Details

analyze469.0ms (10.7%)

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)

sample1.8s (41.3%)

Results

778.0ms	6294×	body	128	valid
337.0ms	666×	body	2048	valid
336.0ms	527×	body	4096	valid
179.0ms	437×	body	1024	valid
68.0ms	223×	body	512	valid
27.0ms	109×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify6.0ms (0.1%)

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

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

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.7b	(+.f64 re (hypot.f64 re im))

series61.0ms (1.4%)

Counts

2 → 32

Calls

2 calls:

47.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
14.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	(+.f64 re (hypot.f64 re im))

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
517×	`fma-def_binary64`
437×	`associate-r_binary64`
361×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

64 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1270
1	435	1196
2	1255	1148
3	4683	1148
4	5413	1148

prune63.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Error

8.3b

Counts

80 → 7

Alt Table

Status	Error	Program
	27.6b	(.f64 1/2 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))) 3)))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 1870 to 1278 computations (31.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.0b	(sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	0.7b	(+.f64 re (hypot.f64 re im))

series89.0ms (2%)

Counts

3 → 40

Calls

3 calls:

47.0ms

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

31.0ms

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

12.0ms

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

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-div_binary64`
31×	`sqrt-prod_binary64`
31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`pow1_binary64`

Counts

3 → 107

Calls

3 calls:

9.0ms

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

9.0ms

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

2.0ms

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

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
437×	`times-frac_binary64`
417×	`associate-/l*_binary64`
400×	`cancel-sign-sub-inv_binary64`
308×	`fma-neg_binary64`

Counts

147 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	3119
1	632	2887
2	1949	2776
3	4823	2776
4	4957	2776

prune223.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	313	7	320

Error

8.3b

Counts

320 → 7

Alt Table

Status	Error	Program
▶	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 (hypot.f64 re im) re))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 8938 to 4414 computations (50.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 (hypot.f64 re im) re)))))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 (hypot.f64 re im) re)))
✓	0.7b	(+.f64 (hypot.f64 re im) re)
	0.7b	(+.f64 re (hypot.f64 re im))

series76.0ms (1.7%)

Counts

3 → 56

Calls

3 calls:

51.0ms

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

13.0ms

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

12.0ms

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

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-div_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`sqrt-prod_binary64`
13×	`flip-+_binary64`

Counts

3 → 82

Calls

3 calls:

9.0ms

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

8.0ms

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

2.0ms

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

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-r_binary64`
538×	`fma-def_binary64`
505×	`associate-l_binary64`
248×	`cancel-sign-sub-inv_binary64`
225×	`associate-/l*_binary64`

Counts

138 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	2988
1	542	2824
2	1478	2701
3	4950	2701

prune135.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	205	7	212

Error

8.3b

Counts

212 → 7

Alt Table

Status	Error	Program
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 (hypot.f64 re im) re))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 6035 to 2719 computations (54.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))))
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3))
✓	0.6b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)
	0.7b	(+.f64 re (hypot.f64 re im))

series134.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

83.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)

35.0ms

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

16.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`sqrt-prod_binary64`
69×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
32×	`sqrt-div_binary64`
29×	`cube-prod_binary64`

Counts

3 → 153

Calls

3 calls:

14.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3))

5.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)

3.0ms

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

simplify172.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

400×	`cancel-sign-sub-inv_binary64`
377×	`associate-r_binary64`
317×	`associate-l_binary64`
245×	`fma-neg_binary64`
205×	`sqr-pow_binary64`

Counts

225 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	390	6031
1	1068	5509
2	3669	5187
3	4684	5089
4	4896	5089

prune331.0ms (7.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	410	0	410
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	410	7	417

Error

8.3b

Counts

417 → 7

Alt Table

Status	Error	Program
✓	12.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 (hypot.f64 re im) re))))))
	49.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im)))) 3)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 14440 to 7870 computations (45.5% saved)

regimes317.0ms (7.2%)

Accuracy

Total 2.7b remaining (27.6%)

Threshold costs 0b (0%)

Counts

36 → 2

Compiler

Compiled 4442 to 3164 computations (28.8% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end108.0ms (2.5%)

Compiler: Compiled 185 to 134 computations (27.6% saved)

Details

analyze469.0ms (10.7%)

sample1.8s (41.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series61.0ms (1.4%)

rewrite7.0ms (0.2%)

simplify61.0ms (1.4%)

prune63.0ms (1.4%)

localize8.0ms (0.2%)

series89.0ms (2%)

rewrite31.0ms (0.7%)

simplify100.0ms (2.3%)

prune223.0ms (5.1%)

localize11.0ms (0.3%)

series76.0ms (1.7%)

rewrite27.0ms (0.6%)

simplify76.0ms (1.7%)

prune135.0ms (3.1%)

localize11.0ms (0.3%)

series134.0ms (3.1%)

rewrite38.0ms (0.9%)

simplify172.0ms (3.9%)

prune331.0ms (7.6%)

regimes317.0ms (7.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end108.0ms (2.5%)

Profiling