Details

analyze183.0ms (5%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.1s (31.1%)

Results

990.0ms	8256×	body	128	valid
56.0ms	425×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify127.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

680×	`unsub-neg_binary64`
594×	`fma-neg_binary64`
560×	`sub-neg_binary64`
520×	`fma-def_binary64`
399×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	30	25
2	71	23
3	194	16
4	573	14
5	1779	14
6	3048	14
7	4137	14
8	4615	14
9	4749	14
10	4784	14
11	4907	14
12	4998	14

prune3.0ms (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

6.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
▶	6.9b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))

Compiler

Compiled 97 to 51 computations (47.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))
✓	0.1b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
✓	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	6.5b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series48.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

14.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
13.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
12.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
8.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 79

Calls

4 calls:

6.0ms	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
5.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
5.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
3.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify119.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

245×	`times-frac_binary64`
240×	`associate-l_binary64`
214×	`associate-r_binary64`
204×	`fma-neg_binary64`
200×	`distribute-rgt-out_binary64`

Counts

175 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2858
1	447	2479
2	1756	2377
3	3539	2365
4	4775	2365
5	5089	2365

prune118.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	137	7	144

Error

0.1b

Counts

144 → 7

Alt Table

Status	Error	Program
	7.4b	(-.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	6.9b	(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re (neg.f64 (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)))
	37.6b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (.f64 2 (*.f64 x.re x.im)) (sqrt.f64 x.im)) (sqrt.f64 x.im)))
▶	0.2b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	7.2b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re))) (cbrt.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)))) (.f64 x.im (cbrt.f64 (.f64 2 (.f64 x.re x.im))))))
	6.9b	(-.f64 (pow.f64 x.re 3) (.f64 3 (.f64 x.re (pow.f64 x.im 2))))

Compiler

Compiled 4358 to 909 computations (79.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x.re x.im) x.re)
✓	0.1b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	0.2b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

series33.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

14.0ms

(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))

14.0ms

(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

5.0ms

(*.f64 (-.f64 x.re x.im) x.re)

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*l/_binary64`
17×	`flip-+_binary64`
17×	`flip3-+_binary64`
16×	`frac-sub_binary64`
12×	`frac-times_binary64`

Counts

3 → 85

Calls

3 calls:

10.0ms

(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))

9.0ms

(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

5.0ms

(*.f64 (-.f64 x.re x.im) x.re)

simplify115.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
595×	`associate-l_binary64`
551×	`associate-r_binary64`
324×	`cancel-sign-sub-inv_binary64`
307×	`distribute-rgt-in_binary64`

Counts

157 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3654
1	775	2962
2	3646	2738
3	4358	2738
4	4695	2738

prune190.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	6	187
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	0.7b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (.f64 (cbrt.f64 (+.f64 x.re x.im)) (.f64 (-.f64 x.re x.im) x.re))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
	37.6b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (.f64 (.f64 2 (*.f64 x.re x.im)) (sqrt.f64 x.im)) (sqrt.f64 x.im)))
	0.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))) (cbrt.f64 (-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im)))) (cbrt.f64 (-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	0.5b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im)) (cbrt.f64 (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))) (cbrt.f64 (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
	41.6b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (/.f64 (.f64 x.im (.f64 2 (pow.f64 (.f64 x.re x.im) 3))) (+.f64 (.f64 (.f64 x.re x.im) (.f64 x.re x.im)) (-.f64 (.f64 (.f64 x.im x.re) (.f64 x.im x.re)) (.f64 (.f64 x.re x.im) (.f64 x.im x.re))))))
	6.9b	(-.f64 (pow.f64 x.re 3) (.f64 3 (.f64 x.re (pow.f64 x.im 2))))

Compiler

Compiled 6791 to 1460 computations (78.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x.re x.im) -2)
	0.0b	(*.f64 (-.f64 x.re x.im) x.re)
✓	0.1b	(.f64 x.im (.f64 (*.f64 x.re x.im) -2))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))

series32.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

17.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
11.0ms	(.f64 x.im (.f64 (*.f64 x.re x.im) -2))
5.0ms	(.f64 (.f64 x.re x.im) -2)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 53

Calls

3 calls:

5.0ms	(.f64 x.im (.f64 (*.f64 x.re x.im) -2))
4.0ms	(.f64 (.f64 x.re x.im) -2)
0.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-neg_binary64`
443×	`unswap-sqr_binary64`
385×	`*-commutative_binary64`
248×	`fma-def_binary64`
216×	`distribute-rgt-in_binary64`

Counts

125 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1604
1	204	1449
2	711	1403
3	1297	1381
4	2577	1381
5	4732	1381
6	5201	1381

prune137.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Error

Counts

132 → 7

Alt Table

Status	Error	Program
	34.9b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 (sqrt.f64 x.im) (.f64 (sqrt.f64 x.im) (.f64 (*.f64 x.re x.im) -2))))
▶	0.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	41.6b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (/.f64 (.f64 x.im (.f64 2 (pow.f64 (.f64 x.re x.im) 3))) (+.f64 (.f64 (.f64 x.re x.im) (.f64 x.re x.im)) (-.f64 (.f64 (.f64 x.im x.re) (.f64 x.im x.re)) (.f64 (.f64 x.re x.im) (.f64 x.im x.re))))))
	6.9b	(-.f64 (pow.f64 x.re 3) (.f64 3 (.f64 x.re (pow.f64 x.im 2))))

Compiler

Compiled 2926 to 1026 computations (64.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.re (cbrt.f64 (-.f64 x.re x.im))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
✓	0.6b	(cbrt.f64 (-.f64 x.re x.im))

series133.0ms (3.6%)

Counts

4 → 96

Calls

4 calls:

44.0ms	(*.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))
39.0ms	(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
30.0ms	(cbrt.f64 (-.f64 x.re x.im))
19.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.re (cbrt.f64 (-.f64 x.re x.im))))

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-div_binary64`
40×	`add-sqr-sqrt_binary64`
39×	`cbrt-prod_binary64`
35×	`flip--_binary64`
35×	`flip3--_binary64`

Counts

4 → 153

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.re (cbrt.f64 (-.f64 x.re x.im))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
8.0ms	(*.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))
2.0ms	(cbrt.f64 (-.f64 x.re x.im))

simplify146.0ms (4%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-r_binary64`
454×	`associate-l_binary64`
380×	`times-frac_binary64`
329×	`unswap-sqr_binary64`
303×	`fma-neg_binary64`

Counts

249 → 283

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	6603
1	1046	5893
2	3469	5703
3	5206	5703

prune321.0ms (8.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	387	7	394

Error

Counts

394 → 7

Alt Table

Status	Error	Program
	34.9b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 (sqrt.f64 x.im) (.f64 (sqrt.f64 x.im) (.f64 (*.f64 x.re x.im) -2))))
✓	0.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	41.6b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)) (/.f64 (.f64 x.im (.f64 2 (pow.f64 (.f64 x.re x.im) 3))) (+.f64 (.f64 (.f64 x.re x.im) (.f64 x.re x.im)) (-.f64 (.f64 (.f64 x.im x.re) (.f64 x.im x.re)) (.f64 (.f64 x.re x.im) (.f64 x.im x.re))))))
	6.9b	(-.f64 (pow.f64 x.re 3) (.f64 3 (.f64 x.re (pow.f64 x.im 2))))

Compiler

Compiled 16097 to 6074 computations (62.3% saved)

regimes457.0ms (12.5%)

Accuracy

Total 0.2b remaining (91.7%)

Threshold costs 0.2b (91.7%)

Counts

148 → 1

Compiler

Compiled 11559 to 5796 computations (49.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	18	23
2	23	23
3	25	23
4	26	23
5	26	23

end103.0ms (2.8%)

Compiler: Compiled 200 to 105 computations (47.5% saved)

Details

analyze183.0ms (5%)

sample1.1s (31.1%)

simplify127.0ms (3.5%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series48.0ms (1.3%)

rewrite23.0ms (0.6%)

simplify119.0ms (3.3%)

prune118.0ms (3.2%)

localize10.0ms (0.3%)

series33.0ms (0.9%)

rewrite37.0ms (1%)

simplify115.0ms (3.1%)

prune190.0ms (5.2%)

localize9.0ms (0.2%)

series32.0ms (0.9%)

rewrite14.0ms (0.4%)

simplify92.0ms (2.5%)

prune137.0ms (3.7%)

localize15.0ms (0.4%)

series133.0ms (3.6%)

rewrite48.0ms (1.3%)

simplify146.0ms (4%)

prune321.0ms (8.8%)

regimes457.0ms (12.5%)

simplify3.0ms (0.1%)

end103.0ms (2.8%)

Profiling