Details

analyze895.0ms (10.6%)

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
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)

sample3.3s (39.2%)

Results

1.4s	6218×	body	128	valid
681.0ms	681×	body	2048	valid
592.0ms	526×	body	4096	valid
391.0ms	461×	body	1024	valid
120.0ms	219×	body	512	valid
58.0ms	151×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify13.0ms (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

prune8.0ms (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

17.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	39.9b	(.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)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.0b	(hypot.f64 re im)
✓	1.1b	(+.f64 re (hypot.f64 re im))

series122.0ms (1.4%)

Counts

3 → 56

Calls

3 calls:

79.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
22.0ms	(+.f64 re (hypot.f64 re im))
21.0ms	(hypot.f64 re im)

rewrite103.0ms (1.2%)

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 → 79

Calls

3 calls:

100.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
100.0ms	(hypot.f64 re im)
100.0ms	(+.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

simplify91.0ms (1.1%)

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

135 → 151

Iterations

Useful iterations: 2 (0.0ms)

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

prune207.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	144	9	153

Error

10.2b

Counts

153 → 9

Alt Table

Status	Error	Program
	20.9b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	46.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	33.2b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 3/2) 1/3))
✓	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	19.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
▶	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	19.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))))))

Compiler

Compiled 3208 to 2171 computations (32.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.4b	(cbrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3)
	1.1b	(+.f64 re (hypot.f64 re im))

series205.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

143.0ms	(pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3)
61.0ms	(cbrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite64.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

728×	`log1p-expm1-u_binary64`
728×	`expm1-log1p-u_binary64`
506×	`prod-diff_binary64`
75×	`add-sqr-sqrt_binary64`
72×	`add-cbrt-cube_binary64`

Counts

2 → 64

Calls

2 calls:

61.0ms	(cbrt.f64 (+.f64 re (hypot.f64 re im)))
61.0ms	(pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	157	16
2	1836	16
3	5344	16
0	0	0
1	0	0

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

729×	`associate-/l*_binary64`
641×	`fma-def_binary64`
256×	`cancel-sign-sub-inv_binary64`
210×	`associate-/r/_binary64`
198×	`unswap-sqr_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	1954
1	613	1898
2	2082	1768
3	5249	1768

prune366.0ms (4.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	246	7	253
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	247	15	262

Error

10.2b

Counts

262 → 15

Alt Table

Status	Error	Program
	20.9b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	46.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (pow.f64 (+.f64 re (hypot.f64 re im)) 2/3) 1/3)) 3))))
✓	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	51.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 (*.f64 -1 im) 1/3) 3))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (.f64 (pow.f64 (.f64 1/2 (*.f64 im im)) 1/3) (pow.f64 (/.f64 -1 re) 1/3)) 3))))
▶	19.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))))))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) 3))))
	19.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
✓	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3))))
	50.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (neg.f64 im)) 3))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 im) 3))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 im 1/3) 3))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 6819 to 4831 computations (29.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)
✓	0.5b	(cbrt.f64 (hypot.f64 re im))
✓	13.9b	(+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))

series238.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

113.0ms	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)
74.0ms	(cbrt.f64 (hypot.f64 re im))
28.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))
22.0ms	(+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))

rewrite85.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

759×	`log1p-expm1-u_binary64`
759×	`expm1-log1p-u_binary64`
682×	`prod-diff_binary64`
93×	`egg-rr`
83×	`add-sqr-sqrt_binary64`

Counts

4 → 93

Calls

4 calls:

81.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))
81.0ms	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)
81.0ms	(cbrt.f64 (hypot.f64 re im))
81.0ms	(+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	173	24
2	1927	24
3	5871	24
0	0	0
1	0	0

simplify147.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-neg_binary64`
766×	`fma-def_binary64`
366×	`cancel-sign-sub-inv_binary64`
208×	`times-frac_binary64`
186×	`associate-/r*_binary64`

Counts

189 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2518
1	644	2482
2	1878	2410
3	4732	2410
4	5342	2410

prune359.0ms (4.2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	254	15	269

Error

10.2b

Counts

269 → 15

Alt Table

Status	Error	Program
	20.9b	(.f64 1/2 (exp.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	46.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (pow.f64 (+.f64 re (hypot.f64 re im)) 2/3) 1/3)) 3))))
✓	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	51.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 (*.f64 -1 im) 1/3) 3))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (.f64 (pow.f64 (.f64 1/2 (*.f64 im im)) 1/3) (pow.f64 (/.f64 -1 re) 1/3)) 3))))
✓	19.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))))))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) 3))))
▶	19.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
✓	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3))))
	50.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (neg.f64 im)) 3))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 im) 3))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 im 1/3) 3))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 6805 to 4518 computations (33.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)
	0.5b	(cbrt.f64 (hypot.f64 re im))
✓	19.0b	(fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re)

series124.0ms (1.5%)

Counts

1 → 24

Calls

1 calls:

123.0ms

(fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re)

rewrite62.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
304×	`log-prod_binary64`
168×	`prod-diff_binary64`
129×	`expm1-udef_binary64`

Counts

1 → 32

Calls

1 calls:

61.0ms

(fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	159	7
2	1603	7
3	5072	7
0	0	0
1	0	0

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

658×	`associate-*l/_binary64`
626×	`cancel-sign-sub-inv_binary64`
354×	`fma-neg_binary64`
256×	`associate-/r/_binary64`
220×	`associate-/l/_binary64`

Counts

56 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	394
1	178	388
2	520	382
3	2178	382
4	5082	382

prune388.0ms (4.6%)

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	1	10	11
Picked	0	1	1
Done	0	3	3
Total	300	15	315

Error

10.2b

Counts

315 → 15

Alt Table

Status	Error	Program
	46.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	21.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (pow.f64 (+.f64 re (hypot.f64 re im)) 2/3) 1/3)) 3))))
✓	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	51.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 (*.f64 -1 im) 1/3) 3))))
	50.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (.f64 (pow.f64 (.f64 1/2 (*.f64 im im)) 1/3) (pow.f64 (/.f64 -1 re) 1/3)) 3))))
✓	19.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (cbrt.f64 (hypot.f64 re im)) (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2))))))
	53.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2)) 3))))
✓	19.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
✓	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) 3))))
	50.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 (neg.f64 im)) 3))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (cbrt.f64 im) 3))))
	48.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (pow.f64 im 1/3) 3))))
	20.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 3) 2) (cbrt.f64 (hypot.f64 re im)) re))))
	53.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 7953 to 5069 computations (36.3% saved)

regimes1.0s (12.2%)

Accuracy

Total 2.6b remaining (26%)

Threshold costs 0b (0%)

Counts

60 → 2

Compiler

Compiled 7586 to 5866 computations (22.7% saved)

bsearch4.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end395.0ms (4.7%)

Compiler: Compiled 313 to 244 computations (22% saved)

Details

analyze895.0ms (10.6%)

sample3.3s (39.2%)

simplify13.0ms (0.1%)

prune8.0ms (0.1%)

localize13.0ms (0.1%)

series122.0ms (1.4%)

rewrite103.0ms (1.2%)

simplify91.0ms (1.1%)

prune207.0ms (2.4%)

localize16.0ms (0.2%)

series205.0ms (2.4%)

rewrite64.0ms (0.8%)

simplify92.0ms (1.1%)

prune366.0ms (4.3%)

localize21.0ms (0.2%)

series238.0ms (2.8%)

rewrite85.0ms (1%)

simplify147.0ms (1.7%)

prune359.0ms (4.2%)

localize20.0ms (0.2%)

series124.0ms (1.5%)

rewrite62.0ms (0.7%)

simplify65.0ms (0.8%)

prune388.0ms (4.6%)

regimes1.0s (12.2%)

bsearch4.0ms (0%)

simplify5.0ms (0.1%)

end395.0ms (4.7%)

Profiling