Details

analyze494.0ms (11.2%)

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)

sample1.8s (40%)

Results

767.0ms	6247×	body	128	valid
349.0ms	543×	body	4096	valid
339.0ms	671×	body	2048	valid
182.0ms	442×	body	1024	valid
75.0ms	233×	body	512	valid
28.0ms	120×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify9.0ms (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

13.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.5b	(.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	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
✓	0.0b	(hypot.f64 re im)
✓	0.9b	(+.f64 re (hypot.f64 re im))

series47.0ms (1.1%)

Counts

3 → 56

Calls

3 calls:

28.0ms	(sqrt.f64 (*.f64 2 (+.f64 re (hypot.f64 re im))))
10.0ms	(+.f64 re (hypot.f64 re im))
9.0ms	(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)

simplify87.0ms (2%)

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

prune77.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Error

8.5b

Counts

119 → 6

Alt Table

Status	Error	Program
▶	15.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im)))))
	47.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 2669 to 1828 computations (31.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 re im)
✓	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
✓	0.5b	(cbrt.f64 re)
✓	15.2b	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

series93.0ms (2.1%)

Counts

3 → 48

Calls

3 calls:

35.0ms	(cbrt.f64 re)
35.0ms	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
23.0ms	(fma.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re) (hypot.f64 re im))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

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

simplify92.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
486×	`fma-neg_binary64`
403×	`associate-/r*_binary64`
393×	`distribute-neg-frac_binary64`
314×	`fma-def_binary64`

Counts

113 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1156
1	267	1083
2	861	1037
3	3718	1022
4	4753	1010
5	4987	1010
6	4914	1010

prune135.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	203	7	210

Error

8.5b

Counts

210 → 7

Alt Table

Status	Error	Program
	15.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2) (cbrt.f64 (cbrt.f64 re)))) (cbrt.f64 re) (hypot.f64 re im)))))
	48.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	47.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	57.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
▶	15.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))

Compiler

Compiled 4538 to 2266 computations (50.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 re) (cbrt.f64 re))
	0.5b	(cbrt.f64 re)
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)))
✓	15.2b	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))

series53.0ms (1.2%)

Counts

2 → 36

Calls

2 calls:

29.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)))
24.0ms	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 22

Calls

2 calls:

5.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)))
0.0ms	(fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

432×	`times-frac_binary64`
419×	`fma-neg_binary64`
408×	`distribute-rgt-neg-in_binary64`
314×	`distribute-neg-frac_binary64`
298×	`associate-r_binary64`

Counts

58 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	595
1	210	574
2	641	566
3	3551	565
4	5145	565

prune190.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	282	2	284
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	284	7	291

Error

8.5b

Counts

291 → 7

Alt Table

Status	Error	Program
▶	15.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	47.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	48.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	55.8b	(.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 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))))))

Compiler

Compiled 7723 to 2934 computations (62% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re)))
✓	0.5b	(cbrt.f64 (cbrt.f64 re))
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)
✓	15.1b	(fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))

series544.0ms (12.3%)

Counts

3 → 48

Calls

3 calls:

273.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 re)) 4)

248.0ms

(cbrt.f64 (cbrt.f64 re))

22.0ms

(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 re) (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)) 4)

1.0ms

(cbrt.f64 (cbrt.f64 re))

0.0ms

(fma.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-neg_binary64`
509×	`times-frac_binary64`
458×	`associate-l_binary64`
437×	`associate-r_binary64`
324×	`associate-/r*_binary64`

Counts

100 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1590
1	299	1296
2	820	1282
3	4489	1282
4	4993	1282

prune137.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	154	7	161

Error

8.5b

Counts

161 → 7

Alt Table

Status	Error	Program
	47.2b	(.f64 1/2 (sqrt.f64 (.f64 2 im)))
	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 re)) 4) (pow.f64 (cbrt.f64 (cbrt.f64 re)) 2)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))))))
	48.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	57.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 1/8 (/.f64 (pow.f64 im 4) (pow.f64 re 3)) (fma.f64 (/.f64 (.f64 im im) re) -1/2 (.f64 (/.f64 (pow.f64 im 6) (pow.f64 re 5)) -1/16))))))
	55.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
✓	13.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 re (hypot.f64 re im)))))
	16.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 re) (cbrt.f64 re)) (cbrt.f64 re))) (hypot.f64 re im)))))))

Compiler

Compiled 4815 to 2195 computations (54.4% saved)

regimes343.0ms (7.8%)

Accuracy

Total 2.9b remaining (28.1%)

Threshold costs 0b (0%)

Counts

32 → 3

Compiler

Compiled 5450 to 3345 computations (38.6% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	120
1	54	120
2	54	120

end141.0ms (3.2%)

Compiler: Compiled 383 to 205 computations (46.5% saved)

Details

analyze494.0ms (11.2%)

sample1.8s (40%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series47.0ms (1.1%)

rewrite8.0ms (0.2%)

simplify87.0ms (2%)

prune77.0ms (1.7%)

localize10.0ms (0.2%)

series93.0ms (2.1%)

rewrite11.0ms (0.2%)

simplify92.0ms (2.1%)

prune135.0ms (3.1%)

localize11.0ms (0.3%)

series53.0ms (1.2%)

rewrite9.0ms (0.2%)

simplify51.0ms (1.1%)

prune190.0ms (4.3%)

localize17.0ms (0.4%)

series544.0ms (12.3%)

rewrite6.0ms (0.1%)

simplify77.0ms (1.7%)

prune137.0ms (3.1%)

regimes343.0ms (7.8%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end141.0ms (3.2%)

Profiling