Details

analyze478.0ms (7.5%)

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 (31.2%)

Results

900.0ms	6318×	body	128	valid
379.0ms	672×	body	2048	valid
374.0ms	507×	body	4096	valid
188.0ms	431×	body	1024	valid
70.0ms	212×	body	512	valid
29.0ms	116×	body	256	valid

Compiler

Compiled 57 to 40 computations (29.8% saved)

simplify29.0ms (0.5%)

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

prune3.0ms (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

11.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.2b	(.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 1 expressions with local error:

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

series13.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(-.f64 (hypot.f64 re im) re)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 30

Calls

1 calls:

5.0ms

(-.f64 (hypot.f64 re im) re)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary64`
551×	`times-frac_binary64`
464×	`fma-def_binary64`
384×	`associate-l_binary64`
362×	`associate-r_binary64`

Counts

54 → 65

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1005
1	284	784
2	946	746
3	4329	744
4	4911	743
5	4885	743

prune45.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

5.9b

Counts

66 → 4

Alt Table

Status	Error	Program
▶	12.6b	(.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))))))))
	56.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	11.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 1480 to 833 computations (43.7% saved)

localize58.0ms (0.9%)

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)
✓	12.5b	(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)))))
✓	60.1b	(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))))

series189.0ms (3%)

Counts

4 → 46

Calls

4 calls:

50.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
48.0ms	(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))))
46.0ms	(cbrt.f64 re)
45.0ms	(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)))))

rewrite9.0ms (0.1%)

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)))))

simplify98.0ms (1.5%)

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	950
2	834	854
3	3431	839
4	4624	827
5	4982	827
6	4731	827

prune268.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	400	2	402
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	401	5	406

Error

5.9b

Counts

406 → 5

Alt Table

Status	Error	Program
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (hypot.f64 re im) 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))))))))
	56.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
▶	12.9b	(.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 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))))))
✓	11.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 18201 to 4270 computations (76.5% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 re)
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)
	12.5b	(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)))))
✓	59.0b	(fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))

series340.0ms (5.3%)

Counts

2 → 24

Calls

2 calls:

293.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)

47.0ms

(fma.f64 (neg.f64 (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
9×	`unpow-prod-down_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 36

Calls

2 calls:

2.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)

2.0ms

(fma.f64 (neg.f64 (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (*.f64 (cbrt.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-def_binary64`
599×	`exp-prod_binary64`
342×	`fma-neg_binary64`
273×	`distribute-rgt-neg-in_binary64`
273×	`unswap-sqr_binary64`

Counts

60 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	76	977
1	134	748
2	268	530
3	788	486
4	1852	464
5	3945	464
6	4866	464
7	4372	464

prune362.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	260	5	265

Error

5.9b

Counts

265 → 5

Alt Table

Status	Error	Program
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (hypot.f64 re im) 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))))))))
▶	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 (sqrt.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)))))) (sqrt.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 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))))))
	56.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 13313 to 4421 computations (66.8% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 re)
	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)
	12.5b	(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)))))
	59.0b	(fma.f64 (neg.f64 (cbrt.f64 re)) (.f64 (cbrt.f64 re) (cbrt.f64 re)) (.f64 (cbrt.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))

prune323.0ms (5.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	349	5	354

Error

5.9b

Counts

354 → 5

Alt Table

Status	Error	Program
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	15.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (-.f64 (hypot.f64 re im) 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))))))))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 (sqrt.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)))))) (sqrt.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 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2))))))))
	56.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 24970 to 6168 computations (75.3% saved)

regimes1.8s (28.6%)

Accuracy

Total 2.7b remaining (28%)

Threshold costs 0b (0%)

Counts

155 → 2

Compiler

Compiled 52692 to 26404 computations (49.9% saved)

bsearch11.0ms (0.2%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	27	58
1	37	58
2	42	58
3	44	58
4	45	58
5	45	58

end110.0ms (1.7%)

Compiler: Compiled 216 to 131 computations (39.4% 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

analyze478.0ms (7.5%)

sample2.0s (31.2%)

simplify29.0ms (0.5%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify77.0ms (1.2%)

prune45.0ms (0.7%)

localize58.0ms (0.9%)

series189.0ms (3%)

rewrite9.0ms (0.1%)

simplify98.0ms (1.5%)

prune268.0ms (4.2%)

localize23.0ms (0.4%)

series340.0ms (5.3%)

rewrite6.0ms (0.1%)

simplify80.0ms (1.3%)

prune362.0ms (5.7%)

localize28.0ms (0.4%)

prune323.0ms (5.1%)

regimes1.8s (28.6%)

bsearch11.0ms (0.2%)

simplify4.0ms (0.1%)

end110.0ms (1.7%)

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