Details

analyze325.0ms (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
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)

sample999.0ms (13.7%)

Symmetry

(sort x y)

Results

909.0ms	8256×	body	128	valid
53.0ms	493×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify13.0ms (0.2%)

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

6.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.1b	(/.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
✓	2.9b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	4.2b	(*.f64 y (fma.f64 z z 1))

series96.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

86.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms	(*.f64 y (fma.f64 z z 1))

rewrite13.0ms (0.2%)

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:

6.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms	(*.f64 y (fma.f64 z z 1))

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
451×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
296×	`associate-r_binary64`

Counts

134 → 122

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

prune118.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Error

3.2b

Counts

123 → 6

Alt Table

Status	Error	Program
	6.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	5.9b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
▶	5.7b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	19.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.6b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	6.1b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))

Compiler

Compiled 2250 to 1397 computations (37.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.5b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
✓	4.1b	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

series126.0ms (1.7%)

Counts

2 → 60

Calls

2 calls:

88.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
39.0ms	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

rewrite41.0ms (0.6%)

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:

16.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
5.0ms	(/.f64 (/.f64 1 x) (fma.f64 z z 1))

simplify146.0ms (2%)

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

prune314.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	297	6	303
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	300	9	309

Error

1.6b

Counts

309 → 9

Alt Table

Status	Error	Program
	46.9b	(.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))))
	4.1b	(.f64 (/.f64 1 y) (.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
	19.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	3.6b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	46.9b	(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)) (sqrt.f64 y)))
	6.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	5.9b	(/.f64 1 (.f64 (.f64 x (fma.f64 z z 1)) y))
	6.1b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))
	6.3b	(.f64 (.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (/.f64 1 y))) (/.f64 (cbrt.f64 (/.f64 1 y)) (*.f64 x (fma.f64 z z 1))))

Compiler

Compiled 7042 to 4718 computations (33% 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 x) (hypot.f64 1 z))
✓	0.1b	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
✓	3.5b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))

series203.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

106.0ms	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
47.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
46.0ms	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
3.0ms	(/.f64 1 (hypot.f64 1 z))

rewrite93.0ms (1.3%)

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:

22.0ms	(*.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
13.0ms	(.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))

simplify236.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

442 → 521

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	387	9652
1	940	8532
2	2613	8250
3	4207	8242
4	4946	8242

prune568.0ms (7.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	516	5	521
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	521	9	530

Error

0.0b

Counts

530 → 9

Alt Table

Status	Error	Program
	3.6b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (sqrt.f64 (hypot.f64 1 z)))))
	6.6b	(/.f64 (/.f64 1 (.f64 y x)) (.f64 (hypot.f64 1 z) (hypot.f64 1 z)))
	4.1b	(.f64 (/.f64 1 y) (.f64 (/.f64 1 (hypot.f64 1 z)) (.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (cbrt.f64 (hypot.f64 1 z)) (cbrt.f64 (hypot.f64 1 z)))) (/.f64 (/.f64 1 (cbrt.f64 (hypot.f64 1 z))) (cbrt.f64 x)))))
	6.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	3.7b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
	5.9b	(/.f64 1 (.f64 (.f64 x (fma.f64 z z 1)) y))
▶	1.9b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	19.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.3b	(.f64 (.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (/.f64 1 y))) (/.f64 (cbrt.f64 (/.f64 1 y)) (*.f64 x (fma.f64 z z 1))))

Compiler

Compiled 13807 to 10318 computations (25.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (hypot.f64 1 z))
	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	1.9b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

series119.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

103.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
16.0ms	(*.f64 y (hypot.f64 1 z))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`times-frac_binary64`
76×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
74×	`add-cube-cbrt_binary64`
43×	`associate-/l*_binary64`

Counts

2 → 136

Calls

2 calls:

9.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
3.0ms	(*.f64 y (hypot.f64 1 z))

simplify127.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-/l*_binary64`
464×	`associate-*l/_binary64`
439×	`associate-/r/_binary64`
403×	`fma-def_binary64`
295×	`associate-*r/_binary64`

Counts

196 → 233

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	4685
1	640	4149
2	2037	3837
3	4585	3831
4	4970	3831

prune579.0ms (8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	341	3	344
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	345	8	353

Error

0.0b

Counts

353 → 8

Alt Table

Status	Error	Program
	2.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (hypot.f64 1 z)))
	6.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	3.7b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
	5.9b	(/.f64 1 (.f64 (.f64 x (fma.f64 z z 1)) y))
	1.9b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 z))) y) (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (sqrt.f64 (hypot.f64 1 z))))
✓	1.9b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	2.6b	(/.f64 (.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (hypot.f64 1 z)) (cbrt.f64 (hypot.f64 1 z)))) (/.f64 (/.f64 1 (cbrt.f64 (hypot.f64 1 z))) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))
	6.3b	(.f64 (.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (/.f64 1 y))) (/.f64 (cbrt.f64 (/.f64 1 y)) (*.f64 x (fma.f64 z z 1))))

Compiler

Compiled 8128 to 5569 computations (31.5% saved)

regimes2.7s (36.8%)

Accuracy

Total 0.7b remaining (95%)

Threshold costs 0.7b (95%)

Counts

235 → 3

Compiler

Compiled 40172 to 30567 computations (23.9% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	98
1	36	98
2	35	98

end283.0ms (3.9%)

Compiler: Compiled 437 to 328 computations (24.9% saved)

Details

analyze325.0ms (4.5%)

sample999.0ms (13.7%)

simplify13.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series96.0ms (1.3%)

rewrite13.0ms (0.2%)

simplify129.0ms (1.8%)

prune118.0ms (1.6%)

localize7.0ms (0.1%)

series126.0ms (1.7%)

rewrite41.0ms (0.6%)

simplify146.0ms (2%)

prune314.0ms (4.3%)

localize9.0ms (0.1%)

series203.0ms (2.8%)

rewrite93.0ms (1.3%)

simplify236.0ms (3.2%)

prune568.0ms (7.8%)

localize7.0ms (0.1%)

series119.0ms (1.6%)

rewrite29.0ms (0.4%)

simplify127.0ms (1.7%)

prune579.0ms (8%)

regimes2.7s (36.8%)

bsearch10.0ms (0.1%)

simplify3.0ms (0%)

end283.0ms (3.9%)

Profiling