Details

analyze859.0ms (12.8%)

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)

sample74.0ms (1.1%)

Algorithm

1×

intervals

Results

24.0ms	198×	body	128	valid
14.0ms	19×	body	4096	valid
10.0ms	16×	body	2048	valid
5.0ms	11×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify21.0ms (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

prune6.0ms (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

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 51 to 37 computations (27.5% saved)

localize13.0ms (0.2%)

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))))
✓	1.1b	(+.f64 re (hypot.f64 re im))

rewrite15.0ms (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:

6.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
5.0ms	(+.f64 re (hypot.f64 re im))
1.0ms	(hypot.f64 re im)

series135.0ms (2%)

Counts

3 → 56

Calls

3 calls:

80.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
29.0ms	(+.f64 re (hypot.f64 re im))
26.0ms	(hypot.f64 re im)

simplify151.0ms (2.3%)

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 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1829
1	514	1737
2	1465	1673
3	4990	1673
4	5308	1673

prune155.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	149	6	155
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	149	7	156

Error

6.4b

Counts

156 → 7

Alt Table

Status	Error	Program
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	15.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
▶	12.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 2688 to 1836 computations (31.7% saved)

localize15.0ms (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))))
	1.1b	(+.f64 re (hypot.f64 re im))

rewrite26.0ms (0.4%)

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:

14.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
5.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

series134.0ms (2%)

Counts

2 → 16

Calls

2 calls:

82.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im))))
51.0ms	(sqrt.f64 (+.f64 re (hypot.f64 re im)))

simplify153.0ms (2.3%)

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 → 102

Iterations

Useful iterations: 2 (0.0ms)

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

prune222.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	222	8	230

Error

6.4b

Counts

230 → 8

Alt Table

Status	Error	Program
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	15.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 4042 to 2680 computations (33.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (hypot.f64 re im))
	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	0.6b	(cbrt.f64 (hypot.f64 re im))
✓	9.4b	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`cbrt-prod_binary64`

Counts

2 → 29

Calls

2 calls:

5.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))
1.0ms	(cbrt.f64 (hypot.f64 re im))

series104.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

75.0ms	(cbrt.f64 (hypot.f64 re im))
29.0ms	(+.f64 re (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

simplify170.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-l_binary64`
622×	`fma-def_binary64`
391×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`
175×	`times-frac_binary64`

Counts

77 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	1503
1	536	1476
2	1524	1443
3	4704	1443
4	4989	1443
5	4964	1443

prune255.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	323	8	331

Error

6.4b

Counts

331 → 8

Alt Table

Status	Error	Program
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
▶	15.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 6335 to 3530 computations (44.3% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 re)
	0.6b	(cbrt.f64 re)
✓	0.6b	(cbrt.f64 re)
✓	14.8b	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 23

Calls

2 calls:

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

series539.0ms (8.1%)

Counts

2 → 36

Calls

2 calls:

473.0ms	(cbrt.f64 re)
65.0ms	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))

simplify143.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

468×	`times-frac_binary64`
381×	`fma-def_binary64`
344×	`associate-r_binary64`
294×	`associate-l_binary64`
255×	`associate-/r*_binary64`

Counts

59 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	94	630
1	237	594
2	724	576
3	4160	576
4	4820	576
5	4988	576
6	4868	576

prune117.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	225	8	233

Error

6.4b

Counts

233 → 8

Alt Table

Status	Error	Program
✓	12.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	12.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (hypot.f64 re im)))))
	54.7b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	16.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (exp.f64 (log.f64 (+.f64 re (hypot.f64 re im)))))))
	47.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (.f64 (*.f64 (cbrt.f64 (hypot.f64 re im)) (cbrt.f64 (hypot.f64 re im))) (cbrt.f64 (hypot.f64 re im)))))))))
	46.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))

Compiler

Compiled 2872 to 1087 computations (62.2% saved)

regimes755.0ms (11.3%)

Accuracy

Total 2.8b remaining (27.8%)

Threshold costs 0b (0%)

Compiler

Compiled 5093 to 3311 computations (35% saved)

bsearch3.0ms (0%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	37	58
2	37	58

end2.0ms (0%)

Compiler: Compiled 40 to 30 computations (25% saved)

sample2.6s (38.1%)

Algorithm

1×

intervals

Results

740.0ms	6088×	body	128	valid
422.0ms	656×	body	2048	valid
361.0ms	507×	body	4096	valid
236.0ms	404×	body	1024	valid
91.0ms	220×	body	512	valid
28.0ms	125×	body	256	valid

Compiler

Compiled 223 to 131 computations (41.3% saved)

Details

analyze859.0ms (12.8%)

sample74.0ms (1.1%)

simplify21.0ms (0.3%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite15.0ms (0.2%)

series135.0ms (2%)

simplify151.0ms (2.3%)

prune155.0ms (2.3%)

localize15.0ms (0.2%)

rewrite26.0ms (0.4%)

series134.0ms (2%)

simplify153.0ms (2.3%)

prune222.0ms (3.3%)

localize21.0ms (0.3%)

rewrite9.0ms (0.1%)

series104.0ms (1.6%)

simplify170.0ms (2.5%)

prune255.0ms (3.8%)

localize29.0ms (0.4%)

rewrite4.0ms (0.1%)

series539.0ms (8.1%)

simplify143.0ms (2.1%)

prune117.0ms (1.8%)

regimes755.0ms (11.3%)

bsearch3.0ms (0%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample2.6s (38.1%)

Profiling