Details

analyze1.3s (14%)

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
0%	99.9%	0.1%	5
0%	93.7%	6.3%	6
6.2%	84.3%	9.5%	7
6.2%	82.7%	11%	8
7.8%	78%	14.1%	9
10.1%	73%	16.9%	10
11.3%	70%	18.6%	11
11.7%	69.2%	19.1%	12
12.2%	67.7%	20.1%	13
12.2%	67%	20.9%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample5.6s (60.8%)

Results

4.2s	3368×	body	8192	exit
1.3s	8256×	body	128	valid
30.0ms	219×	body	128	invalid

Compiler

Compiled 43 to 23 computations (46.5% saved)

simplify130.0ms (1.4%)

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

prune4.0ms (0%)

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

6.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.2b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
▶	6.2b	(-.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)

localize13.0ms (0.1%)

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)
✓	5.8b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series46.0ms (0.5%)

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

rewrite25.0ms (0.3%)

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 x.re x.im) (*.f64 x.im x.re)) x.im)
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)
3.0ms	(+.f64 (.f64 x.re x.im) (.f64 x.im x.re))

simplify117.0ms (1.3%)

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

prune131.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Error

0.0b

Counts

144 → 9

Alt Table

Status	Error	Program
▶	0.3b	(-.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))
	6.2b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	6.8b	(.f64 (.f64 (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im))))) (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))))) (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im))))))
	6.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re)) (cbrt.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re))) (cbrt.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))
	6.2b	(fma.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re (.f64 (.f64 x.re (*.f64 x.im x.im)) -2))
	6.2b	(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)))
	17.7b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re (.f64 x.im x.im))) 3)))
	6.1b	(-.f64 (-.f64 (pow.f64 x.re 3) (.f64 x.re (pow.f64 x.im 2))) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.im))
	15.3b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re x.im)) 3)) x.im))

Compiler

Compiled 4512 to 951 computations (78.9% saved)

localize11.0ms (0.1%)

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.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))

series27.0ms (0.3%)

Counts

2 → 48

Calls

2 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))
13.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

rewrite84.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 61

Calls

2 calls:

68.0ms	(-.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))
8.0ms	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))

simplify101.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
525×	`associate-l_binary64`
507×	`associate-r_binary64`
326×	`neg-sub0_binary64`
325×	`neg-mul-1_binary64`

Counts

109 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3168
1	732	2601
2	3424	2376
3	4095	2376
4	4702	2376

prune170.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	169	9	178

Error

0.0b

Counts

178 → 9

Alt Table

Status	Error	Program
✓	0.3b	(-.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))
	6.2b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.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))
	6.8b	(.f64 (.f64 (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im))))) (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im)))))) (cbrt.f64 (.f64 x.re (-.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) (.f64 x.im (+.f64 x.im x.im))))))
	6.1b	(+.f64 (pow.f64 x.re 3) (.f64 (.f64 x.re (*.f64 x.im x.im)) -3))
▶	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	6.2b	(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)))
	17.7b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re (.f64 x.im x.im))) 3)))
	15.3b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re x.im)) 3)) x.im))

Compiler

Compiled 6245 to 1397 computations (77.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series40.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

18.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
11.0ms	(.f64 x.im (.f64 2 (*.f64 x.re x.im)))
7.0ms	(*.f64 (-.f64 x.re x.im) x.re)
5.0ms	(.f64 2 (.f64 x.re x.im))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`associate-l_binary64`

Counts

4 → 77

Calls

4 calls:

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

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
590×	`fma-neg_binary64`
401×	`*-commutative_binary64`
288×	`unswap-sqr_binary64`
263×	`associate-+l+_binary64`

Counts

149 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1941
1	284	1669
2	944	1623
3	1958	1541
4	4786	1541
5	5251	1541

prune138.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	118	8	126

Error

Counts

126 → 8

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
▶	0.3b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
	6.2b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.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))
	6.1b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))
	21.0b	(fma.f64 (+.f64 x.re x.im) (cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x.re x.im) x.re) (.f64 (-.f64 x.re x.im) x.re)) (.f64 (-.f64 x.re x.im) x.re))) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	6.2b	(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)))
	17.7b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re (.f64 x.im x.im))) 3)))

Compiler

Compiled 2917 to 1124 computations (61.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
✓	0.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
✓	0.3b	(.f64 (sqrt.f64 2) (.f64 x.re x.im))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))

series97.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

33.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
30.0ms	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
25.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
9.0ms	(.f64 (sqrt.f64 2) (.f64 x.re x.im))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
32×	`pow1_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

4 → 85

Calls

4 calls:

8.0ms	(.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x.re x.im))))
7.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
5.0ms	(.f64 (sqrt.f64 2) (.f64 x.re x.im))
0.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-neg_binary64`
541×	`fma-def_binary64`
502×	`*-commutative_binary64`
302×	`distribute-rgt-in_binary64`
284×	`associate-r_binary64`

Counts

181 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	2296
1	294	2018
2	1047	1972
3	2026	1884
4	4825	1884
5	5208	1884

prune151.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	131	7	138

Error

Counts

138 → 7

Alt Table

Status	Error	Program
	6.1b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))
	6.2b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.re (.f64 2 (.f64 x.im x.im)))))
	6.2b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	0.3b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (neg.f64 (.f64 x.im (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 x.re (*.f64 x.im (pow.f64 (sqrt.f64 2) 3/2)))))))
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re)))) (cbrt.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) (neg.f64 (.f64 x.im (.f64 2 (.f64 x.re x.im)))))
	17.7b	(-.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.re) (cbrt.f64 (pow.f64 (.f64 2 (.f64 x.re (.f64 x.im x.im))) 3)))

Compiler

Compiled 3506 to 1754 computations (50% saved)

regimes651.0ms (7.1%)

Accuracy

Total 0.2b remaining (87.8%)

Threshold costs 0.2b (87.8%)

Counts

122 → 1

Compiler

Compiled 10001 to 5307 computations (46.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	26	23
2	42	23
3	54	23
4	60	23
5	63	23
6	64	23
7	63	23

end107.0ms (1.2%)

Compiler: Compiled 190 to 102 computations (46.3% saved)

Details

analyze1.3s (14%)

sample5.6s (60.8%)

simplify130.0ms (1.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series46.0ms (0.5%)

rewrite25.0ms (0.3%)

simplify117.0ms (1.3%)

prune131.0ms (1.4%)

localize11.0ms (0.1%)

series27.0ms (0.3%)

rewrite84.0ms (0.9%)

simplify101.0ms (1.1%)

prune170.0ms (1.8%)

localize10.0ms (0.1%)

series40.0ms (0.4%)

rewrite18.0ms (0.2%)

simplify91.0ms (1%)

prune138.0ms (1.5%)

localize12.0ms (0.1%)

series97.0ms (1.1%)

rewrite26.0ms (0.3%)

simplify109.0ms (1.2%)

prune151.0ms (1.6%)

regimes651.0ms (7.1%)

simplify4.0ms (0%)

end107.0ms (1.2%)

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