Details

analyze509.0ms (11.1%)

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 (43.5%)

Results

783.0ms	6250×	body	128	valid
464.0ms	686×	body	2048	valid
336.0ms	526×	body	4096	valid
266.0ms	442×	body	1024	valid
77.0ms	243×	body	512	valid
24.0ms	109×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify31.0ms (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

13.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	41.4b	(.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)
✓	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.9b	(-.f64 (hypot.f64 re im) re)

series82.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

56.0ms	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
13.0ms	(-.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:

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)

simplify88.0ms (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

prune92.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Error

0.2b

Counts

138 → 7

Alt Table

Status	Error	Program
✓	14.0b	(.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)))))
▶	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	16.6b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	51.1b	(.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))))
	45.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 3387 to 2220 computations (34.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
✓	0.1b	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
	0.9b	(-.f64 (hypot.f64 re im) re)

series94.0ms (2%)

Counts

2 → 32

Calls

2 calls:

50.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
44.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`sqrt-pow1_binary64`
63×	`pow1_binary64`
31×	`sqrt-prod_binary64`
28×	`sqrt-div_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

2 → 104

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
4.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))

simplify122.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
385×	`cancel-sign-sub-inv_binary64`
284×	`fma-neg_binary64`
236×	`associate-r_binary64`
232×	`associate-l_binary64`

Counts

136 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	4120
1	819	3789
2	2559	3619
3	4975	3619
4	4964	3619

prune342.0ms (7.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	412	7	419

Error

0.2b

Counts

419 → 7

Alt Table

Status	Error	Program
✓	14.0b	(.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)))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
▶	16.6b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	51.1b	(.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))))
	45.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 15442 to 9849 computations (36.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
	0.0b	(sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))
	0.9b	(-.f64 (hypot.f64 re im) re)
✓	2.8b	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))

series191.0ms (4.1%)

Counts

2 → 16

Calls

2 calls:

147.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))
44.0ms	(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	(expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re)))))
0.0ms	(log1p.f64 (sqrt.f64 (*.f64 2 (-.f64 (hypot.f64 re im) re))))

simplify54.0ms (1.2%)

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

prune114.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	155	7	162

Error

0.2b

Counts

162 → 7

Alt Table

Status	Error	Program
✓	14.0b	(.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)))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
✓	16.6b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
▶	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	51.1b	(.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))))
	45.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 4834 to 3470 computations (28.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
✓	0.0b	(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
✓	17.5b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series144.0ms (3.1%)

Counts

3 → 26

Calls

3 calls:

86.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

39.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

19.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 38

Calls

3 calls:

2.0ms

(sqrt.f64 (*.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))

1.0ms

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

1.0ms

(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify101.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-def_binary64`
337×	`associate-/l*_binary64`
311×	`times-frac_binary64`
291×	`fma-neg_binary64`
289×	`cancel-sign-sub-inv_binary64`

Counts

64 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	1414
1	518	1316
2	1585	1263
3	4927	1261
4	5024	1261

prune144.0ms (3.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	207	7	214

Error

0.2b

Counts

214 → 7

Alt Table

Status	Error	Program
✓	14.0b	(.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)))))
✓	14.3b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re)))) (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
✓	16.6b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))))
✓	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	51.1b	(.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))))
	45.4b	(.f64 1/2 (.f64 (.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) im)) (sqrt.f64 (/.f64 1 re))))

Compiler

Compiled 5635 to 3271 computations (42% saved)

regimes240.0ms (5.2%)

Accuracy

Total 7.2b remaining (97.2%)

Threshold costs 0b (0%)

Counts

25 → 2

Compiler

Compiled 3090 to 2341 computations (24.2% saved)

bsearch40.0ms (0.9%)

Steps

Iters	Range		Point
10	3.246039163223559e-76	1.7203817805254752e-63	1.6953129666289624e-63

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-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	23	43
1	33	43
2	37	43
3	39	43
4	40	43
5	39	43

end118.0ms (2.6%)

Compiler: Compiled 191 to 150 computations (21.5% 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

analyze509.0ms (11.1%)

sample2.0s (43.5%)

simplify31.0ms (0.7%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series82.0ms (1.8%)

rewrite13.0ms (0.3%)

simplify88.0ms (1.9%)

prune92.0ms (2%)

localize12.0ms (0.3%)

series94.0ms (2%)

rewrite32.0ms (0.7%)

simplify122.0ms (2.7%)

prune342.0ms (7.4%)

localize9.0ms (0.2%)

series191.0ms (4.1%)

rewrite2.0ms (0%)

simplify54.0ms (1.2%)

prune114.0ms (2.5%)

localize9.0ms (0.2%)

series144.0ms (3.1%)

rewrite5.0ms (0.1%)

simplify101.0ms (2.2%)

prune144.0ms (3.1%)

regimes240.0ms (5.2%)

bsearch40.0ms (0.9%)

simplify3.0ms (0.1%)

end118.0ms (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