Details

analyze454.0ms (10.6%)

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)

sample58.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	194×	body	128	valid
8.0ms	20×	body	4096	valid
7.0ms	16×	body	2048	valid
4.0ms	14×	body	1024	valid
2.0ms	9×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify12.0ms (0.3%)

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

12.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.7b	(.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)
✓	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	1.0b	(+.f64 re (hypot.f64 re im))

series76.0ms (1.8%)

Counts

3 → 56

Calls

3 calls:

48.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
14.0ms	(+.f64 re (hypot.f64 re im))
13.0ms	(hypot.f64 re im)

rewrite8.0ms (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:

4.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
3.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify79.0ms (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

prune88.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Error

7.5b

Counts

119 → 8

Alt Table

Status	Error	Program
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	12.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))))))
	14.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	15.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 2737 to 1857 computations (32.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
	1.0b	(+.f64 re (hypot.f64 re im))

series81.0ms (1.9%)

Counts

2 → 16

Calls

2 calls:

46.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
34.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

rewrite12.0ms (0.3%)

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)))

simplify75.0ms (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

prune132.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	170	9	179

Error

7.5b

Counts

179 → 9

Alt Table

Status	Error	Program
▶	12.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))))
	13.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (+.f64 re (hypot.f64 re im))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))) (cbrt.f64 (+.f64 re (hypot.f64 re im)))))))
	14.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	15.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	14.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	46.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))

Compiler

Compiled 4149 to 2740 computations (34% saved)

localize9.0ms (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	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	1.0b	(+.f64 re (hypot.f64 re im))

series98.0ms (2.3%)

Counts

2 → 16

Calls

2 calls:

50.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
48.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (+.f64 re (hypot.f64 re im))))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
16×	`rem-sqrt-square_binary64`
14×	`pow1_binary64`

Counts

2 → 77

Calls

2 calls:

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

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
440×	`fma-neg_binary64`
341×	`cancel-sign-sub-inv_binary64`
263×	`associate-+l+_binary64`
215×	`associate-r_binary64`

Counts

93 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2355
1	541	2218
2	1749	2162
3	4834	2162
4	5136	2162

prune204.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	198	10	208

Error

7.5b

Counts

208 → 10

Alt Table

Status	Error	Program
	14.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	54.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 (/.f64 (*.f64 im im) re) -1/2)))))
	14.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	46.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))))
	48.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
	15.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	12.8b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))

Compiler

Compiled 5705 to 4056 computations (28.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 re (hypot.f64 re im)))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
✓	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))
	1.0b	(+.f64 re (hypot.f64 re im))

series47.0ms (1.1%)

Counts

2 → 8

Calls

2 calls:

47.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
0.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`sqrt-prod_binary64`
76×	`add-sqr-sqrt_binary64`
35×	`sqrt-pow1_binary64`
33×	`pow1_binary64`
28×	`rem-sqrt-square_binary64`

Counts

2 → 120

Calls

2 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

359×	`*-commutative_binary64`
340×	`fma-def_binary64`
304×	`unswap-sqr_binary64`
299×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`

Counts

128 → 139

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	1550
1	393	1455
2	1241	1403
3	2825	1370
4	4943	1366
5	4923	1366

prune174.0ms (4.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	220	11	231

Error

7.5b

Counts

231 → 11

Alt Table

Status	Error	Program
	14.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	54.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (.f64 (/.f64 (*.f64 im im) re) -1/2)))))
	14.8b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (*.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)))))))
	46.5b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (neg.f64 im)))))
	48.8b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 im))))
	15.4b	(.f64 1/2 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	48.7b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	12.8b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	16.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	48.8b	(.f64 1/2 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 im)))

Compiler

Compiled 5500 to 3809 computations (30.7% saved)

regimes984.0ms (23%)

Accuracy

Total 2.5b remaining (26.4%)

Threshold costs 0b (0%)

Counts

110 → 3

Compiler

Compiled 12802 to 10289 computations (19.6% saved)

bsearch4.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	99
1	45	99
2	45	99

end1.0ms (0%)

Compiler: Compiled 67 to 39 computations (41.8% saved)

sample1.4s (32.7%)

Algorithm

1×

intervals

Results

422.0ms	6157×	body	128	valid
205.0ms	518×	body	4096	valid
191.0ms	592×	body	2048	valid
117.0ms	395×	body	1024	valid
42.0ms	221×	body	512	valid
14.0ms	117×	body	256	valid

Compiler

Compiled 259 to 190 computations (26.6% saved)

Details

analyze454.0ms (10.6%)

sample58.0ms (1.4%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series76.0ms (1.8%)

rewrite8.0ms (0.2%)

simplify79.0ms (1.9%)

prune88.0ms (2%)

localize7.0ms (0.2%)

series81.0ms (1.9%)

rewrite12.0ms (0.3%)

simplify75.0ms (1.7%)

prune132.0ms (3.1%)

localize9.0ms (0.2%)

series98.0ms (2.3%)

rewrite28.0ms (0.6%)

simplify93.0ms (2.2%)

prune204.0ms (4.8%)

localize10.0ms (0.2%)

series47.0ms (1.1%)

rewrite38.0ms (0.9%)

simplify96.0ms (2.2%)

prune174.0ms (4.1%)

regimes984.0ms (23%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.4s (32.7%)

Profiling