Details

analyze1.8s (30%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.8s (30.6%)

Results

816.0ms	6248×	body	128	valid
352.0ms	694×	body	2048	valid
330.0ms	521×	body	4096	valid
183.0ms	433×	body	1024	valid
70.0ms	230×	body	512	valid
28.0ms	130×	body	256	valid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify7.0ms (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

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

13.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.4b	(.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 3 expressions with local error:

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

series109.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

51.0ms	(+.f64 re (hypot.f64 re im))
44.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
14.0ms	(hypot.f64 re im)

rewrite8.0ms (0.1%)

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:

3.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
2.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify96.0ms (1.6%)

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

prune83.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Error

7.0b

Counts

119 → 7

Alt Table

Status	Error	Program
✓	13.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	16.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 2683 to 1824 computations (32% saved)

localize9.0ms (0.2%)

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 re (hypot.f64 re im))))))
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
	0.4b	(+.f64 re (hypot.f64 re im))
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

series97.0ms (1.6%)

Counts

3 → 40

Calls

3 calls:

54.0ms

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

30.0ms

(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))))

rewrite34.0ms (0.6%)

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:

12.0ms

(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))))

3.0ms

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

simplify119.0ms (2%)

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 → 184

Iterations

Useful iterations: 2 (0.0ms)

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

prune218.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	314	7	321

Error

7.0b

Counts

321 → 7

Alt Table

Status	Error	Program
✓	13.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	14.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	16.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 8915 to 4401 computations (50.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
✓	0.5b	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
✓	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	10.6b	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

series136.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

66.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
41.0ms	(cbrt.f64 (hypot.f64 re im))
15.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
14.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))
5.0ms	(*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im)))
3.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))
1.0ms	(cbrt.f64 (hypot.f64 re im))

simplify155.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

458×	`fma-neg_binary64`
418×	`cancel-sign-sub-inv_binary64`
227×	`unswap-sqr_binary64`
210×	`associate-r_binary64`
209×	`distribute-rgt-neg-in_binary64`

Counts

205 → 247

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	3864
1	805	3722
2	2328	3622
3	4699	3595
4	4982	3595
5	4934	3595

prune227.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	339	2	341
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	341	7	348

Error

7.0b

Counts

348 → 7

Alt Table

Status	Error	Program
✓	13.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6) (cbrt.f64 (hypot.f64 re im)))))))
▶	14.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im)))))))))

Compiler

Compiled 10286 to 5398 computations (47.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (cbrt.f64 (hypot.f64 re im)))
✓	0.6b	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6))
✓	1.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)
✓	9.4b	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))))

series207.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

107.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)
47.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6))
39.0ms	(cbrt.f64 (cbrt.f64 (hypot.f64 re im)))
13.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64`
18×	`unpow-prod-down_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6))
3.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im))))))
2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)
1.0ms	(cbrt.f64 (cbrt.f64 (hypot.f64 re im)))

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Rules

495×	`cancel-sign-sub-inv_binary64`
317×	`unswap-sqr_binary64`
305×	`distribute-rgt-neg-in_binary64`
251×	`associate-r_binary64`
242×	`fma-neg_binary64`

Counts

177 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	4874
1	872	4636
2	2696	4382
3	5016	4382

prune189.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	247	6	253

Error

7.0b

Counts

253 → 6

Alt Table

Status	Error	Program
✓	13.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	48.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	55.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	17.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 re im))) 6)) (cbrt.f64 (cbrt.f64 (hypot.f64 re im)))))))))))
	47.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 10247 to 5102 computations (50.2% saved)

regimes384.0ms (6.4%)

Accuracy

Total 2.8b remaining (27.5%)

Threshold costs 0b (0%)

Counts

42 → 2

Compiler

Compiled 5590 to 3853 computations (31.1% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0%)

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

end100.0ms (1.7%)

Compiler: Compiled 178 to 126 computations (29.2% saved)

Details

analyze1.8s (30%)

sample1.8s (30.6%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series109.0ms (1.8%)

rewrite8.0ms (0.1%)

simplify96.0ms (1.6%)

prune83.0ms (1.4%)

localize9.0ms (0.2%)

series97.0ms (1.6%)

rewrite34.0ms (0.6%)

simplify119.0ms (2%)

prune218.0ms (3.6%)

localize10.0ms (0.2%)

series136.0ms (2.2%)

rewrite22.0ms (0.4%)

simplify155.0ms (2.6%)

prune227.0ms (3.8%)

localize16.0ms (0.3%)

series207.0ms (3.4%)

rewrite14.0ms (0.2%)

simplify122.0ms (2%)

prune189.0ms (3.1%)

regimes384.0ms (6.4%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end100.0ms (1.7%)

Profiling