Details

analyze508.0ms (12.9%)

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)

sample1.8s (45.9%)

Results

788.0ms	6235×	body	128	valid
325.0ms	547×	body	4096	valid
321.0ms	657×	body	2048	valid
217.0ms	431×	body	1024	valid
80.0ms	260×	body	512	valid
26.0ms	126×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify30.0ms (0.8%)

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

13.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	36.4b	(.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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.5b	(-.f64 (hypot.f64 re im) re)

series20.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(-.f64 (hypot.f64 re im) re)
9.0ms	(hypot.f64 re im)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

5.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

952×	`fma-neg_binary64`
648×	`fma-def_binary64`
605×	`times-frac_binary64`
452×	`associate-l_binary64`
282×	`associate-/r*_binary64`

Counts

88 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1564
1	361	1325
2	1177	1271
3	4676	1269
4	5270	1269

prune72.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

7.0b

Counts

106 → 6

Alt Table

Status	Error	Program
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 1/2 (/.f64 (.f64 im im) re))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	29.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))
	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))

Compiler

Compiled 2368 to 1430 computations (39.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (hypot.f64 re im))
	0.0b	(hypot.f64 re im)
✓	14.9b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series45.0ms (1.1%)

Counts

2 → 18

Calls

2 calls:

30.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))
15.0ms	(sqrt.f64 (hypot.f64 re im))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

1.0ms	(sqrt.f64 (hypot.f64 re im))
0.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
289×	`distribute-rgt-neg-in_binary64`
287×	`distribute-lft-neg-in_binary64`
276×	`associate-r_binary64`
249×	`fma-def_binary64`

Counts

43 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	692
1	281	642
2	748	630
3	2893	630
4	4838	630
5	4935	630

prune114.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	172	6	178

Error

7.0b

Counts

178 → 6

Alt Table

Status	Error	Program
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 1/2 (/.f64 (.f64 im im) re))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	29.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))
	18.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))

Compiler

Compiled 4632 to 2550 computations (44.9% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	0.6b	(cbrt.f64 re)
✓	14.8b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))
✓	60.2b	(fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))

series148.0ms (3.8%)

Counts

4 → 46

Calls

4 calls:

47.0ms	(fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))
35.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
34.0ms	(cbrt.f64 re)
32.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 75

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
1.0ms	(cbrt.f64 re)
0.0ms	(fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))
0.0ms	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))

simplify94.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

694×	`times-frac_binary64`
657×	`fma-neg_binary64`
363×	`distribute-neg-frac_binary64`
343×	`associate-/r*_binary64`
273×	`associate-/l*_binary64`

Counts

121 → 132

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1113
1	257	994
2	834	908
3	3431	893
4	4624	881
5	4982	881
6	4731	881

prune256.0ms (6.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	401	1	402
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	402	6	408

Error

7.0b

Counts

408 → 6

Alt Table

Status	Error	Program
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 3)) (fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))
	29.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 1/2 (/.f64 (.f64 im im) re))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	18.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))))

Compiler

Compiled 18239 to 4286 computations (76.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (hypot.f64 re im))
	0.0b	(hypot.f64 re im)
✓	4.8b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))
	14.9b	(fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))

series31.0ms (0.8%)

Counts

1 → 10

Calls

1 calls:

31.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
3×	`exp-sum_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 17

Calls

1 calls:

2.0ms

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

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
469×	`fma-neg_binary64`
442×	`cancel-sign-sub-inv_binary64`
237×	`associate-/r/_binary64`
213×	`associate-/l/_binary64`

Counts

27 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	592
1	172	355
2	446	353
3	1804	345
4	4720	345
5	5026	345

prune118.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	213	8	221

Error

7.0b

Counts

221 → 8

Alt Table

Status	Error	Program
	55.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (.f64 1/2 (/.f64 (.f64 im im) re)))))))
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 re im) re) 3)) (fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (cbrt.f64 re) (cbrt.f64 re))))))))
	29.8b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) -1/8 (.f64 1/2 (/.f64 (.f64 im im) re))))))
	54.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	32.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 im)))))
	20.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))) (cbrt.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re)))))) (cbrt.f64 (log.f64 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) (neg.f64 re))))))))

Compiler

Compiled 5894 to 3276 computations (44.4% saved)

regimes259.0ms (6.6%)

Accuracy

Total 4.8b remaining (39.5%)

Threshold costs 0b (0%)

Counts

25 → 2

Compiler

Compiled 4114 to 2515 computations (38.9% saved)

bsearch56.0ms (1.4%)

Steps

Iters	Range		Point
7	1.529553500823353e+128	1.1538653277564137e+130	2.7128668689896868e+129

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	20	39
1	27	39
2	32	39
3	34	39
4	35	39
5	35	39

end122.0ms (3.1%)

Compiler: Compiled 221 to 146 computations (33.9% 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

analyze508.0ms (12.9%)

sample1.8s (45.9%)

simplify30.0ms (0.8%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify77.0ms (1.9%)

prune72.0ms (1.8%)

localize10.0ms (0.2%)

series45.0ms (1.1%)

rewrite2.0ms (0.1%)

simplify61.0ms (1.5%)

prune114.0ms (2.9%)

localize16.0ms (0.4%)

series148.0ms (3.8%)

rewrite10.0ms (0.3%)

simplify94.0ms (2.4%)

prune256.0ms (6.5%)

localize13.0ms (0.3%)

series31.0ms (0.8%)

rewrite3.0ms (0.1%)

simplify50.0ms (1.3%)

prune118.0ms (3%)

regimes259.0ms (6.6%)

bsearch56.0ms (1.4%)

simplify3.0ms (0.1%)

end122.0ms (3.1%)

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