Details

analyze212.0ms (5.4%)

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)

sample1.2s (30.3%)

Results

1.0s	8256×	body	128	valid
71.0ms	616×	body	128	invalid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify130.0ms (3.3%)

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

11.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.5b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
▶	11.4b	(+.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)

localize11.0ms (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.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
✓	0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
✓	10.7b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series44.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

16.0ms	(+.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))
13.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
10.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
5.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

rewrite26.0ms (0.7%)

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 → 77

Calls

4 calls:

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

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

727×	`distribute-rgt-in_binary64`
685×	`distribute-lft-in_binary64`
245×	`associate-l_binary64`
206×	`associate-r_binary64`
181×	`distribute-rgt-out_binary64`

Counts

173 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2758
1	427	2398
2	1675	2360
3	4822	2360

prune131.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Error

0.1b

Counts

141 → 7

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	11.5b	(.f64 x.im (fma.f64 x.re (.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
	24.3b	(+.f64 (neg.f64 (pow.f64 x.im 3)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	11.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im))) (cbrt.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) (.f64 (cbrt.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))
	11.8b	(+.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	11.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im)) (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im))) (cbrt.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))
✓	11.4b	(+.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 4342 to 946 computations (78.2% saved)

localize11.0ms (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 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	0.2b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
✓	0.2b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))

series27.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

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

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`associate-*l/_binary64`
18×	`flip-+_binary64`
18×	`flip3-+_binary64`
16×	`frac-add_binary64`
12×	`frac-times_binary64`

Counts

2 → 59

Calls

2 calls:

10.0ms	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
10.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))

simplify105.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

535×	`associate-l_binary64`
483×	`associate-r_binary64`
427×	`fma-neg_binary64`
304×	`distribute-rgt-out_binary64`
299×	`distribute-rgt-in_binary64`

Counts

107 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	3975
1	667	3223
2	3176	2270
3	4304	2268
4	4675	2268

prune167.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	4	1	5
Picked	1	0	1
Done	1	0	1
Total	165	8	173

Error

0.0b

Counts

173 → 8

Alt Table

Status	Error	Program
	11.8b	(+.f64 (.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
	11.4b	(-.f64 (.f64 3 (.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
	11.4b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 2 (.f64 x.im (*.f64 x.re x.re))))
	0.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
	0.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (.f64 (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re)))) (cbrt.f64 (.f64 x.re (.f64 2 (.f64 x.im x.re))))) (cbrt.f64 (.f64 x.re (.f64 2 (*.f64 x.im x.re))))))
	9.5b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (*.f64 x.im x.re)) 3)) x.re))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 6119 to 1378 computations (77.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
6.0ms	(*.f64 (-.f64 x.re x.im) x.im)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
5×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 34

Calls

2 calls:

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

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
381×	`*-commutative_binary64`
379×	`exp-prod_binary64`
293×	`fma-neg_binary64`
252×	`associate-l_binary64`

Counts

82 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1147
1	144	995
2	409	995
3	1394	925
4	3300	925
5	4985	925
6	4958	925

prune128.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Error

0.0b

Counts

136 → 7

Alt Table

Status	Error	Program
	11.4b	(-.f64 (.f64 3 (.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	11.4b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 2 (.f64 x.im (.f64 x.re x.re))))
▶	0.6b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
	0.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im)) (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 3333 to 773 computations (76.8% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))
✓	0.2b	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
✓	0.5b	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
✓	0.6b	(cbrt.f64 x.re)

series461.0ms (11.8%)

Counts

3 → 48

Calls

3 calls:

382.0ms	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
42.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
37.0ms	(cbrt.f64 x.re)

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
18×	`add-cbrt-cube_binary64`

Counts

3 → 85

Calls

3 calls:

8.0ms	(.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
4.0ms	(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
1.0ms	(cbrt.f64 x.re)

simplify115.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
540×	`*-commutative_binary64`
347×	`sqr-pow_binary64`
311×	`log-prod_binary64`
280×	`exp-prod_binary64`

Counts

133 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1633
1	255	1319
2	1003	1194
3	1808	1180
4	3003	1088
5	4591	1088
6	4978	1088
7	4879	1088

prune189.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	199	7	206

Error

0.0b

Counts

206 → 7

Alt Table

Status	Error	Program
	11.4b	(-.f64 (.f64 3 (.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
	0.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	0.7b	(+.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)) (.f64 (.f64 (.f64 2 (.f64 x.im x.re)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))) (cbrt.f64 (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))))) (cbrt.f64 x.re)))
	0.6b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im)) (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (-.f64 x.re x.im) x.im))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))
	11.4b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 2 (.f64 x.im (.f64 x.re x.re))))
	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im)))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 6102 to 1810 computations (70.3% saved)

regimes594.0ms (15.1%)

Accuracy

Total 0.2b remaining (87.5%)

Threshold costs 0.2b (87.5%)

Counts

184 → 1

Compiler

Compiled 15183 to 7803 computations (48.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	10	24
1	16	24
2	21	24
3	23	24
4	24	24
5	24	24

end106.0ms (2.7%)

Compiler: Compiled 236 to 104 computations (55.9% saved)

Details

analyze212.0ms (5.4%)

sample1.2s (30.3%)

simplify130.0ms (3.3%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

series44.0ms (1.1%)

rewrite26.0ms (0.7%)

simplify72.0ms (1.8%)

prune131.0ms (3.3%)

localize11.0ms (0.3%)

series27.0ms (0.7%)

rewrite29.0ms (0.7%)

simplify105.0ms (2.7%)

prune167.0ms (4.2%)

localize12.0ms (0.3%)

series25.0ms (0.6%)

rewrite6.0ms (0.2%)

simplify92.0ms (2.3%)

prune128.0ms (3.3%)

localize18.0ms (0.5%)

series461.0ms (11.8%)

rewrite19.0ms (0.5%)

simplify115.0ms (2.9%)

prune189.0ms (4.8%)

regimes594.0ms (15.1%)

simplify3.0ms (0.1%)

end106.0ms (2.7%)

Profiling