Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample843.0ms (23.3%)

Results

742.0ms

8256×

body

128

valid

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

7.0b

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)))
	10.0b	(-.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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x.im x.im) -3)
✓	2.0b	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
✓	5.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))

series29.0ms (0.8%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
9.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
2.0ms	(.f64 (.f64 x.im x.im) -3)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 53

Calls

3 calls:

5.0ms	(.f64 (.f64 x.im x.im) -3)
3.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
0.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

652×	`distribute-rgt-in_binary64`
645×	`distribute-lft-in_binary64`
429×	`fma-def_binary64`
175×	`*-commutative_binary64`
160×	`associate-+l+_binary64`

Counts

113 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1459
1	181	1302
2	525	1293
3	1135	1293
4	4953	1293

prune84.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	90	5	95

Error

4.9b

Counts

95 → 5

Alt Table

Status	Error	Program
	16.3b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (pow.f64 x.im 6) -27))))
	29.4b	(pow.f64 x.re 3)
	10.0b	(-.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))
	7.3b	(.f64 (.f64 x.re (.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3))))
▶	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))

Compiler

Compiled 1607 to 793 computations (50.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3)))
✓	0.2b	(.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))
✓	2.0b	(fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3)))
✓	5.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))

series232.0ms (6.4%)

Counts

4 → 72

Calls

4 calls:

78.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
68.0ms	(fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3)))
44.0ms	(.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))
41.0ms	(.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3)))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64`
36×	`add-exp-log_binary64`
28×	`pow-prod-down_binary64`
23×	`add-cbrt-cube_binary64`
22×	`cbrt-unprod_binary64`

Counts

4 → 95

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))
8.0ms	(.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3)))
3.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
0.0ms	(fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3)))

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

658×	`distribute-rgt-in_binary64`
540×	`unswap-sqr_binary64`
515×	`fma-def_binary64`
411×	`*-commutative_binary64`
242×	`associate-l_binary64`

Counts

167 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	2245
1	255	1919
2	946	1876
3	1929	1874
4	5503	1874

prune140.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

4.9b

Counts

145 → 5

Alt Table

Status	Error	Program
	16.3b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (pow.f64 x.im 6) -27))))
	29.4b	(pow.f64 x.re 3)
	10.0b	(-.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))
▶	7.3b	(.f64 (.f64 x.re (.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3))))
✓	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))

Compiler

Compiled 3150 to 1988 computations (36.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3))))
	2.0b	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
✓	6.0b	(.f64 x.re (.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))))
✓	30.1b	(cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3)))

series157.0ms (4.3%)

Counts

3 → 72

Calls

3 calls:

71.0ms

(*.f64 x.re (*.f64 (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))

46.0ms

(*.f64 (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))))

40.0ms

(cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
15×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 76

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))))

6.0ms

(*.f64 x.re (*.f64 (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))

1.0ms

(cbrt.f64 (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))

simplify146.0ms (4%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
790×	`times-frac_binary64`
260×	`associate-r_binary64`
185×	`fma-neg_binary64`
178×	`associate-l_binary64`

Counts

148 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	5590
1	919	5281
2	2971	4782
3	4978	4782
4	4957	4782

prune440.0ms (12.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	391	5	396

Error

4.9b

Counts

396 → 5

Alt Table

Status	Error	Program
	16.3b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (pow.f64 x.im 6) -27))))
	29.4b	(pow.f64 x.re 3)
▶	10.0b	(-.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))
✓	7.3b	(.f64 (.f64 x.re (.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3))))
✓	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))

Compiler

Compiled 17103 to 10186 computations (40.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	2.8b	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))
✓	3.4b	(-.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))
✓	5.0b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series46.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

16.0ms	(-.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))
12.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
11.0ms	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
7.0ms	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))

rewrite28.0ms (0.8%)

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 → 82

Calls

4 calls:

9.0ms	(-.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))
6.0ms	(.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.re) (.f64 x.im x.im))

simplify97.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

343×	`unswap-sqr_binary64`
222×	`associate-l_binary64`
210×	`distribute-rgt-out_binary64`
207×	`fma-neg_binary64`
202×	`cancel-sign-sub-inv_binary64`

Counts

178 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3003
1	452	2674
2	1764	2513
3	3592	2504
4	4795	2504

prune143.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	146	5	151

Error

0.0b

Counts

151 → 5

Alt Table

Status	Error	Program
	16.3b	(.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (.f64 (pow.f64 x.im 6) -27))))
	29.4b	(pow.f64 x.re 3)
✓	7.0b	(.f64 x.re (fma.f64 x.re x.re (.f64 (.f64 (.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
	3.8b	(-.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))
✓	7.3b	(.f64 (.f64 x.re (.f64 (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))))) (cbrt.f64 (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3))))

Compiler

Compiled 4213 to 796 computations (81.1% saved)

regimes725.0ms (20%)

Accuracy

Total 2.2b remaining (97.7%)

Threshold costs 0b (0%)

Counts

132 → 3

Compiler

Compiled 8338 to 4997 computations (40.1% saved)

bsearch34.0ms (0.9%)

Steps

Iters	Range		Point
7	2.947827716034381e+194	4.150526837819337e+196	3.1664951455267414e+196
9	-2.9520782217183094e+163	-2.8173716230720835e+155	-2.6528090666816572e+163

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	35	46
2	49	46
3	63	46
4	70	46
5	73	46
6	74	46
7	74	46

end101.0ms (2.8%)

Compiler: Compiled 157 to 94 computations (40.1% saved)

Details

analyze1.0ms (0%)

sample843.0ms (23.3%)

simplify127.0ms (3.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series29.0ms (0.8%)

rewrite10.0ms (0.3%)

simplify57.0ms (1.6%)

prune84.0ms (2.3%)

localize9.0ms (0.3%)

series232.0ms (6.4%)

rewrite35.0ms (1%)

simplify79.0ms (2.2%)

prune140.0ms (3.9%)

localize10.0ms (0.3%)

series157.0ms (4.3%)

rewrite21.0ms (0.6%)

simplify146.0ms (4%)

prune440.0ms (12.2%)

localize13.0ms (0.3%)

series46.0ms (1.3%)

rewrite28.0ms (0.8%)

simplify97.0ms (2.7%)

prune143.0ms (3.9%)

regimes725.0ms (20%)

bsearch34.0ms (0.9%)

simplify5.0ms (0.1%)

end101.0ms (2.8%)

Profiling