Details

analyze463.0ms (10.8%)

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)

sample1.7s (40.4%)

Results

748.0ms	6197×	body	128	valid
347.0ms	576×	body	4096	valid
330.0ms	653×	body	2048	valid
176.0ms	448×	body	1024	valid
79.0ms	253×	body	512	valid
26.0ms	129×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.1%)

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

prune7.0ms (0.2%)

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

14.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	1.2b	(+.f64 re (hypot.f64 re im))

series47.0ms (1.1%)

Counts

3 → 56

Calls

3 calls:

29.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
9.0ms	(hypot.f64 re im)
9.0ms	(+.f64 re (hypot.f64 re im))

rewrite59.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

844×	`log1p-expm1-u_binary64`
844×	`expm1-log1p-u_binary64`
589×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
84×	`add-log-exp_binary64`

Counts

3 → 82

Calls

3 calls:

58.0ms	(hypot.f64 re im)
58.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
58.0ms	(+.f64 re (hypot.f64 re im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	177	23
2	2126	23
3	6259	23
0	0	0
1	0	0

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
527×	`fma-def_binary64`
416×	`associate-r_binary64`
335×	`associate-l_binary64`
287×	`cancel-sign-sub-inv_binary64`

Counts

138 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1348
1	411	1280
2	1256	1216
3	4693	1216
4	5232	1216

prune101.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Error

6.9b

Counts

156 → 7

Alt Table

Status	Error	Program
	14.8b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	14.5b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))

Compiler

Compiled 3192 to 2160 computations (32.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
	0.0b	(hypot.f64 re im)
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))
	1.2b	(+.f64 re (hypot.f64 re im))

series48.0ms (1.1%)

Counts

2 → 16

Calls

2 calls:

27.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))
20.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite55.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

856×	`log1p-expm1-u_binary64`
856×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`

Counts

2 → 44

Calls

2 calls:

54.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
53.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2))

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

simplify57.0ms (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

60 → 73

Iterations

Useful iterations: 2 (0.0ms)

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

prune111.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	186	7	193

Error

6.9b

Counts

193 → 7

Alt Table

Status	Error	Program
▶	14.8b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	14.5b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))

Compiler

Compiled 4107 to 2841 computations (30.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.3b	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4)
✓	0.4b	(pow.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2)
	1.2b	(+.f64 re (hypot.f64 re im))

series66.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(pow.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2)
29.0ms	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4)

rewrite56.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

506×	`prod-diff_binary64`
460×	`log-prod_binary64`
201×	`fma-def_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Counts

2 → 57

Calls

2 calls:

54.0ms	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4)
54.0ms	(pow.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	225	25
2	2456	25
3	5082	25
0	0	0
1	0	0

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
324×	`associate-/r/_binary64`
307×	`cancel-sign-sub-inv_binary64`
187×	`unswap-sqr_binary64`
179×	`associate-r_binary64`

Counts

105 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	2695
1	774	2559
2	2527	2357
3	5040	2357

prune198.0ms (4.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	255	7	262
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	255	14	269

Error

4.8b

Counts

269 → 14

Alt Table

Status	Error	Program
	53.9b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) 2) 1/4) 2))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	14.8b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.0b	(.f64 1/2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 2) (log.f64 (/.f64 1 im))))) 2))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(*.f64 1/2 (pow.f64 (exp.f64 (fma.f64 2 (log.f64 im) (log.f64 (/.f64 -1 re)))) 1/2))
	57.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
✓	14.5b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	48.7b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (neg.f64 im) 2) 1/4) 2))
	52.8b	(.f64 1/2 (pow.f64 (fma.f64 (.f64 (.f64 (/.f64 im re) (/.f64 im re)) (.f64 (pow.f64 (/.f64 -1 re) 1/4) (pow.f64 (.f64 im im) 1/4))) -1/16 (.f64 (pow.f64 (/.f64 -1 re) 1/4) (pow.f64 (*.f64 im im) 1/4))) 2))
▶	44.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.8b	(.f64 1/2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im))))) 2))
	46.2b	(*.f64 1/2 (pow.f64 (exp.f64 (+.f64 (log.f64 2) (log.f64 im))) 1/2))

Compiler

Compiled 7516 to 5555 computations (26.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 im))

series5.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 im))

rewrite72.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

706×	`log1p-udef_binary64`
392×	`log1p-expm1-u_binary64`
392×	`expm1-log1p-u_binary64`
340×	`unpow-prod-down_binary64`
338×	`pow1_binary64`

Counts

1 → 56

Calls

1 calls:

71.0ms

(sqrt.f64 (*.f64 2 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1053	6
3	4712	6
4	5794	6
0	0	0
1	0	0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune37.0ms (0.9%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	1	9	10
Picked	1	0	1
Done	0	3	3
Total	54	16	70

Error

4.8b

Counts

70 → 16

Alt Table

Status	Error	Program
	53.9b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (.f64 (/.f64 (.f64 im im) re) -1/2) 2) 1/4) 2))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	14.8b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/4) 2))
✓	14.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	46.8b	(*.f64 1/2 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 im im)))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (+.f64 im im))))))
	46.0b	(.f64 1/2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 2) (log.f64 (/.f64 1 im))))) 2))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(*.f64 1/2 (pow.f64 (exp.f64 (fma.f64 2 (log.f64 im) (log.f64 (/.f64 -1 re)))) 1/2))
	57.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
✓	14.5b	(.f64 1/2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 2)))
	48.7b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (neg.f64 im) 2) 1/4) 2))
	48.4b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (+.f64 im im) 5/4) 1/3) (cbrt.f64 (pow.f64 (+.f64 im im) 1/4))))
	49.8b	(.f64 1/2 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 im im)) 4) 1/3) (cbrt.f64 (pow.f64 (+.f64 im im) 1/6))))
	52.8b	(.f64 1/2 (pow.f64 (fma.f64 (.f64 (.f64 (/.f64 im re) (/.f64 im re)) (.f64 (pow.f64 (/.f64 -1 re) 1/4) (pow.f64 (.f64 im im) 1/4))) -1/16 (.f64 (pow.f64 (/.f64 -1 re) 1/4) (pow.f64 (*.f64 im im) 1/4))) 2))
	49.8b	(.f64 1/2 (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im))))) 2))
	46.3b	(*.f64 1/2 (pow.f64 (exp.f64 1/2) (log.f64 (+.f64 im im))))

Compiler

Compiled 927 to 599 computations (35.4% saved)

regimes767.0ms (17.9%)

Accuracy

Total 4.8b remaining (50.4%)

Threshold costs 0b (0%)

Counts

70 → 3

Compiler

Compiled 7881 to 6372 computations (19.1% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	123
1	43	123
2	43	123

end233.0ms (5.4%)

Compiler: Compiled 445 to 314 computations (29.4% saved)

Details

analyze463.0ms (10.8%)

sample1.7s (40.4%)

simplify6.0ms (0.1%)

prune7.0ms (0.2%)

localize6.0ms (0.1%)

series47.0ms (1.1%)

rewrite59.0ms (1.4%)

simplify63.0ms (1.5%)

prune101.0ms (2.3%)

localize7.0ms (0.2%)

series48.0ms (1.1%)

rewrite55.0ms (1.3%)

simplify57.0ms (1.3%)

prune111.0ms (2.6%)

localize9.0ms (0.2%)

series66.0ms (1.5%)

rewrite56.0ms (1.3%)

simplify69.0ms (1.6%)

prune198.0ms (4.6%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite72.0ms (1.7%)

simplify6.0ms (0.1%)

prune37.0ms (0.9%)

regimes767.0ms (17.9%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end233.0ms (5.4%)

Profiling