Details

analyze464.0ms (11.4%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.8s (43.5%)

Results

809.0ms	6279×	body	128	valid
343.0ms	671×	body	2048	valid
330.0ms	548×	body	4096	valid
160.0ms	408×	body	1024	valid
75.0ms	236×	body	512	valid
25.0ms	114×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

prune3.0ms (0.1%)

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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.8b	(+.f64 re (hypot.f64 re im))

series55.0ms (1.3%)

Counts

2 → 32

Calls

2 calls:

42.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
12.0ms	(+.f64 re (hypot.f64 re im))

rewrite53.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

60× egg-rr

Counts

2 → 60

Calls

2 calls:

52.0ms	((+.f64 re (hypot.f64 re im)) (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	177	19
2	2126	19
3	6259	19
0	0	0
1	0	0

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-neg_binary64`
433×	`fma-def_binary64`
392×	`associate-r_binary64`
311×	`associate-l_binary64`
236×	`cancel-sign-sub-inv_binary64`

Counts

92 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	860
1	340	810
2	1053	762
3	4471	762
4	5138	762

prune74.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

5.2b

Counts

106 → 8

Alt Table

Status	Error	Program
	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (*.f64 re re) (pow.f64 (hypot.f64 re im) 2)) (-.f64 re (hypot.f64 re im))))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	11.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 2283 to 1536 computations (32.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))
	0.8b	(+.f64 re (hypot.f64 re im))

series70.0ms (1.7%)

Counts

2 → 16

Calls

2 calls:

43.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))
27.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite52.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

43× egg-rr

Counts

2 → 43

Calls

2 calls:

51.0ms	((*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	190	21
2	2184	21
3	6175	21
0	0	0
1	0	0

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

999×	`fma-neg_binary64`
527×	`fma-def_binary64`
439×	`associate-r_binary64`
360×	`associate-l_binary64`
310×	`cancel-sign-sub-inv_binary64`

Counts

59 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	800
1	339	731
2	1119	664
3	4613	664
4	5488	664

prune96.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Error

5.2b

Counts

145 → 9

Alt Table

Status	Error	Program
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) (sqrt.f64 2)))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (*.f64 re re) (pow.f64 (hypot.f64 re im) 2)) (-.f64 re (hypot.f64 re im))))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 3179 to 2195 computations (31% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.2b	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))
✓	0.4b	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)
	0.8b	(+.f64 re (hypot.f64 re im))

series89.0ms (2.2%)

Counts

2 → 16

Calls

2 calls:

45.0ms	(sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)))
44.0ms	(pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2)

rewrite51.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

65× egg-rr

Counts

2 → 65

Calls

2 calls:

50.0ms	((pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2) (sqrt.f64 (*.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	195	19
2	2223	19
3	6253	19
0	0	0
1	0	0

simplify93.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
370×	`associate-r_binary64`
364×	`fma-def_binary64`
298×	`associate-l_binary64`
205×	`cancel-sign-sub-inv_binary64`

Counts

81 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	571
1	284	509
2	902	465
3	3925	465
4	4905	465
5	4984	465
6	4996	465
7	4936	465

prune134.0ms (3.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	200	10	210

Error

5.2b

Counts

210 → 10

Alt Table

Status	Error	Program
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) (sqrt.f64 2)))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	47.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))
▶	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (hypot.f64 re im) 2) (*.f64 re re)) (-.f64 (hypot.f64 re im) re))) 2))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 4574 to 3033 computations (33.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im))))
✓	0.5b	(pow.f64 (cbrt.f64 re) 2)
✓	0.6b	(cbrt.f64 re)
✓	12.9b	(fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im))

series165.0ms (4.1%)

Counts

4 → 56

Calls

4 calls:

66.0ms	(sqrt.f64 (*.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im))))
40.0ms	(pow.f64 (cbrt.f64 re) 2)
34.0ms	(cbrt.f64 re)
24.0ms	(fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im))

rewrite52.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

88× egg-rr

Counts

4 → 88

Calls

2 calls:

50.0ms	((fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)) (cbrt.f64 re) (pow.f64 (cbrt.f64 re) 2) (sqrt.f64 (*.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	199	26
2	2051	26
3	5070	26
0	0	0
1	0	0

simplify90.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

558×	`times-frac_binary64`
523×	`fma-def_binary64`
503×	`associate-/l*_binary64`
371×	`associate-/r*_binary64`
310×	`cancel-sign-sub-inv_binary64`

Counts

144 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1128
1	433	1082
2	1495	1039
3	4673	1035
4	4990	1035
5	5000	1035
6	4946	1035

prune118.0ms (2.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	5	6
Picked	0	1	1
Done	0	3	3
Total	166	10	176

Error

5.2b

Counts

176 → 10

Alt Table

Status	Error	Program
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) (sqrt.f64 2)))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	47.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 im) 2))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) 2))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	25.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (cbrt.f64 (*.f64 re re)) (cbrt.f64 re) (hypot.f64 re im)))))
✓	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 3449 to 2237 computations (35.1% saved)

regimes360.0ms (8.8%)

Accuracy

Total 3.2b remaining (30.6%)

Threshold costs 0b (0%)

Counts

37 → 3

Compiler

Compiled 4444 to 3451 computations (22.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	96
1	45	96
2	45	96

end134.0ms (3.3%)

Compiler: Compiled 261 to 182 computations (30.3% saved)

Details

analyze464.0ms (11.4%)

sample1.8s (43.5%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series55.0ms (1.3%)

rewrite53.0ms (1.3%)

simplify54.0ms (1.3%)

prune74.0ms (1.8%)

localize7.0ms (0.2%)

series70.0ms (1.7%)

rewrite52.0ms (1.3%)

simplify54.0ms (1.3%)

prune96.0ms (2.3%)

localize8.0ms (0.2%)

series89.0ms (2.2%)

rewrite51.0ms (1.3%)

simplify93.0ms (2.3%)

prune134.0ms (3.3%)

localize10.0ms (0.2%)

series165.0ms (4.1%)

rewrite52.0ms (1.3%)

simplify90.0ms (2.2%)

prune118.0ms (2.9%)

regimes360.0ms (8.8%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end134.0ms (3.3%)

Profiling