Details

analyze180.0ms (7.2%)

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%	62.4%	12.6%	6
31.2%	50%	18.8%	7
40.6%	37.5%	22%	8
45.3%	26.5%	28.2%	9
46.8%	19.5%	33.7%	10
48.8%	14%	37.2%	11
51.7%	10.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	5.1%	41.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.0s (40.6%)

Results

944.0ms	8256×	body	128	valid
51.0ms	452×	body	128	invalid

Compiler

Compiled 44 to 24 computations (45.5% saved)

preprocess39.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

375×	`fma-neg_binary64`
355×	`unsub-neg_binary64`
328×	`distribute-rgt-in_binary64`
325×	`distribute-neg-in_binary64`
293×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	58	50
2	140	46
3	427	32
4	1255	32
5	3995	32
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 11 computations (47.6% saved)

simplify21.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-neg_binary64`
507×	`fma-def_binary64`
396×	`cancel-sign-sub-inv_binary64`
243×	`associate--l+_binary64`
211×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	31	25
2	78	23
3	241	16
4	745	14
5	2583	14

Stop Event

1×	node limit

Counts

1 → 2

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

5.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.9b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	5.9b	(-.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 55 computations (43.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x.im (.f64 x.im -3))
✓	5.5b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))

series17.0ms (0.7%)

Counts

2 → 36

Calls

9 calls:

5.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))	x.im	inf
2.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))	x.re	0
2.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))	x.re	-inf
2.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))	x.re	inf
2.0ms	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))	x.im	-inf

rewrite39.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`pow1_binary64`
747×	`log1p-expm1-u_binary64`
747×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	189	21
2	2068	21

Stop Event

1×	node limit

Counts

2 → 39

simplify43.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

984×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
342×	`fma-neg_binary64`
255×	`distribute-rgt-neg-in_binary64`
232×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	414
1	37	414
2	92	378
3	251	378
4	757	378
5	1495	378
6	2222	378
7	3499	378

Stop Event

1×	node limit

Counts

75 → 46

prune39.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Error

0.0b

Counts

48 → 4

Alt Table

Status	Error	Program
✓	5.9b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	5.9b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	24.1b	(.f64 (.f64 x.im x.im) (*.f64 -3 x.re))

Compiler

Compiled 741 to 454 computations (38.7% saved)

localize12.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
✓	0.2b	(.f64 x.im (.f64 -3 x.re))

series15.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))	x.im	0
2.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))	x.im	-inf
2.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))	x.im	inf
2.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))	x.re	0
1.0ms	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))	x.re	inf

rewrite44.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`pow1_binary64`
761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	190	21
2	2099	21

Stop Event

1×	node limit

Counts

2 → 38

simplify46.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

989×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
342×	`fma-neg_binary64`
322×	`cancel-sign-sub-inv_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	498
1	40	498
2	96	462
3	248	462
4	723	462
5	1466	462
6	2182	462
7	3412	462

Stop Event

1×	node limit

Counts

86 → 45

prune38.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	42	7	49

Error

0.0b

Counts

49 → 7

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))
✓	5.9b	(fma.f64 x.re (.f64 x.im (.f64 x.im -3)) (pow.f64 x.re 3))
	5.9b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	24.1b	(.f64 (.f64 x.im x.im) (*.f64 -3 x.re))
	22.5b	(pow.f64 (sqrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)

Compiler

Compiled 804 to 533 computations (33.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))
✓	0.2b	(.f64 -3 (.f64 x.re x.im))

series22.0ms (0.9%)

Counts

2 → 24

Calls

12 calls:

8.0ms	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))	x.re	-inf
2.0ms	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))	x.im	0
2.0ms	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))	x.im	inf
2.0ms	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))	x.im	-inf
1.0ms	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))	x.re	inf

rewrite47.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

820×	`pow1_binary64`
761×	`log1p-expm1-u_binary64`
761×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	190	21
2	2100	21

Stop Event

1×	node limit

Counts

2 → 36

simplify41.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
593×	`unswap-sqr_binary64`
340×	`fma-neg_binary64`
336×	`cancel-sign-sub-inv_binary64`
254×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	330
1	35	330
2	88	294
3	245	294
4	709	294
5	1449	294
6	2170	294
7	3404	294

Stop Event

1×	node limit

Counts

60 → 41

prune34.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	42	6	48

Error

0.0b

Counts

48 → 6

Alt Table

Status	Error	Program
	5.9b	(.f64 x.re (fma.f64 (.f64 x.im x.im) -3 (*.f64 x.re x.re)))
▶	0.9b	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)
✓	0.1b	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))
	5.9b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	22.5b	(pow.f64 (sqrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 2)

Compiler

Compiled 736 to 450 computations (38.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	0.2b	(.f64 x.im (.f64 -3 x.re))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)
✓	14.6b	(cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3)))

series386.0ms (15.5%)

Counts

2 → 24

Calls

12 calls:

276.0ms	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)	x.re	-inf
32.0ms	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)	x.im	0
32.0ms	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)	x.re	inf
24.0ms	(cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3)))	x.re	-inf
4.0ms	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)	x.im	-inf

rewrite50.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`log1p-expm1-u_binary64`
842×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`pow1_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	234	30
2	2379	30

Stop Event

1×	node limit

Counts

2 → 49

simplify32.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

652×	`cancel-sign-sub-inv_binary64`
593×	`fma-neg_binary64`
565×	`associate-/l/_binary64`
540×	`fma-def_binary64`
209×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	426
1	151	426
2	456	408
3	2154	400

Stop Event

1×	node limit

Counts

73 → 67

prune95.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	112	6	118

Error

0.0b

Counts

118 → 6

Alt Table

Status	Error	Program
	5.9b	(.f64 x.re (fma.f64 (.f64 x.im x.im) -3 (*.f64 x.re x.re)))
✓	0.9b	(pow.f64 (cbrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 3)
✓	0.1b	(fma.f64 x.im (.f64 -3 (.f64 x.re x.im)) (pow.f64 x.re 3))
	5.9b	(-.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	(fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))
	22.5b	(pow.f64 (sqrt.f64 (fma.f64 x.im (.f64 x.im (.f64 -3 x.re)) (pow.f64 x.re 3))) 2)

Compiler

Compiled 2190 to 1570 computations (28.3% saved)

regimes121.0ms (4.9%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Counts

42 → 1

Compiler

Compiled 1662 to 1164 computations (30% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end92.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 111 to 72 computations (35.1% saved)

Details

analyze180.0ms (7.2%)

sample1.0s (40.6%)

preprocess39.0ms (1.6%)

simplify21.0ms (0.8%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series17.0ms (0.7%)

rewrite39.0ms (1.6%)

simplify43.0ms (1.7%)

prune39.0ms (1.6%)

localize12.0ms (0.5%)

series15.0ms (0.6%)

rewrite44.0ms (1.8%)

simplify46.0ms (1.8%)

prune38.0ms (1.5%)

localize6.0ms (0.3%)

series22.0ms (0.9%)

rewrite47.0ms (1.9%)

simplify41.0ms (1.7%)

prune34.0ms (1.4%)

localize8.0ms (0.3%)

series386.0ms (15.5%)

rewrite50.0ms (2%)

simplify32.0ms (1.3%)

prune95.0ms (3.8%)

regimes121.0ms (4.9%)

simplify2.0ms (0.1%)

end92.0ms (3.7%)

Profiling