status	Error	Program
✓	5.3b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	5.4b	(/.f64 (/.f64 1 (*.f64 x (fma.f64 z z 1))) y)
	51.1b	(/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (fma.f64 y (.f64 z z) y) (sqrt.f64 x)))
	48.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (.f64 (hypot.f64 1 z) (sqrt.f64 x))) (/.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 (hypot.f64 1 z) (sqrt.f64 x))))
	5.7b	(/.f64 1 (.f64 (.f64 x (fma.f64 z z 1)) y))
	7.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	7.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))
	6.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 1 (cbrt.f64 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
	5.5b	(.f64 (/.f64 1 y) (/.f64 (/.f64 (/.f64 1 x) (.f64 (cbrt.f64 (fma.f64 z z 1)) (cbrt.f64 (fma.f64 z z 1)))) (cbrt.f64 (fma.f64 z z 1))))
	22.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	2.9b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	3.6b	(.f64 (/.f64 1 y) (.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (hypot.f64 1 z)) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z))))
	8.0b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))) (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x)))) (cbrt.f64 (/.f64 1 (.f64 (fma.f64 y (.f64 z z) y) x))))
	5.5b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))

Compiler

Compiled 7233 to 4815 computations (33.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 1 z))
✓	0.1b	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
✓	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	2.9b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))

series183.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

97.0ms	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
42.0ms	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
40.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
3.0ms	(/.f64 1 (hypot.f64 1 z))

rewrite82.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

451×	`add-exp-log_binary64`
220×	`div-exp_binary64`
191×	`times-frac_binary64`
184×	`prod-exp_binary64`
143×	`add-sqr-sqrt_binary64`

Counts

4 → 346

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
12.0ms	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
7.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
2.0ms	(/.f64 1 (hypot.f64 1 z))

simplify244.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
475×	`*-commutative_binary64`
339×	`fma-neg_binary64`
298×	`associate-/r/_binary64`
256×	`associate-r_binary64`

Counts

442 → 521

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	387	9628
1	940	8532
2	2613	8250
3	4207	8242
4	4946	8242

prune589.0ms (10.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	516	5	521
Fresh	5	7	12
Picked	1	0	1
Done	1	0	1
Total	523	12	535

Error

Counts

535 → 12

Alt Table

Status	Error	Program
	5.7b	(/.f64 1 (.f64 (.f64 x (fma.f64 z z 1)) y))
	7.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	7.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))
	6.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 1 (cbrt.f64 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
	22.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	2.9b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 (/.f64 (hypot.f64 1 z) (/.f64 1 x)))))
	17.9b	(.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (.f64 x (hypot.f64 1 z))))
▶	0.9b	(/.f64 (.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
	2.9b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (hypot.f64 1 z)) y)
	1.7b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	5.5b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	51.1b	(/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (fma.f64 y (.f64 z z) y) (sqrt.f64 x)))

Compiler

Compiled 13882 to 10371 computations (25.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 z)
	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	0.6b	(/.f64 (.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
✓	2.9b	(.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z))))

series207.0ms (3.6%)

Counts

3 → 84

Calls

3 calls:

106.0ms	(/.f64 (.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
99.0ms	(.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
2.0ms	(hypot.f64 1 z)

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

367×	`add-exp-log_binary64`
185×	`div-exp_binary64`
168×	`prod-exp_binary64`
78×	`1-exp_binary64`
77×	`add-cbrt-cube_binary64`

Counts

3 → 167

Calls

3 calls:

15.0ms	(/.f64 (.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
10.0ms	(.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
0.0ms	(hypot.f64 1 z)

simplify217.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-neg_binary64`
438×	`associate-/r/_binary64`
387×	`sub-neg_binary64`
377×	`fma-def_binary64`
316×	`*-commutative_binary64`

Counts

251 → 273

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	5260
1	673	4472
2	2069	4345
3	3944	4293
4	4910	4293
5	4983	4293
6	5000	4293
7	4933	4293

prune455.0ms (7.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	418	11	429

Error

Counts

429 → 11

Alt Table

Status	Error	Program
	3.5b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
	7.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z z 1))))
	7.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))
	6.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 1 (cbrt.f64 y)) (/.f64 (/.f64 1 x) (fma.f64 z z 1))))
	2.9b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 1 (/.f64 (hypot.f64 1 z) (/.f64 1 x)))))
	17.9b	(.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (.f64 x (hypot.f64 1 z))))
✓	0.9b	(/.f64 (.f64 (/.f64 1 y) (.f64 1 (/.f64 (/.f64 1 x) (hypot.f64 1 z)))) (hypot.f64 1 z))
	2.9b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (hypot.f64 1 z)) y)
	1.7b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	51.1b	(/.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (fma.f64 y (.f64 z z) y) (sqrt.f64 x)))
	3.1b	(/.f64 (/.f64 1 y) (.f64 (hypot.f64 1 z) (.f64 x (hypot.f64 1 z))))

Compiler

Compiled 10486 to 7698 computations (26.6% saved)

regimes1.2s (19.8%)

Accuracy

Total 1.4b remaining (98.3%)

Threshold costs 0b (0%)

Counts

146 → 1

Compiler

Compiled 22653 to 16321 computations (28% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	14	22
2	13	22

end284.0ms (4.9%)

Compiler: Compiled 283 to 207 computations (26.9% saved)

Details

analyze331.0ms (5.7%)

sample983.0ms (16.9%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series95.0ms (1.6%)

rewrite16.0ms (0.3%)

simplify130.0ms (2.2%)

prune132.0ms (2.3%)

localize12.0ms (0.2%)

series121.0ms (2.1%)

rewrite44.0ms (0.8%)

simplify132.0ms (2.3%)

prune335.0ms (5.7%)

localize9.0ms (0.1%)

series183.0ms (3.1%)

rewrite82.0ms (1.4%)

simplify244.0ms (4.2%)

prune589.0ms (10.1%)

localize9.0ms (0.1%)

series207.0ms (3.6%)

rewrite48.0ms (0.8%)

simplify217.0ms (3.7%)

prune455.0ms (7.8%)

regimes1.2s (19.8%)

simplify3.0ms (0.1%)

end284.0ms (4.9%)

Profiling