Details

analyze509.0ms (11.2%)

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 (39.3%)

Results

793.0ms	6232×	body	128	valid
340.0ms	671×	body	2048	valid
337.0ms	540×	body	4096	valid
188.0ms	424×	body	1024	valid
78.0ms	253×	body	512	valid
28.0ms	136×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify10.0ms (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

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

16.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	38.4b	(.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))))
✓	0.9b	(+.f64 re (hypot.f64 re im))

series66.0ms (1.5%)

Counts

3 → 56

Calls

3 calls:

43.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
11.0ms	(+.f64 re (hypot.f64 re im))
11.0ms	(hypot.f64 re im)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
531×	`fma-neg_binary64`
460×	`associate-r_binary64`
385×	`associate-l_binary64`
294×	`cancel-sign-sub-inv_binary64`

Counts

98 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1829
1	514	1737
2	1465	1673
3	4990	1673
4	5308	1673

prune88.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	111	9	120

Error

8.1b

Counts

120 → 9

Alt Table

Status	Error	Program
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	17.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
✓	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 2731 to 1868 computations (31.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.2b	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
✓	9.2b	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

series69.0ms (1.5%)

Counts

3 → 56

Calls

3 calls:

44.0ms

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

13.0ms

(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))

12.0ms

(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
19×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))

3.0ms

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

2.0ms

(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-neg_binary64`
680×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
255×	`associate-/l*_binary64`
239×	`times-frac_binary64`

Counts

140 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2236
1	567	2078
2	1681	1994
3	4673	1994
4	5330	1994

prune166.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	259	9	268

Error

8.1b

Counts

268 → 9

Alt Table

Status	Error	Program
	20.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	17.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
✓	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))

Compiler

Compiled 6399 to 3638 computations (43.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
✓	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	10.4b	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

series103.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

42.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
37.0ms	(cbrt.f64 (hypot.f64 re im))
12.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))
12.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
6.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
2.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))
1.0ms	(cbrt.f64 (hypot.f64 re im))

simplify146.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

458×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
227×	`unswap-sqr_binary64`
210×	`associate-r_binary64`
209×	`distribute-rgt-neg-in_binary64`

Counts

205 → 247

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	3864
1	805	3722
2	2328	3622
3	4699	3595
4	4982	3595
5	4934	3595

prune202.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	341	9	350

Error

8.1b

Counts

350 → 9

Alt Table

Status	Error	Program
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	17.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
✓	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))

Compiler

Compiled 10319 to 5431 computations (47.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	0.6b	(cbrt.f64 re)
✓	17.2b	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

series104.0ms (2.3%)

Counts

3 → 48

Calls

3 calls:

44.0ms

(*.f64 (cbrt.f64 re) (cbrt.f64 re))

33.0ms

(cbrt.f64 re)

26.0ms

(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (*.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

4.0ms

(*.f64 (cbrt.f64 re) (cbrt.f64 re))

1.0ms

(cbrt.f64 re)

0.0ms

(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (*.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
474×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
393×	`distribute-neg-frac_binary64`
316×	`fma-def_binary64`

Counts

113 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1156
1	271	1039
2	866	983
3	3731	968
4	4785	956
5	4933	956

prune180.0ms (3.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	306	9	315

Error

8.1b

Counts

315 → 9

Alt Table

Status	Error	Program
	56.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	17.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
✓	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	49.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	45.7b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
✓	18.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))

Compiler

Compiled 10691 to 4462 computations (58.3% saved)

regimes633.0ms (13.9%)

Accuracy

Total 5.0b remaining (40%)

Threshold costs 0b (0%)

Counts

72 → 2

Compiler

Compiled 9693 to 6665 computations (31.2% saved)

bsearch37.0ms (0.8%)

Steps

Iters	Range		Point
7	-2287938048.985166	-23397556.316107932	-2231979313.139372

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	27	39
2	27	39

end119.0ms (2.6%)

Compiler: Compiled 191 to 139 computations (27.2% saved)

Details

analyze509.0ms (11.2%)

sample1.8s (39.3%)

simplify10.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series66.0ms (1.5%)

rewrite7.0ms (0.2%)

simplify74.0ms (1.6%)

prune88.0ms (1.9%)

localize13.0ms (0.3%)

series69.0ms (1.5%)

rewrite15.0ms (0.3%)

simplify85.0ms (1.9%)

prune166.0ms (3.6%)

localize11.0ms (0.2%)

series103.0ms (2.3%)

rewrite22.0ms (0.5%)

simplify146.0ms (3.2%)

prune202.0ms (4.4%)

localize13.0ms (0.3%)

series104.0ms (2.3%)

rewrite8.0ms (0.2%)

simplify77.0ms (1.7%)

prune180.0ms (3.9%)

regimes633.0ms (13.9%)

bsearch37.0ms (0.8%)

simplify2.0ms (0%)

end119.0ms (2.6%)

Profiling