Details

analyze465.0ms (11%)

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)

sample1.7s (40.7%)

Results

783.0ms	6286×	body	128	valid
340.0ms	676×	body	2048	valid
300.0ms	495×	body	4096	valid
178.0ms	444×	body	1024	valid
71.0ms	236×	body	512	valid
27.0ms	119×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify10.0ms (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

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

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(.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)
✓	0.5b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.6b	(+.f64 re (hypot.f64 re im))

series71.0ms (1.7%)

Counts

3 → 56

Calls

3 calls:

46.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
12.0ms	(+.f64 re (hypot.f64 re im))
12.0ms	(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))))
2.0ms	(+.f64 re (hypot.f64 re im))
0.0ms	(hypot.f64 re im)

simplify77.0ms (1.8%)

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 (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Error

6.5b

Counts

119 → 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)))
	49.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.6b	(.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)))

Compiler

Compiled 2655 to 1821 computations (31.4% saved)

localize8.0ms (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))))

series72.0ms (1.7%)

Counts

3 → 56

Calls

3 calls:

46.0ms

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

13.0ms

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

12.0ms

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

rewrite18.0ms (0.4%)

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:

7.0ms

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

3.0ms

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

2.0ms

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

simplify89.0ms (2.1%)

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

prune168.0ms (4%)

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
	54.6b	(.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)))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 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)))))))

Compiler

Compiled 6343 to 3592 computations (43.4% saved)

localize7.0ms (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))

series47.0ms (1.1%)

Counts

1 → 8

Calls

1 calls:

47.0ms

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

rewrite9.0ms (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:

7.0ms

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

simplify75.0ms (1.8%)

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

prune91.0ms (2.2%)

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
	54.6b	(.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)))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 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)))))))

Compiler

Compiled 3108 to 2064 computations (33.6% saved)

localize10.0ms (0.2%)

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)))))

series128.0ms (3%)

Counts

4 → 80

Calls

4 calls:

54.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))
49.0ms	(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)))))))
13.0ms	(+.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)))))
13.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))

rewrite39.0ms (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:

12.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im))))
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 re im))) (sqrt.f64 (hypot.f64 re im)))
3.0ms	(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)))))))
3.0ms	(+.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)))))

simplify123.0ms (2.9%)

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

prune175.0ms (4.1%)

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
	54.6b	(.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)))
	44.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	17.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 7599 to 3904 computations (48.6% saved)

regimes620.0ms (14.6%)

Accuracy

Total 3.3b remaining (32.8%)

Threshold costs 0b (0%)

Counts

68 → 3

Compiler

Compiled 7407 to 5624 computations (24.1% saved)

bsearch2.0ms (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`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	91
1	46	91
2	44	91

end108.0ms (2.5%)

Compiler: Compiled 227 to 148 computations (34.8% saved)

Details

analyze465.0ms (11%)

sample1.7s (40.7%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series71.0ms (1.7%)

rewrite8.0ms (0.2%)

simplify77.0ms (1.8%)

prune83.0ms (1.9%)

localize8.0ms (0.2%)

series72.0ms (1.7%)

rewrite18.0ms (0.4%)

simplify89.0ms (2.1%)

prune168.0ms (4%)

localize7.0ms (0.2%)

series47.0ms (1.1%)

rewrite9.0ms (0.2%)

simplify75.0ms (1.8%)

prune91.0ms (2.2%)

localize10.0ms (0.2%)

series128.0ms (3%)

rewrite39.0ms (0.9%)

simplify123.0ms (2.9%)

prune175.0ms (4.1%)

regimes620.0ms (14.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end108.0ms (2.5%)

Profiling