Details

analyze524.0ms (11%)

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 (40.2%)

Results

885.0ms	6228×	body	128	valid
339.0ms	653×	body	2048	valid
337.0ms	545×	body	4096	valid
191.0ms	454×	body	1024	valid
80.0ms	246×	body	512	valid
27.0ms	130×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify30.0ms (0.6%)

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

13.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	39.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re 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)
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.2b	(-.f64 (hypot.f64 re im) re)

series68.0ms (1.4%)

Counts

3 → 56

Calls

3 calls:

42.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
13.0ms	(hypot.f64 re im)
13.0ms	(-.f64 (hypot.f64 re im) re)

rewrite12.0ms (0.2%)

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 (1.8%)

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

prune86.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Error

0.1b

Counts

138 → 5

Alt Table

Status	Error	Program
▶	14.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	52.1b	(.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))))
	46.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 3303 to 2166 computations (34.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (hypot.f64 re im) re))
	0.0b	(hypot.f64 re im)
	0.2b	(-.f64 (hypot.f64 re im) re)
✓	0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))

series71.0ms (1.5%)

Counts

2 → 16

Calls

2 calls:

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

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
3.0ms	(sqrt.f64 (-.f64 (hypot.f64 re im) re))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
344×	`associate-/l*_binary64`
291×	`times-frac_binary64`
285×	`fma-neg_binary64`
275×	`associate-*l/_binary64`

Counts

72 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	1877
1	534	1832
2	1757	1756
3	4935	1754
4	5005	1754

prune173.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	188	6	194

Error

0.1b

Counts

194 → 6

Alt Table

Status	Error	Program
✓	14.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	55.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (-.f64 (fma.f64 1/32 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (fma.f64 im (.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1 re))) (.f64 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))) 1/256))) (fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 5))) (/.f64 (pow.f64 im 3) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 9))) (.f64 1/256 (/.f64 (pow.f64 im 5) (sqrt.f64 1/2))) (.f64 (sqrt.f64 (/.f64 1 (pow.f64 re 13))) (+.f64 (.f64 1/8192 (/.f64 (pow.f64 im 7) (pow.f64 (sqrt.f64 1/2) 5))) (*.f64 5/256 (/.f64 (pow.f64 im 7) (sqrt.f64 1/2))))))))))
▶	46.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))
	46.6b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 4883 to 3215 computations (34.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))
✓	0.2b	(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
✓	0.3b	(sqrt.f64 (/.f64 1 re))
✓	0.4b	(*.f64 (sqrt.f64 1/2) im)

series50.0ms (1%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
19.0ms	(.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))
5.0ms	(sqrt.f64 (/.f64 1 re))
3.0ms	(*.f64 (sqrt.f64 1/2) im)

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`pow1_binary64`

Counts

4 → 115

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))
8.0ms	(.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))
4.0ms	(*.f64 (sqrt.f64 1/2) im)
3.0ms	(sqrt.f64 (/.f64 1 re))

simplify123.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

414×	`unswap-sqr_binary64`
403×	`*-commutative_binary64`
315×	`sqr-pow_binary64`
297×	`pow-sqr_binary64`
280×	`associate-/l*_binary64`

Counts

127 → 143

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	125	1867
1	250	1756
2	792	1756
3	1302	1756
4	2389	1756
5	3227	1756
6	4494	1416
7	4838	1416
8	4949	1416

prune120.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	137	6	143
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	140	9	149

Error

0.0b

Counts

149 → 9

Alt Table

Status	Error	Program
▶	46.5b	(.f64 1/2 (.f64 im (sqrt.f64 (/.f64 1 re))))
	46.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))))
	47.3b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (exp.f64 (log.f64 (sqrt.f64 (/.f64 1 re)))))))
	46.5b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 im (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (.f64 im (sqrt.f64 (/.f64 1 re))))))
✓	14.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	46.5b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))))
	54.3b	(.f64 1/2 (cbrt.f64 (pow.f64 (.f64 im (sqrt.f64 (/.f64 1 re))) 3)))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	53.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 3105 to 2615 computations (15.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 im (sqrt.f64 (/.f64 1 re)))
	0.3b	(sqrt.f64 (/.f64 1 re))

series13.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(*.f64 im (sqrt.f64 (/.f64 1 re)))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`

Counts

1 → 37

Calls

1 calls:

7.0ms

(*.f64 im (sqrt.f64 (/.f64 1 re)))

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

652×	`unswap-sqr_binary64`
253×	`log-div_binary64`
229×	`sqr-pow_binary64`
220×	`associate-/l*_binary64`
204×	`associate-/l/_binary64`

Counts

49 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	548
1	89	530
2	208	530
3	272	530
4	401	530
5	659	530
6	906	530
7	2394	530
8	3784	530
9	4718	530
10	4996	530
11	4898	530

prune52.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	86	7	93

Error

0.0b

Counts

93 → 7

Alt Table

Status	Error	Program
✓	46.5b	(.f64 1/2 (.f64 im (sqrt.f64 (/.f64 1 re))))
	46.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (*.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))))
	46.4b	(*.f64 1/2 (/.f64 im (sqrt.f64 re)))
	46.5b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re))))))
✓	14.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	47.8b	(*.f64 1/2 (exp.f64 (+.f64 (log.f64 im) (log.f64 (sqrt.f64 (/.f64 1 re))))))
✓	13.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 1281 to 956 computations (25.4% saved)

regimes1.1s (22.7%)

Accuracy

Total 6.3b remaining (98.3%)

Threshold costs 0b (0%)

Counts

111 → 2

Compiler

Compiled 15420 to 12831 computations (16.8% saved)

bsearch4.0ms (0.1%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	29	44
2	34	44
3	36	44
4	37	44
5	37	44

end98.0ms (2.1%)

Compiler: Compiled 164 to 128 computations (22% 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

analyze524.0ms (11%)

sample1.9s (40.2%)

simplify30.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series68.0ms (1.4%)

rewrite12.0ms (0.2%)

simplify86.0ms (1.8%)

prune86.0ms (1.8%)

localize7.0ms (0.1%)

series71.0ms (1.5%)

rewrite14.0ms (0.3%)

simplify77.0ms (1.6%)

prune173.0ms (3.6%)

localize9.0ms (0.2%)

series50.0ms (1%)

rewrite30.0ms (0.6%)

simplify123.0ms (2.6%)

prune120.0ms (2.5%)

localize7.0ms (0.1%)

series13.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify89.0ms (1.9%)

prune52.0ms (1.1%)

regimes1.1s (22.7%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end98.0ms (2.1%)

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