Details

analyze461.0ms (12%)

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 (50.3%)

Results

857.0ms	6235×	body	128	valid
367.0ms	549×	body	4096	valid
346.0ms	667×	body	2048	valid
190.0ms	423×	body	1024	valid
79.0ms	235×	body	512	valid
34.0ms	147×	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

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

14.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (-.f64 (hypot.f64 re im) re))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.2b	(-.f64 (hypot.f64 re im) re)

series26.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(-.f64 (hypot.f64 re im) re)
12.0ms	(hypot.f64 re im)

rewrite5.0ms (0.1%)

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:

3.0ms	(-.f64 (hypot.f64 re im) re)
0.0ms	(hypot.f64 re im)

simplify75.0ms (2%)

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

prune67.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Error

7.4b

Counts

105 → 4

Alt Table

Status	Error	Program
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	14.2b	(.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)))))
▶	16.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (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 2278 to 1372 computations (39.8% 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)
✓	10.0b	(fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))
✓	60.8b	(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))))

series138.0ms (3.6%)

Counts

4 → 60

Calls

4 calls:

46.0ms	(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))))
36.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
34.0ms	(cbrt.f64 re)
21.0ms	(fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))

rewrite9.0ms (0.2%)

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:

4.0ms	(*.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 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))

simplify94.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
694×	`times-frac_binary64`
355×	`associate-/r*_binary64`
335×	`fma-def_binary64`
273×	`associate-/l*_binary64`

Counts

135 → 144

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1344
1	311	1217
2	1044	1127
3	3953	1111
4	4584	1019
5	4822	1019

prune300.0ms (7.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	399	1	400
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	400	4	404

Error

7.4b

Counts

404 → 4

Alt Table

Status	Error	Program
	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	14.2b	(.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)))))
▶	27.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (expm1.f64 (log1p.f64 (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 16307 to 4814 computations (70.5% saved)

localize21.0ms (0.5%)

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)
	10.0b	(fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re)))))
	60.8b	(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))))

prune270.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	400	4	404

Error

7.4b

Counts

404 → 4

Alt Table

Status	Error	Program
▶	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	14.2b	(.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)))))
✓	27.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (expm1.f64 (log1p.f64 (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 17066 to 5263 computations (69.2% saved)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

7.4b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	30.9b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	14.2b	(.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)))))
✓	27.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (fma.f64 1 (hypot.f64 re im) (neg.f64 (.f64 (cbrt.f64 re) (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (expm1.f64 (log1p.f64 (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 75 to 47 computations (37.3% saved)

regimes259.0ms (6.7%)

Accuracy

Total 2.6b remaining (25.5%)

Threshold costs 0b (0%)

Counts

22 → 2

Compiler

Compiled 4350 to 2481 computations (43% saved)

bsearch1.0ms (0%)

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

end112.0ms (2.9%)

Compiler: Compiled 155 to 107 computations (31% 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

analyze461.0ms (12%)

sample1.9s (50.3%)

simplify30.0ms (0.8%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series26.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify75.0ms (2%)

prune67.0ms (1.8%)

localize16.0ms (0.4%)

series138.0ms (3.6%)

rewrite9.0ms (0.2%)

simplify94.0ms (2.5%)

prune300.0ms (7.8%)

localize21.0ms (0.5%)

prune270.0ms (7%)

localize4.0ms (0.1%)

prune3.0ms (0.1%)

regimes259.0ms (6.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end112.0ms (2.9%)

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