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)

sample848.0ms (29.9%)

Infinites

44.7% of outputs are infinite.

Results

741.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify129.0ms (4.5%)

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

4.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	9.8b	(-.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)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x.im x.im) -3)
✓	0.5b	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
✓	3.5b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))

series29.0ms (1%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
8.0ms	(fma.f64 x.re x.re (.f64 (.f64 x.im x.im) -3))
2.0ms	(.f64 (.f64 x.im x.im) -3)

rewrite11.0ms (0.4%)

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:

6.0ms	(.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))

simplify52.0ms (1.8%)

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

prune64.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Error

3.5b

Counts

95 → 4

Alt Table

Status	Error	Program
✓	4.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
▶	9.8b	(-.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))
	25.7b	(pow.f64 x.re 3)
	10.8b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))

Compiler

Compiled 1513 to 734 computations (51.5% saved)

localize10.0ms (0.4%)

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)
✓	2.7b	(-.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))
✓	3.7b	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))
✓	3.8b	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series46.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

14.0ms	(.f64 (-.f64 (.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
13.0ms	(-.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.im) (*.f64 x.im x.re)) x.im)
7.0ms	(-.f64 (.f64 x.re x.re) (.f64 x.im x.im))

rewrite24.0ms (0.9%)

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:

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

simplify90.0ms (3.2%)

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	2905
1	453	2632
2	1764	2513
3	3592	2504
4	4795	2504

prune104.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
✓	4.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
▶	3.1b	(-.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))
✓	9.8b	(-.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))
	25.7b	(pow.f64 x.re 3)
	10.8b	(fma.f64 -3 (.f64 x.re (.f64 x.im x.im)) (pow.f64 x.re 3))

Compiler

Compiled 4231 to 804 computations (81% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x.re x.im) x.re)
✓	0.1b	(.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re))
	0.1b	(.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
✓	2.7b	(-.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))

series38.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

19.0ms

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

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))

5.0ms

(*.f64 (-.f64 x.re x.im) x.re)

rewrite41.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

10.0ms

(-.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))

5.0ms

(*.f64 (-.f64 x.re x.im) x.re)

simplify126.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
595×	`associate-l_binary64`
550×	`associate-r_binary64`
324×	`cancel-sign-sub-inv_binary64`
307×	`distribute-rgt-in_binary64`

Counts

157 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3654
1	775	2962
2	3646	2738
3	4358	2738
4	4695	2738

prune211.0ms (7.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	186	6	192

Error

Counts

192 → 6

Alt Table

Status	Error	Program
	25.7b	(pow.f64 x.re 3)
	3.4b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 x.re (cbrt.f64 (-.f64 x.re x.im))))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
▶	3.1b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
✓	4.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	3.5b	(.f64 (.f64 (cbrt.f64 (-.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))) (cbrt.f64 (-.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)))) (cbrt.f64 (-.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))))
	3.4b	(-.f64 (.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re))) (.f64 (+.f64 (.f64 x.re x.im) (*.f64 x.im x.re)) x.im))

Compiler

Compiled 6529 to 1346 computations (79.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x.re x.im) -2)
	0.0b	(*.f64 (-.f64 x.re x.im) x.re)
✓	0.1b	(.f64 x.im (.f64 (*.f64 x.re x.im) -2))
✓	2.7b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))

series42.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
13.0ms	(.f64 x.im (.f64 (*.f64 x.re x.im) -2))
5.0ms	(.f64 (.f64 x.re x.im) -2)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 53

Calls

3 calls:

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

simplify90.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-neg_binary64`
443×	`unswap-sqr_binary64`
385×	`*-commutative_binary64`
248×	`fma-def_binary64`
216×	`distribute-rgt-in_binary64`

Counts

125 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1604
1	204	1449
2	711	1403
3	1297	1381
4	2577	1381
5	4732	1381
6	5201	1381

prune149.0ms (5.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Error

Counts

129 → 6

Alt Table

Status	Error	Program
✓	3.1b	(fma.f64 (+.f64 x.re x.im) (.f64 (-.f64 x.re x.im) x.re) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
✓	4.1b	(.f64 x.re (fma.f64 x.re x.re (.f64 (*.f64 x.im x.im) -3)))
	3.3b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	3.3b	(fma.f64 (+.f64 x.re x.im) (.f64 (.f64 (-.f64 x.re x.im) (.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (.f64 x.im (.f64 (.f64 x.re x.im) -2)))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 x.re (fma.f64 (.f64 x.im x.im) -2 (.f64 (+.f64 x.re x.im) (-.f64 x.re x.im))))) (cbrt.f64 (.f64 x.re (fma.f64 (.f64 x.im x.im) -2 (.f64 (+.f64 x.re x.im) (-.f64 x.re x.im)))))) (cbrt.f64 (.f64 x.re (fma.f64 (.f64 x.im x.im) -2 (*.f64 (+.f64 x.re x.im) (-.f64 x.re x.im))))))
	25.7b	(pow.f64 x.re 3)

Compiler

Compiled 2754 to 933 computations (66.1% saved)

regimes550.0ms (19.4%)

Accuracy

Total 1.9b remaining (99.1%)

Threshold costs 0b (0%)

Counts

111 → 3

Compiler

Compiled 8187 to 4245 computations (48.1% saved)

bsearch27.0ms (0.9%)

Steps

Iters	Range		Point
1	6.683892221046906e+46	6.425934896900342e+47	2.0298236451026524e+47
2	-128084.29530163761	-69.54409892658597	-20274.627700358556

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	29	70
1	42	70
2	47	70
3	49	70
4	50	70
5	50	70

end103.0ms (3.6%)

Compiler: Compiled 238 to 123 computations (48.3% saved)

Details

analyze1.0ms (0%)

sample848.0ms (29.9%)

simplify129.0ms (4.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series29.0ms (1%)

rewrite11.0ms (0.4%)

simplify52.0ms (1.8%)

prune64.0ms (2.2%)

localize10.0ms (0.4%)

series46.0ms (1.6%)

rewrite24.0ms (0.9%)

simplify90.0ms (3.2%)

prune104.0ms (3.7%)

localize14.0ms (0.5%)

series38.0ms (1.3%)

rewrite41.0ms (1.4%)

simplify126.0ms (4.4%)

prune211.0ms (7.4%)

localize9.0ms (0.3%)

series42.0ms (1.5%)

rewrite12.0ms (0.4%)

simplify90.0ms (3.2%)

prune149.0ms (5.2%)

regimes550.0ms (19.4%)

bsearch27.0ms (0.9%)

simplify4.0ms (0.1%)

end103.0ms (3.6%)

Profiling