Details

analyze103.0ms (2.6%)

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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.0s (25.8%)

Results

965.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (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
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

series83.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
33.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(hypot.f64 a b)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`fma-def_binary64`
7×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
279×	`associate-r_binary64`
275×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2123
1	343	2010
2	979	1901
3	4070	1899
4	4922	1899
5	4944	1899

prune113.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Error

Counts

122 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
	17.1b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 2521 to 1596 computations (36.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b b (.f64 2 (.f64 a a)))
✓	0.0b	(.f64 2 (.f64 a a))
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

series51.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

21.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
16.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))
12.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))
3.0ms	(.f64 2 (.f64 a a))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(.f64 2 (.f64 a a))
3.0ms	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))
0.0ms	(fma.f64 b b (.f64 2 (.f64 a a)))
0.0ms	(fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (*.f64 a a))) (pow.f64 a 4))

simplify102.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
359×	`fma-def_binary64`
344×	`distribute-rgt-in_binary64`
339×	`distribute-lft-in_binary64`

Counts

144 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	2635
1	242	2459
2	680	2315
3	3080	2315
4	4844	2315
5	5073	2315

prune271.0ms (6.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

Counts

117 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
	17.1b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (*.f64 b b) -1)) 3))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 3349 to 1871 computations (44.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a b)
✓	0.1b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
✓	0.4b	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
✓	18.7b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series347.0ms (8.6%)

Counts

3 → 72

Calls

3 calls:

239.0ms

(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))

57.0ms

(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))

50.0ms

(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`cbrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
23×	`unpow-prod-down_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))

1.0ms

(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))

simplify140.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-def_binary64`
498×	`unswap-sqr_binary64`
312×	`*-commutative_binary64`
275×	`fma-neg_binary64`
227×	`cancel-sign-sub-inv_binary64`

Counts

165 → 175

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	201	4579
1	461	4352
2	1287	3938
3	2774	3911
4	4849	3847
5	4920	3847

prune547.0ms (13.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	379	1	380
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	381	3	384

Error

Counts

384 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
▶	11.1b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 13485 to 8437 computations (37.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a b)
✓	0.1b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))
	18.7b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))
✓	25.3b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))

series272.0ms (6.8%)

Counts

2 → 48

Calls

2 calls:

217.0ms	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))
55.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`unpow-prod-down_binary64`

Counts

2 → 27

Calls

2 calls:

1.0ms	(cbrt.f64 (pow.f64 (hypot.f64 a b) 8))
0.0ms	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

472×	`unswap-sqr_binary64`
440×	`fma-neg_binary64`
395×	`cancel-sign-sub-inv_binary64`
316×	`associate-r_binary64`
316×	`fma-def_binary64`

Counts

75 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	2010
1	263	1893
2	693	1794
3	2390	1779
4	4558	1779
5	5022	1779

prune181.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	184	3	187

Error

Counts

187 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
✓	11.1b	(fma.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 8)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 5296 to 3404 computations (35.7% saved)

regimes377.0ms (9.3%)

Accuracy

Total 0.0b remaining (26.4%)

Threshold costs 0.0b (26.4%)

Counts

59 → 1

Compiler

Compiled 7370 to 5187 computations (29.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end93.0ms (2.3%)

Compiler: Compiled 91 to 62 computations (31.9% saved)

Details

analyze103.0ms (2.6%)

sample1.0s (25.8%)

simplify43.0ms (1.1%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series83.0ms (2.1%)

rewrite8.0ms (0.2%)

simplify94.0ms (2.3%)

prune113.0ms (2.8%)

localize14.0ms (0.3%)

series51.0ms (1.3%)

rewrite11.0ms (0.3%)

simplify102.0ms (2.5%)

prune271.0ms (6.7%)

localize10.0ms (0.3%)

series347.0ms (8.6%)

rewrite18.0ms (0.4%)

simplify140.0ms (3.5%)

prune547.0ms (13.5%)

localize12.0ms (0.3%)

series272.0ms (6.8%)

rewrite3.0ms (0.1%)

simplify86.0ms (2.1%)

prune181.0ms (4.5%)

regimes377.0ms (9.3%)

simplify2.0ms (0%)

end93.0ms (2.3%)

Profiling