Details

analyze519.0ms (12%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.9s (45.2%)

Results

840.0ms	6262×	body	128	valid
380.0ms	541×	body	4096	valid
354.0ms	680×	body	2048	valid
189.0ms	434×	body	1024	valid
110.0ms	235×	body	512	valid
22.0ms	104×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
142×	`fma-neg_binary64`
51×	`distribute-rgt-in_binary64`
42×	`cancel-sign-sub-inv_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	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

10.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	37.2b	(.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)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.9b	(-.f64 (hypot.f64 re im) re)

series73.0ms (1.7%)

Counts

3 → 56

Calls

3 calls:

46.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
15.0ms	(-.f64 (hypot.f64 re im) re)
12.0ms	(hypot.f64 re im)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`pow1_binary64`

Counts

3 → 55

Calls

3 calls:

6.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

simplify86.0ms (2%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
747×	`times-frac_binary64`
413×	`cancel-sign-sub-inv_binary64`
173×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

111 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2332
1	611	2069
2	2078	1999
3	4466	1989
4	5015	1989

prune96.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

0.1b

Counts

138 → 6

Alt Table

Status	Error	Program
▶	11.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	52.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	48.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	37.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 3337 to 2190 computations (34.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
	0.9b	(-.f64 (hypot.f64 re im) re)

series47.0ms (1.1%)

Counts

1 → 8

Calls

1 calls:

47.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
12×	`sqrt-prod_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

1 → 37

Calls

1 calls:

9.0ms

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

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary64`
515×	`associate-l_binary64`
429×	`fma-def_binary64`
260×	`associate-/l*_binary64`
230×	`times-frac_binary64`

Counts

45 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1187
1	372	1154
2	1241	1113
3	4710	1111
4	5528	1111

prune114.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	153	6	159

Error

0.1b

Counts

159 → 6

Alt Table

Status	Error	Program
✓	11.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	52.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	48.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	37.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 3750 to 2435 computations (35.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 re re) (.f64 im im))
✓	0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
✓	0.9b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
✓	30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series83.0ms (1.9%)

Counts

4 → 80

Calls

4 calls:

47.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
15.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
14.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(+.f64 (.f64 re re) (.f64 im im))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify153.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-neg_binary64`
493×	`cancel-sign-sub-inv_binary64`
252×	`neg-mul-1_binary64`
200×	`fma-def_binary64`
189×	`distribute-rgt-neg-in_binary64`

Counts

170 → 202

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	270	3076
1	704	2606
2	2505	2502
3	4547	2488
4	4856	2476
5	4845	2472
6	4946	2472

prune121.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Error

0.1b

Counts

208 → 7

Alt Table

Status	Error	Program
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	37.6b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (+.f64 (*.f64 im im) 0))) (sqrt.f64 (+.f64 re (hypot.f64 im re)))))
✓	11.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	52.6b	(.f64 1/2 (fma.f64 (sqrt.f64 1/2) (.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (/.f64 1 re))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (.f64 (/.f64 (.f64 (pow.f64 im 3) (sqrt.f64 2)) (sqrt.f64 1/2)) -1/16))))
	48.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	37.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 5191 to 2820 computations (45.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (+.f64 (.f64 im im) 0))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0))) (sqrt.f64 (+.f64 re (hypot.f64 im re))))
✓	0.3b	(+.f64 re (hypot.f64 im re))
✓	30.3b	(sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0)))

series68.0ms (1.6%)

Counts

4 → 56

Calls

4 calls:

49.0ms	(/.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0))) (sqrt.f64 (+.f64 re (hypot.f64 im re))))
13.0ms	(+.f64 re (hypot.f64 im re))
3.0ms	(sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0)))
3.0ms	(.f64 2 (+.f64 (.f64 im im) 0))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
29×	`sqrt-prod_binary64`
28×	`times-frac_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`

Counts

4 → 114

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0))) (sqrt.f64 (+.f64 re (hypot.f64 im re))))
5.0ms	(.f64 2 (+.f64 (.f64 im im) 0))
4.0ms	(sqrt.f64 (.f64 2 (+.f64 (.f64 im im) 0)))
3.0ms	(+.f64 re (hypot.f64 im re))

simplify138.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
512×	`fma-neg_binary64`
508×	`times-frac_binary64`
236×	`cancel-sign-sub-inv_binary64`
217×	`distribute-rgt-in_binary64`

Counts

170 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	291	3544
1	698	3372
2	2131	3293
3	4552	3291
4	4998	3291
5	4963	3291

prune131.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	209	5	214
Fresh	2	1	3
Picked	1	0	1
Done	2	1	3
Total	214	7	221

Error

0.0b

Counts

221 → 7

Alt Table

Status	Error	Program
	16.8b	(*.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (+.f64 re (hypot.f64 im re))) im)))
	16.5b	(.f64 1/2 (.f64 (sqrt.f64 2) (/.f64 im (sqrt.f64 (+.f64 re (hypot.f64 im re))))))
	16.6b	(.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 im re))))) (/.f64 im (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 im re)))))))
	37.7b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 im im)))) (sqrt.f64 (+.f64 re (hypot.f64 im re))))))
	48.1b	(.f64 1/2 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (pow.f64 im 4))) im) (sqrt.f64 (+.f64 re (hypot.f64 im re)))))
✓	10.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 5934 to 3283 computations (44.7% saved)

regimes369.0ms (8.6%)

Accuracy

Total 0.4b remaining (89.9%)

Threshold costs 0.4b (89.9%)

Counts

35 → 2

Compiler

Compiled 4511 to 3445 computations (23.6% saved)

bsearch28.0ms (0.6%)

Steps

Iters	Range		Point
9	1.925452034007193e-243	5.086813408843877e-234	4.982407308203682e-234

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	28	41
2	33	41
3	35	41
4	36	41
5	36	41

end113.0ms (2.6%)

Compiler: Compiled 183 to 130 computations (29% saved)

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15

Details

analyze519.0ms (12%)

sample1.9s (45.2%)

simplify28.0ms (0.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series73.0ms (1.7%)

rewrite15.0ms (0.3%)

simplify86.0ms (2%)

prune96.0ms (2.2%)

localize7.0ms (0.2%)

series47.0ms (1.1%)

rewrite11.0ms (0.3%)

simplify64.0ms (1.5%)

prune114.0ms (2.6%)

localize10.0ms (0.2%)

series83.0ms (1.9%)

rewrite31.0ms (0.7%)

simplify153.0ms (3.5%)

prune121.0ms (2.8%)

localize12.0ms (0.3%)

series68.0ms (1.6%)

rewrite30.0ms (0.7%)

simplify138.0ms (3.2%)

prune131.0ms (3%)

regimes369.0ms (8.6%)

bsearch28.0ms (0.6%)

simplify3.0ms (0.1%)

end113.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	13	15
1	20	15
2	33	15
3	50	15
4	69	15
5	98	15
6	151	15
7	211	15
8	263	15
9	305	15
10	343	15
11	379	15
12	396	15
13	415	15
14	428	15
15	465	15
16	477	15
17	486	15
18	449	15