Details

analyze199.0ms (7.4%)

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%	74.9%	0.1%	6
31.2%	50%	18.8%	7
34.3%	43.7%	22%	8
45.3%	26.5%	28.2%	9
46.8%	23.4%	29.8%	10
48.8%	14%	37.2%	11
49.8%	12.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	6.1%	40.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.1s (42.1%)

Results

967.0ms	8256×	body	128	valid
75.0ms	582×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify129.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

613×	`sub-neg_binary64`
578×	`fma-neg_binary64`
529×	`neg-mul-1_binary64`
501×	`neg-sub0_binary64`
455×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	23
2	60	23
3	130	16
4	335	16
5	881	16
6	1496	16
7	3511	16
8	4061	16
9	3977	16
10	4614	16
11	4771	16
12	4918	16
13	4914	16

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

5.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.1b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	5.2b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 100 to 54 computations (46% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))
✓	4.8b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))

series22.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
10.0ms	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
0.0ms	(fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))

simplify104.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

435×	`exp-prod_binary64`
356×	`unswap-sqr_binary64`
355×	`fma-def_binary64`
319×	`*-commutative_binary64`
271×	`associate-l_binary64`

Counts

80 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	1276
1	116	1183
2	336	1183
3	1136	1183
4	2105	1183
5	4465	1183
6	4949	1183
7	4916	1183

prune52.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	63	5	68

Error

4.9b

Counts

68 → 5

Alt Table

Status	Error	Program
	25.8b	(.f64 x.im (neg.f64 (.f64 x.im x.im)))
▶	5.1b	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
✓	5.1b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	28.8b	(.f64 x.im (cbrt.f64 (pow.f64 (-.f64 (.f64 3 (.f64 x.re x.re)) (.f64 x.im x.im)) 3)))
	5.2b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))

Compiler

Compiled 1214 to 587 computations (51.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
✓	0.2b	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
✓	5.5b	(*.f64 (pow.f64 x.re 2) x.im)

series29.0ms (1.1%)

Counts

3 → 6

Calls

3 calls:

12.0ms	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
10.0ms	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
7.0ms	(*.f64 (pow.f64 x.re 2) x.im)

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`cancel-sign-sub-inv_binary64`

Counts

3 → 88

Calls

3 calls:

7.0ms	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
5.0ms	(.f64 3 (.f64 (pow.f64 x.re 2) x.im))
4.0ms	(*.f64 (pow.f64 x.re 2) x.im)

simplify99.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

648×	`fma-neg_binary64`
481×	`exp-prod_binary64`
468×	`*-commutative_binary64`
413×	`fma-def_binary64`
317×	`unswap-sqr_binary64`

Counts

94 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	160	1355
1	289	1222
2	1184	1137
3	2992	1109
4	4413	1106
5	4958	1106
6	4637	1106

prune126.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	120	6	126

Error

0.0b

Counts

126 → 6

Alt Table

Status	Error	Program
	5.2b	(-.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 (pow.f64 x.re 2) x.im))) (pow.f64 x.im 3))
✓	5.1b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
	28.8b	(.f64 x.im (cbrt.f64 (pow.f64 (-.f64 (.f64 3 (.f64 x.re x.re)) (.f64 x.im x.im)) 3)))
	34.7b	(-.f64 (.f64 3 (.f64 (.f64 x.re (sqrt.f64 x.im)) (.f64 x.re (sqrt.f64 x.im)))) (pow.f64 x.im 3))
	5.2b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))

Compiler

Compiled 2405 to 1614 computations (32.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
✓	0.2b	(.f64 x.re (.f64 x.re x.im))
✓	0.2b	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))

series32.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
9.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))
7.0ms	(.f64 x.re (.f64 x.re x.im))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`

Counts

3 → 81

Calls

3 calls:

10.0ms	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
5.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))
4.0ms	(.f64 x.re (.f64 x.re x.im))

simplify116.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
528×	`*-commutative_binary64`
437×	`exp-prod_binary64`
436×	`fma-def_binary64`
264×	`unswap-sqr_binary64`

Counts

153 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	1985
1	287	1839
2	1229	1753
3	3076	1740
4	4487	1739
5	4962	1739
6	4661	1739

prune105.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	107	6	113

Error

0.0b

Counts

113 → 6

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (cbrt.f64 x.re) (*.f64 x.re x.im)))) (pow.f64 x.im 3))
	0.6b	(-.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 x.re x.im))) (cbrt.f64 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.re (*.f64 x.re x.im))))) (pow.f64 x.im 3))
▶	0.1b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
	28.8b	(.f64 x.im (cbrt.f64 (pow.f64 (-.f64 (.f64 3 (.f64 x.re x.re)) (.f64 x.im x.im)) 3)))
	5.2b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))

Compiler

Compiled 2197 to 1170 computations (46.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
✓	0.2b	(.f64 (.f64 3 x.re) (*.f64 x.re x.im))

series24.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
9.0ms	(.f64 (.f64 3 x.re) (*.f64 x.re x.im))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`prod-diff_binary64`

Counts

2 → 62

Calls

2 calls:

7.0ms	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
5.0ms	(.f64 (.f64 3 x.re) (*.f64 x.re x.im))

simplify96.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-neg_binary64`
486×	`*-commutative_binary64`
474×	`fma-def_binary64`
434×	`exp-prod_binary64`
249×	`unswap-sqr_binary64`

Counts

110 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	139	1609
1	267	1508
2	1149	1429
3	3065	1419
4	4514	1418
5	4644	1418

prune63.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
	0.5b	(-.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) (.f64 (cbrt.f64 x.re) (*.f64 x.re x.im)))) (pow.f64 x.im 3))
	0.6b	(-.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 x.re x.im))) (cbrt.f64 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 x.re (*.f64 x.re x.im))))) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
	28.8b	(.f64 x.im (cbrt.f64 (pow.f64 (-.f64 (.f64 3 (.f64 x.re x.re)) (.f64 x.im x.im)) 3)))
	5.2b	(.f64 x.im (-.f64 (.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))

Compiler

Compiled 1639 to 956 computations (41.7% saved)

regimes190.0ms (7%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

63 → 1

Compiler

Compiled 3117 to 2199 computations (29.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-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	9	16
1	14	16
2	19	16
3	21	16
4	22	16
5	22	16

end86.0ms (3.2%)

Compiler: Compiled 129 to 81 computations (37.2% saved)

Details

analyze199.0ms (7.4%)

sample1.1s (42.1%)

simplify129.0ms (4.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.8%)

rewrite4.0ms (0.2%)

simplify104.0ms (3.8%)

prune52.0ms (1.9%)

localize6.0ms (0.2%)

series29.0ms (1.1%)

rewrite20.0ms (0.7%)

simplify99.0ms (3.7%)

prune126.0ms (4.7%)

localize7.0ms (0.3%)

series32.0ms (1.2%)

rewrite23.0ms (0.8%)

simplify116.0ms (4.3%)

prune105.0ms (3.9%)

localize6.0ms (0.2%)

series24.0ms (0.9%)

rewrite16.0ms (0.6%)

simplify96.0ms (3.5%)

prune63.0ms (2.3%)

regimes190.0ms (7%)

simplify3.0ms (0.1%)

end86.0ms (3.2%)

Profiling