Details

analyze733.0ms (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample2.5s (34.7%)

Results

1.1s	6286×	body	128	valid
538.0ms	676×	body	2048	valid
433.0ms	495×	body	4096	valid
250.0ms	444×	body	1024	valid
108.0ms	236×	body	512	valid
34.0ms	119×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	25	15
2	29	15
3	31	15
4	31	15

prune10.0ms (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

13.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	37.6b	(.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)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 re im)
✓	0.5b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.6b	(+.f64 re (hypot.f64 re im))

series117.0ms (1.6%)

Counts

3 → 56

Calls

3 calls:

76.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
21.0ms	(hypot.f64 re im)
20.0ms	(+.f64 re (hypot.f64 re im))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 42

Calls

3 calls:

8.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
4.0ms	(+.f64 re (hypot.f64 re im))
1.0ms	(hypot.f64 re im)

simplify139.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-def_binary64`
531×	`fma-neg_binary64`
460×	`associate-r_binary64`
385×	`associate-l_binary64`
294×	`cancel-sign-sub-inv_binary64`

Counts

98 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1829
1	514	1737
2	1465	1673
3	4990	1673
4	5308	1673

prune173.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Error

6.5b

Counts

120 → 7

Alt Table

Status	Error	Program
▶	14.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	17.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	47.3b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	49.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 2655 to 1821 computations (31.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.5b	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))
✓	8.1b	(+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))

series140.0ms (1.9%)

Counts

3 → 56

Calls

3 calls:

69.0ms

(sqrt.f64 (*.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))

47.0ms

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

23.0ms

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

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
19×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

18.0ms

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

6.0ms

(sqrt.f64 (*.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im))))))

4.0ms

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

simplify190.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-neg_binary64`
680×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
255×	`associate-/l*_binary64`
239×	`times-frac_binary64`

Counts

140 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2236
1	567	2078
2	1681	1994
3	4673	1994
4	5330	1994

prune377.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	259	7	266

Error

6.5b

Counts

266 → 7

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	13.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
✓	14.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	15.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))))))
	17.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 6343 to 3592 computations (43.4% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	0.6b	(+.f64 re (hypot.f64 re im))

series77.0ms (1.1%)

Counts

1 → 8

Calls

1 calls:

77.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

1 → 36

Calls

1 calls:

11.0ms

(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

simplify149.0ms (2%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-neg_binary64`
450×	`associate-r_binary64`
420×	`associate-l_binary64`
310×	`fma-def_binary64`
242×	`distribute-rgt-neg-in_binary64`

Counts

44 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1011
1	313	991
2	914	951
3	3063	927
4	4881	923
5	5148	923

prune191.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Error

6.5b

Counts

144 → 7

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
✓	14.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))))))
	17.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 3108 to 2064 computations (33.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))
✓	0.4b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))
✓	0.5b	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))))
✓	8.3b	(+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))

series265.0ms (3.6%)

Counts

4 → 80

Calls

4 calls:

99.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))
92.0ms	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))))
42.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))
31.0ms	(+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`sqrt-pow1_binary64`
53×	`pow1_binary64`
45×	`add-sqr-sqrt_binary64`
38×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

4 → 131

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))
10.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))
5.0ms	(+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))
4.0ms	(sqrt.f64 (.f64 2 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))))))

simplify269.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-neg_binary64`
493×	`cancel-sign-sub-inv_binary64`
257×	`associate-/l*_binary64`
243×	`associate-r_binary64`
239×	`times-frac_binary64`

Counts

211 → 268

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	3990
1	864	3675
2	2632	3479
3	4846	3475
4	5043	3475

prune315.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	268	7	275

Error

6.5b

Counts

275 → 7

Alt Table

Status	Error	Program
	54.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.6b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
✓	14.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	17.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	17.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 7599 to 3904 computations (48.6% saved)

regimes1.2s (15.7%)

Accuracy

Total 3.3b remaining (32.8%)

Threshold costs 0b (0%)

Counts

68 → 3

Compiler

Compiled 7407 to 5624 computations (24.1% saved)

bsearch4.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	94
1	47	94
2	47	94

end268.0ms (3.6%)

Compiler: Compiled 229 to 152 computations (33.6% saved)

Details

analyze733.0ms (10%)

sample2.5s (34.7%)

simplify13.0ms (0.2%)

prune10.0ms (0.1%)

localize12.0ms (0.2%)

series117.0ms (1.6%)

rewrite16.0ms (0.2%)

simplify139.0ms (1.9%)

prune173.0ms (2.4%)

localize17.0ms (0.2%)

series140.0ms (1.9%)

rewrite38.0ms (0.5%)

simplify190.0ms (2.6%)

prune377.0ms (5.1%)

localize14.0ms (0.2%)

series77.0ms (1.1%)

rewrite15.0ms (0.2%)

simplify149.0ms (2%)

prune191.0ms (2.6%)

localize21.0ms (0.3%)

series265.0ms (3.6%)

rewrite66.0ms (0.9%)

simplify269.0ms (3.7%)

prune315.0ms (4.3%)

regimes1.2s (15.7%)

bsearch4.0ms (0.1%)

simplify7.0ms (0.1%)

end268.0ms (3.6%)

Profiling