Details

analyze494.0ms (9.6%)

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)

sample1.9s (36.6%)

Results

836.0ms	6244×	body	128	valid
350.0ms	536×	body	4096	valid
339.0ms	648×	body	2048	valid
200.0ms	439×	body	1024	valid
87.0ms	241×	body	512	valid
34.0ms	148×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% 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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

13.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	38.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
▶	13.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 85 to 61 computations (28.2% 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))))
✓	0.4b	(+.f64 re (hypot.f64 re im))

series58.0ms (1.1%)

Counts

2 → 32

Calls

2 calls:

43.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
15.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (0.1%)

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))

simplify68.0ms (1.3%)

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

prune65.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Error

9.0b

Counts

81 → 7

Alt Table

Status	Error	Program
	27.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	16.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	13.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 1886 to 1287 computations (31.8% 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))))

series88.0ms (1.7%)

Counts

3 → 40

Calls

3 calls:

44.0ms

(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))))

rewrite38.0ms (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:

12.0ms

(*.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))))))

3.0ms

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

simplify102.0ms (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

prune203.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	314	7	321

Error

9.0b

Counts

321 → 7

Alt Table

Status	Error	Program
	27.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
▶	15.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	16.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 8923 to 4410 computations (50.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)
✓	14.6b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series168.0ms (3.3%)

Counts

4 → 56

Calls

4 calls:

66.0ms	(sqrt.f64 (.f64 2 (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))
36.0ms	(cbrt.f64 re)
27.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite13.0ms (0.2%)

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:

7.0ms	(*.f64 (cbrt.f64 re) (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))))
1.0ms	(cbrt.f64 re)
0.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

simplify122.0ms (2.4%)

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

prune155.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	197	7	204

Error

9.0b

Counts

204 → 7

Alt Table

Status	Error	Program
	27.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
	16.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (+.f64 re (hypot.f64 re im))) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))))
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 5) (cbrt.f64 (cbrt.f64 re))) (cbrt.f64 re) (hypot.f64 re im)))))

Compiler

Compiled 4550 to 2398 computations (47.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (cbrt.f64 re))
	0.6b	(cbrt.f64 re)
✓	1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 5)
✓	14.5b	(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 5) (cbrt.f64 (cbrt.f64 re))) (cbrt.f64 re) (hypot.f64 re im))

series596.0ms (11.6%)

Counts

3 → 48

Calls

3 calls:

308.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 5)
262.0ms	(cbrt.f64 (cbrt.f64 re))
26.0ms	(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 5) (cbrt.f64 (cbrt.f64 re))) (cbrt.f64 re) (hypot.f64 re im))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 5)
1.0ms	(cbrt.f64 (cbrt.f64 re))
0.0ms	(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 5) (cbrt.f64 (cbrt.f64 re))) (cbrt.f64 re) (hypot.f64 re im))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

592×	`cancel-sign-sub-inv_binary64`
565×	`fma-neg_binary64`
312×	`associate-r_binary64`
307×	`associate-l_binary64`
186×	`times-frac_binary64`

Counts

100 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1306
1	313	1242
2	804	1128
3	3075	1128
4	4906	1128
5	4894	1128

prune130.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	179	7	186

Error

9.0b

Counts

186 → 7

Alt Table

Status	Error	Program
	44.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	15.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 5) (cbrt.f64 (cbrt.f64 re))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 re)) (cbrt.f64 (cbrt.f64 re))) (cbrt.f64 (cbrt.f64 re))) (hypot.f64 re im)))))
	27.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 re) (sqrt.f64 re) (hypot.f64 re im)))))
	16.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (+.f64 re (hypot.f64 re im)))))))
	49.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.8b	(.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 4249 to 2173 computations (48.9% saved)

regimes814.0ms (15.8%)

Counts: 96 → 2
Compiler: Compiled 13458 to 9103 computations (32.4% saved)

bsearch2.0ms (0%)

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

Details

analyze494.0ms (9.6%)

sample1.9s (36.6%)

simplify7.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series58.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify68.0ms (1.3%)

prune65.0ms (1.3%)

localize9.0ms (0.2%)

series88.0ms (1.7%)

rewrite38.0ms (0.7%)

simplify102.0ms (2%)

prune203.0ms (3.9%)

localize9.0ms (0.2%)

series168.0ms (3.3%)

rewrite13.0ms (0.2%)

simplify122.0ms (2.4%)

prune155.0ms (3%)

localize13.0ms (0.3%)

series596.0ms (11.6%)

rewrite6.0ms (0.1%)

simplify81.0ms (1.6%)

prune130.0ms (2.5%)

regimes814.0ms (15.8%)

bsearch2.0ms (0%)

end0.0ms (0%)

Profiling