Details

analyze458.0ms (11.1%)

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 (43.4%)

Results

800.0ms	6279×	body	128	valid
355.0ms	671×	body	2048	valid
334.0ms	548×	body	4096	valid
169.0ms	408×	body	1024	valid
73.0ms	236×	body	512	valid
27.0ms	114×	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

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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.8b	(+.f64 re (hypot.f64 re im))

series53.0ms (1.3%)

Counts

2 → 32

Calls

2 calls:

42.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
11.0ms	(+.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))

simplify64.0ms (1.6%)

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

prune62.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Error

5.2b

Counts

80 → 8

Alt Table

Status	Error	Program
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
▶	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 1914 to 1300 computations (32.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	0.8b	(+.f64 re (hypot.f64 re im))

series70.0ms (1.7%)

Counts

2 → 16

Calls

2 calls:

43.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
27.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
7×	`associate-r_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
3.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
601×	`fma-def_binary64`
441×	`times-frac_binary64`
335×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`

Counts

71 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	1642
1	461	1585
2	1487	1518
3	4539	1518
4	4997	1518

prune100.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	131	9	140

Error

5.2b

Counts

140 → 9

Alt Table

Status	Error	Program
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
▶	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (/.f64 (-.f64 (.f64 re re) (.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 3256 to 2125 computations (34.7% 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)))
✓	0.2b	(sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.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))))
	0.8b	(+.f64 re (hypot.f64 re im))

series56.0ms (1.4%)

Counts

2 → 32

Calls

2 calls:

41.0ms	(sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
15.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-div_binary64`
27×	`sqrt-prod_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`pow1_binary64`

Counts

2 → 88

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
9.0ms	(sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-def_binary64`
488×	`fma-neg_binary64`
312×	`*-commutative_binary64`
244×	`cancel-sign-sub-inv_binary64`
227×	`associate-/l*_binary64`

Counts

120 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	2490
1	504	2295
2	1489	2211
3	4432	2186
4	4997	2186
5	4963	2186

prune223.0ms (5.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	313	9	322

Error

5.2b

Counts

322 → 9

Alt Table

Status	Error	Program
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
▶	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (/.f64 (-.f64 (.f64 re re) (*.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))))
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 8971 to 4447 computations (50.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	0.6b	(cbrt.f64 re)
✓	12.9b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series212.0ms (5.1%)

Counts

4 → 56

Calls

4 calls:

73.0ms	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
57.0ms	(cbrt.f64 re)
44.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))
38.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
2.0ms	(cbrt.f64 re)
2.0ms	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify115.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
702×	`associate-/l*_binary64`
325×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
220×	`unswap-sqr_binary64`

Counts

134 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	1923
1	518	1757
2	1867	1664
3	4667	1645
4	4862	1645
5	4985	1645
6	4962	1645

prune128.0ms (3.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	197	9	206

Error

5.2b

Counts

206 → 9

Alt Table

Status	Error	Program
	54.9b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)) (hypot.f64 re im)))))
✓	11.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
✓	11.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	47.3b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	49.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (/.f64 (-.f64 (.f64 re re) (*.f64 (hypot.f64 re im) (hypot.f64 re im))) (-.f64 re (hypot.f64 re im))))))))
	54.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	11.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 4508 to 2361 computations (47.6% saved)

regimes376.0ms (9.1%)

Accuracy

Total 3.2b remaining (30.6%)

Threshold costs 0b (0%)

Counts

37 → 3

Compiler

Compiled 4591 to 3514 computations (23.5% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	98
1	45	98
2	45	98

end129.0ms (3.1%)

Compiler: Compiled 274 to 174 computations (36.5% saved)

Details

analyze458.0ms (11.1%)

sample1.8s (43.4%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series53.0ms (1.3%)

rewrite7.0ms (0.2%)

simplify64.0ms (1.6%)

prune62.0ms (1.5%)

localize7.0ms (0.2%)

series70.0ms (1.7%)

rewrite19.0ms (0.5%)

simplify72.0ms (1.7%)

prune100.0ms (2.4%)

localize8.0ms (0.2%)

series56.0ms (1.4%)

rewrite32.0ms (0.8%)

simplify104.0ms (2.5%)

prune223.0ms (5.4%)

localize9.0ms (0.2%)

series212.0ms (5.1%)

rewrite12.0ms (0.3%)

simplify115.0ms (2.8%)

prune128.0ms (3.1%)

regimes376.0ms (9.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end129.0ms (3.1%)

Profiling