Details

analyze488.0ms (10.1%)

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)

sample2.0s (40.3%)

Results

861.0ms	6269×	body	128	valid
385.0ms	672×	body	2048	valid
370.0ms	532×	body	4096	valid
179.0ms	410×	body	1024	valid
77.0ms	248×	body	512	valid
28.0ms	125×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

13.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series72.0ms (1.5%)

Counts

3 → 56

Calls

3 calls:

45.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
14.0ms	(-.f64 (hypot.f64 re im) re)
13.0ms	(hypot.f64 re im)

rewrite13.0ms (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:

7.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
3.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

simplify90.0ms (1.9%)

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

prune90.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

0.2b

Counts

137 → 6

Alt Table

Status	Error	Program
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	13.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	16.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	51.6b	(.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))))
	46.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 3331 to 2188 computations (34.3% 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)
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
	0.9b	(-.f64 (hypot.f64 re im) re)

series72.0ms (1.5%)

Counts

2 → 16

Calls

2 calls:

44.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
28.0ms	(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:

7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re)))
3.0ms	(sqrt.f64 (-.f64 (hypot.f64 re im) re))

simplify79.0ms (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

prune123.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	188	7	195

Error

0.2b

Counts

195 → 7

Alt Table

Status	Error	Program
	53.9b	(.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))))))))))
	46.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
▶	16.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	46.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 4911 to 3237 computations (34.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.0b	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
	0.9b	(-.f64 (hypot.f64 re im) re)
✓	3.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

series193.0ms (4%)

Counts

2 → 16

Calls

2 calls:

148.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
45.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

916×	`associate-/l*_binary64`
784×	`fma-def_binary64`
288×	`cancel-sign-sub-inv_binary64`
234×	`associate-/r/_binary64`
180×	`fma-neg_binary64`

Counts

38 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	1632
1	546	1465
2	2056	1423
3	5498	1423

prune150.0ms (3.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	161	8	169

Error

0.2b

Counts

169 → 8

Alt Table

Status	Error	Program
	53.9b	(.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))))))))))
▶	46.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	54.0b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (.f64 1/2 (/.f64 (.f64 im im) re)))))))
✓	13.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
✓	16.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	46.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 4825 to 3444 computations (28.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 re))
✓	0.1b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
✓	0.4b	(*.f64 (sqrt.f64 2) im)
✓	0.5b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))

series43.0ms (0.9%)

Counts

4 → 0

Calls

4 calls:

27.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
6.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
6.0ms	(sqrt.f64 (/.f64 1 re))
4.0ms	(*.f64 (sqrt.f64 2) im)

rewrite32.0ms (0.7%)

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 → 114

Calls

4 calls:

13.0ms	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))
8.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im))
4.0ms	(*.f64 (sqrt.f64 2) im)
2.0ms	(sqrt.f64 (/.f64 1 re))

simplify107.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-/l*_binary64`
416×	`*-commutative_binary64`
403×	`unswap-sqr_binary64`
271×	`sqr-pow_binary64`
214×	`associate-l_binary64`

Counts

114 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	121	1600
1	239	1498
2	789	1498
3	1286	1498
4	2620	1498
5	3060	1498
6	4473	1498
7	5012	1498

prune100.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	2	2	4
Picked	1	0	1
Done	0	3	3
Total	120	11	131

Error

0.1b

Counts

131 → 11

Alt Table

Status	Error	Program
✓	13.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (hypot.f64 re im) re))))
	46.9b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (*.f64 (sqrt.f64 2) im)) (sqrt.f64 (sqrt.f64 (/.f64 1 re)))) (sqrt.f64 (sqrt.f64 (/.f64 1 re)))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	54.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	46.8b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) im))) (sqrt.f64 (/.f64 1 re))))
✓	16.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	46.9b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (.f64 (sqrt.f64 2) im)) (sqrt.f64 (.f64 (sqrt.f64 2) im)))) (sqrt.f64 (/.f64 1 re))))
	47.0b	(.f64 1/2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re)))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))))
	46.9b	(.f64 1/2 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (sqrt.f64 (/.f64 1 (cbrt.f64 re)))))
	48.0b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 1/2) (exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 im)))) (sqrt.f64 (/.f64 1 re))))
	46.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 1/2) im) (sqrt.f64 (/.f64 1 re)))))

Compiler

Compiled 2745 to 2321 computations (15.4% saved)

regimes919.0ms (19%)

Accuracy

Total 5.9b remaining (98.4%)

Threshold costs 0b (0%)

Counts

92 → 2

Compiler

Compiled 13787 to 11502 computations (16.6% saved)

bsearch4.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	30	66
1	42	66
2	47	66
3	49	66
4	50	66
5	49	66

end178.0ms (3.7%)

Compiler: Compiled 314 to 259 computations (17.5% 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

analyze488.0ms (10.1%)

sample2.0s (40.3%)

simplify29.0ms (0.6%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series72.0ms (1.5%)

rewrite13.0ms (0.3%)

simplify90.0ms (1.9%)

prune90.0ms (1.9%)

localize7.0ms (0.1%)

series72.0ms (1.5%)

rewrite14.0ms (0.3%)

simplify79.0ms (1.6%)

prune123.0ms (2.5%)

localize9.0ms (0.2%)

series193.0ms (4%)

rewrite2.0ms (0%)

simplify54.0ms (1.1%)

prune150.0ms (3.1%)

localize9.0ms (0.2%)

series43.0ms (0.9%)

rewrite32.0ms (0.7%)

simplify107.0ms (2.2%)

prune100.0ms (2.1%)

regimes919.0ms (19%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end178.0ms (3.7%)

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