Details

analyze88.0ms (5.3%)

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%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample766.0ms (45.6%)

Results

731.0ms	8256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

prune3.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series8.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

simplify63.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	35	371
2	66	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune17.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Error

0.0b

Counts

26 → 5

Alt Table

Status	Error	Program
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))))
	35.4b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 3))
▶	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 447 to 237 computations (47% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.2b	(.f64 3 (.f64 y y))

series9.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

7.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))
2.0ms	(.f64 3 (.f64 y y))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

4.0ms	(.f64 3 (.f64 y y))
0.0ms	(fma.f64 x x (.f64 3 (.f64 y y)))

simplify66.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-/l/_binary64`
648×	`distribute-rgt-in_binary64`
638×	`distribute-lft-in_binary64`
461×	`fma-def_binary64`
358×	`*-commutative_binary64`

Counts

67 → 45

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	53	697
1	95	638
2	217	629
3	554	629
4	1003	629
5	2324	629
6	3738	629
7	5212	629

prune36.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	40	5	45
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 y (*.f64 y (sqrt.f64 3)))))
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
	0.3b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))
	0.3b	(fma.f64 x x (.f64 (sqrt.f64 (.f64 3 (.f64 y y))) (sqrt.f64 (.f64 3 (*.f64 y y)))))
▶	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 728 to 393 computations (46% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))

series12.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 3 (*.f64 y y) (*.f64 x x))

simplify63.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

912×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
324×	`*-commutative_binary64`

Counts

34 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	32	371
2	65	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune15.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	23	6	29

Error

Counts

29 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 y (*.f64 y (sqrt.f64 3)))))
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
▶	0.3b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))
	0.3b	(fma.f64 x x (.f64 (sqrt.f64 (.f64 3 (.f64 y y))) (sqrt.f64 (.f64 3 (*.f64 y y)))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 424 to 225 computations (46.9% saved)

localize11.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y)))
✓	0.3b	(.f64 (cbrt.f64 3) (.f64 y y))

series40.0ms (2.4%)

Counts

3 → 48

Calls

3 calls:

23.0ms	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))
11.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y)))
5.0ms	(.f64 (cbrt.f64 3) (.f64 y y))

rewrite19.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 65

Calls

3 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y)))
5.0ms	(.f64 (cbrt.f64 3) (.f64 y y))
0.0ms	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))

simplify107.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
410×	`times-frac_binary64`
335×	`sqr-pow_binary64`
280×	`*-commutative_binary64`
270×	`associate-/l*_binary64`

Counts

113 → 97

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	86	1286
1	159	1095
2	475	1065
3	837	1065
4	1288	1065
5	2670	1065
6	4068	1060
7	4692	1060
8	4879	1060

prune86.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 y (*.f64 y (sqrt.f64 3)))))
	0.4b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
✓	0.3b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y y))))
	0.3b	(fma.f64 x x (.f64 (sqrt.f64 (.f64 3 (.f64 y y))) (sqrt.f64 (.f64 3 (*.f64 y y)))))
✓	0.1b	(fma.f64 3 (.f64 y y) (.f64 x x))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 1946 to 1301 computations (33.1% saved)

regimes159.0ms (9.5%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts

33 → 1

Compiler

Compiled 2557 to 1651 computations (35.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11
2	9	11

end77.0ms (4.6%)

Compiler: Compiled 103 to 68 computations (34% saved)

Details

analyze88.0ms (5.3%)

sample766.0ms (45.6%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series8.0ms (0.5%)

rewrite1.0ms (0%)

simplify63.0ms (3.8%)

prune17.0ms (1%)

localize7.0ms (0.4%)

series9.0ms (0.6%)

rewrite5.0ms (0.3%)

simplify66.0ms (3.9%)

prune36.0ms (2.2%)

localize4.0ms (0.3%)

series12.0ms (0.7%)

rewrite1.0ms (0%)

simplify63.0ms (3.8%)

prune15.0ms (0.9%)

localize11.0ms (0.6%)

series40.0ms (2.4%)

rewrite19.0ms (1.2%)

simplify107.0ms (6.4%)

prune86.0ms (5.1%)

regimes159.0ms (9.5%)

simplify2.0ms (0.1%)

end77.0ms (4.6%)

Profiling