Details

analyze373.0ms (5.6%)

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)

sample1.5s (22.7%)

Infinites

0% of outputs are infinite.

Results

721.0ms	6254×	body	128	valid
290.0ms	612×	body	4096	valid
247.0ms	644×	body	2048	valid
123.0ms	407×	body	1024	valid
47.0ms	205×	body	512	valid
22.0ms	134×	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

prune8.0ms (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

12.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	38.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 85 to 61 computations (28.2% 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))))
✓	1.3b	(+.f64 re (hypot.f64 re im))

series71.0ms (1.1%)

Counts

3 → 56

Calls

3 calls:

45.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
14.0ms	(hypot.f64 re im)
12.0ms	(+.f64 re (hypot.f64 re im))

rewrite7.0ms (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)

simplify74.0ms (1.1%)

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

prune94.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

6.7b

Counts

120 → 8

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
▶	13.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	45.9b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))

Compiler

Compiled 2729 to 1871 computations (31.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
	0.2b	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
	1.3b	(+.f64 re (hypot.f64 re im))

series95.0ms (1.4%)

Counts

2 → 32

Calls

2 calls:

49.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))
45.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`sqrt-pow1_binary64`
63×	`pow1_binary64`
31×	`sqrt-prod_binary64`
28×	`sqrt-div_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

2 → 104

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))))
4.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im)))))

simplify144.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
431×	`cancel-sign-sub-inv_binary64`
329×	`fma-neg_binary64`
263×	`associate-r_binary64`
223×	`associate-l_binary64`

Counts

136 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	3834
1	774	3581
2	2480	3442
3	4578	3322
4	4976	3322
5	4930	3322

prune363.0ms (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	381	8	389

Error

6.7b

Counts

389 → 8

Alt Table

Status	Error	Program
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
✓	13.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	45.9b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))

Compiler

Compiled 13622 to 8850 computations (35% saved)

localize9.0ms (0.1%)

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)
✓	15.4b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series225.0ms (3.4%)

Counts

4 → 56

Calls

4 calls:

90.0ms	(cbrt.f64 re)
65.0ms	(sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))))
43.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
26.0ms	(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))

simplify134.0ms (2%)

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

prune138.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	196	9	205

Error

6.7b

Counts

205 → 9

Alt Table

Status	Error	Program
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
▶	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	18.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))
	45.9b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))

Compiler

Compiled 4647 to 2458 computations (47.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))))
✓	0.5b	(cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))
	0.6b	(cbrt.f64 re)
✓	15.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im))

series786.0ms (11.9%)

Counts

3 → 48

Calls

3 calls:

396.0ms

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))))

360.0ms

(cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))

30.0ms

(fma.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`cbrt-prod_binary64`
7×	`pow1/3_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 57

Calls

3 calls:

8.0ms

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))))

3.0ms

(cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))

1.0ms

(fma.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

459×	`unswap-sqr_binary64`
453×	`fma-neg_binary64`
340×	`associate-l_binary64`
312×	`associate-r_binary64`
291×	`times-frac_binary64`

Counts

105 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1728
1	280	1459
2	756	1363
3	3359	1345
4	4942	1345

prune248.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	273	9	282

Error

6.7b

Counts

282 → 9

Alt Table

Status	Error	Program
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)))) (sqrt.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)))) (sqrt.f64 (cbrt.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)))))) (cbrt.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im)))))
	45.9b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	47.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	54.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (.f64 (/.f64 (.f64 im im) re) -1/2)))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	16.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	18.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (expm1.f64 (log1p.f64 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))))
	49.6b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
✓	13.2b	(.f64 1/2 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im))))) (sqrt.f64 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))))

Compiler

Compiled 9127 to 2864 computations (68.6% saved)

regimes2.0s (30.6%)

Accuracy

Total 2.6b remaining (26.3%)

Threshold costs 0b (0%)

Counts

191 → 3

Compiler

Compiled 36226 to 20607 computations (43.1% saved)

bsearch8.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	98
1	51	98
2	49	98

end145.0ms (2.2%)

Compiler: Compiled 302 to 183 computations (39.4% saved)

Details

analyze373.0ms (5.6%)

sample1.5s (22.7%)

simplify7.0ms (0.1%)

prune8.0ms (0.1%)

localize6.0ms (0.1%)

series71.0ms (1.1%)

rewrite7.0ms (0.1%)

simplify74.0ms (1.1%)

prune94.0ms (1.4%)

localize8.0ms (0.1%)

series95.0ms (1.4%)

rewrite32.0ms (0.5%)

simplify144.0ms (2.2%)

prune363.0ms (5.5%)

localize9.0ms (0.1%)

series225.0ms (3.4%)

rewrite13.0ms (0.2%)

simplify134.0ms (2%)

prune138.0ms (2.1%)

localize15.0ms (0.2%)

series786.0ms (11.9%)

rewrite14.0ms (0.2%)

simplify72.0ms (1.1%)

prune248.0ms (3.7%)

regimes2.0s (30.6%)

bsearch8.0ms (0.1%)

simplify4.0ms (0.1%)

end145.0ms (2.2%)

Profiling