Details

analyze204.0ms (7.5%)

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%	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 (41.7%)

Results

968.0ms	8256×	body	128	valid
71.0ms	587×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify128.0ms (4.7%)

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

8.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.7b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	8.7b	(+.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)))
✓	8.1b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))

series23.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.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)))

simplify106.0ms (3.9%)

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

prune53.0ms (2%)

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

8.3b

Counts

68 → 5

Alt Table

Status	Error	Program
✓	8.7b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	31.9b	(.f64 (.f64 x.im (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))))
	9.3b	(.f64 (.f64 (cbrt.f64 (.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im))))) (cbrt.f64 (.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))))) (cbrt.f64 (.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
	27.1b	(.f64 x.im (neg.f64 (.f64 x.im x.im)))
▶	8.6b	(-.f64 (.f64 3 (.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))

Compiler

Compiled 1286 to 615 computations (52.2% saved)

localize8.0ms (0.3%)

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))
✓	9.0b	(*.f64 (pow.f64 x.re 2) x.im)

series33.0ms (1.2%)

Counts

3 → 6

Calls

3 calls:

15.0ms	(-.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))
8.0ms	(*.f64 (pow.f64 x.re 2) x.im)

rewrite21.0ms (0.8%)

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

simplify101.0ms (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

prune121.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
✓	8.7b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	8.6b	(fma.f64 3 (*.f64 (pow.f64 x.re 2) x.im) (neg.f64 (pow.f64 x.im 3)))
	33.1b	(-.f64 (.f64 3 (.f64 (pow.f64 (sqrt.f64 x.re) 2) (*.f64 x.im x.re))) (pow.f64 x.im 3))
	2.8b	(-.f64 (.f64 3 (.f64 (pow.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)) 2) (.f64 (pow.f64 (cbrt.f64 x.re) 2) x.im))) (pow.f64 x.im 3))
	31.9b	(.f64 (.f64 x.im (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (.f64 x.re 3) (neg.f64 (.f64 x.im x.im)))))
	34.4b	(-.f64 (.f64 3 (.f64 (.f64 x.re (sqrt.f64 x.im)) (.f64 x.re (sqrt.f64 x.im)))) (pow.f64 x.im 3))
	36.4b	(-.f64 (.f64 3 (.f64 (.f64 x.re (.f64 x.re (sqrt.f64 x.im))) (sqrt.f64 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))

Compiler

Compiled 2493 to 1662 computations (33.3% 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))
✓	0.1b	(.f64 x.re (.f64 x.re x.im))
✓	0.2b	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))

series33.0ms (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))
10.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))
8.0ms	(.f64 x.re (.f64 x.re x.im))

rewrite20.0ms (0.7%)

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:

7.0ms	(-.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))

simplify126.0ms (4.6%)

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

prune106.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	6	0	6
Picked	1	0	1
Done	0	1	1
Total	109	6	115

Error

Counts

115 → 6

Alt Table

Status	Error	Program
✓	8.7b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	0.1b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 x.re (.f64 x.re x.im)))) (pow.f64 x.im 3))
	0.2b	(fma.f64 3 (.f64 x.re (.f64 x.re x.im)) (neg.f64 (pow.f64 x.im 3)))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 3 (.f64 x.re (.f64 x.re x.im))))) (cbrt.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))))) (pow.f64 x.im 3))
	0.6b	(-.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))

Compiler

Compiled 2207 to 1183 computations (46.4% saved)

localize7.0ms (0.3%)

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))

series25.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
10.0ms	(.f64 (.f64 3 x.re) (*.f64 x.re x.im))

rewrite19.0ms (0.7%)

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:

11.0ms	(-.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))

simplify88.0ms (3.2%)

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

prune71.0ms (2.6%)

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

Counts

83 → 6

Alt Table

Status	Error	Program
✓	8.7b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
✓	0.1b	(-.f64 (.f64 (.f64 3 x.re) (*.f64 x.re x.im)) (pow.f64 x.im 3))
	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (.f64 x.re (.f64 x.re x.im)))) (pow.f64 x.im 3))
	0.2b	(fma.f64 3 (.f64 x.re (.f64 x.re x.im)) (neg.f64 (pow.f64 x.im 3)))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 x.re (.f64 x.re x.im)))) (cbrt.f64 (.f64 3 (.f64 x.re (.f64 x.re x.im))))) (cbrt.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))))) (pow.f64 x.im 3))
	0.6b	(-.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))

Compiler

Compiled 1644 to 962 computations (41.5% saved)

regimes174.0ms (6.4%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

63 → 1

Compiler

Compiled 3168 to 2166 computations (31.6% saved)

simplify2.0ms (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

end95.0ms (3.5%)

Compiler: Compiled 134 to 87 computations (35.1% saved)

Details

analyze204.0ms (7.5%)

sample1.1s (41.7%)

simplify128.0ms (4.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series23.0ms (0.9%)

rewrite4.0ms (0.2%)

simplify106.0ms (3.9%)

prune53.0ms (2%)

localize8.0ms (0.3%)

series33.0ms (1.2%)

rewrite21.0ms (0.8%)

simplify101.0ms (3.7%)

prune121.0ms (4.4%)

localize7.0ms (0.3%)

series33.0ms (1.2%)

rewrite20.0ms (0.7%)

simplify126.0ms (4.6%)

prune106.0ms (3.9%)

localize7.0ms (0.3%)

series25.0ms (0.9%)

rewrite19.0ms (0.7%)

simplify88.0ms (3.2%)

prune71.0ms (2.6%)

regimes174.0ms (6.4%)

simplify2.0ms (0.1%)

end95.0ms (3.5%)

Profiling