Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample1.0s (41.1%)

Symmetry

(sort x y)

Results

971.0ms

8256×

body

128

valid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify15.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

33×	`fma-def_binary64`
8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	14
2	45	12
3	68	12
4	70	12
5	70	12

prune9.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

Compiler

Compiled 46 to 24 computations (47.8% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

series11.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

rewrite1.0ms (0.1%)

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:

1.0ms

(fma.f64 x (fma.f64 2 y x) (*.f64 y y))

simplify72.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-+l+_binary64`
820×	`associate-+r+_binary64`
311×	`distribute-lft-in_binary64`
310×	`distribute-rgt-in_binary64`
296×	`distribute-rgt-out_binary64`

Counts

34 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	473
1	48	376
2	92	373
3	310	367
4	1673	367
5	5874	367

prune35.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	2	29

Error

Counts

29 → 2

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
▶	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Status

Error

Program

0.7b

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

▶

0.0b

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 434 to 204 computations (53% saved)

localize16.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

series12.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

rewrite1.0ms (0.1%)

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:

1.0ms

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

simplify76.0ms (3%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-+l+_binary64`
820×	`associate-+r+_binary64`
313×	`distribute-lft-in_binary64`
313×	`distribute-rgt-in_binary64`
298×	`distribute-rgt-out_binary64`

Counts

34 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	473
1	49	373
2	98	367
3	316	367
4	1706	367
5	5952	367

prune43.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Error

Counts

30 → 2

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Status

Error

Program

▶

0.7b

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

✓

0.0b

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 423 to 198 computations (53.2% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (fma.f64 2 y x) (*.f64 y y))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
✓	28.4b	(cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))

series118.0ms (4.7%)

Counts

3 → 72

Calls

3 calls:

54.0ms

(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

51.0ms

(cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))

12.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

rewrite55.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

25.0ms

(*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

15.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

1.0ms

(cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))

simplify169.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

557×	`unswap-sqr_binary64`
485×	`fma-neg_binary64`
355×	`fma-def_binary64`
307×	`*-commutative_binary64`
246×	`cancel-sign-sub-inv_binary64`

Counts

165 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	4187
1	401	3774
2	1131	3388
3	2688	3294
4	4844	3294
5	5099	3294

prune445.0ms (17.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	336	2	338

Error

Counts

338 → 2

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))
✓	0.0b	(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Status

Error

Program

✓

0.7b

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y)))) (cbrt.f64 (fma.f64 x (fma.f64 2 y x) (*.f64 y y))))

✓

0.0b

(fma.f64 y (fma.f64 2 x y) (*.f64 x x))

Compiler

Compiled 12502 to 6223 computations (50.2% saved)

regimes66.0ms (2.6%)

Accuracy

Total 0.0b remaining (74.3%)

Threshold costs 0.0b (74.3%)

Counts

19 → 1

Compiler

Compiled 954 to 551 computations (42.2% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	7	12

end311.0ms (12.3%)

Compiler: Compiled 89 to 47 computations (47.2% saved)

Details

analyze3.0ms (0.1%)

sample1.0s (41.1%)

simplify15.0ms (0.6%)

prune9.0ms (0.4%)

localize11.0ms (0.4%)

series11.0ms (0.5%)

rewrite1.0ms (0.1%)

simplify72.0ms (2.8%)

prune35.0ms (1.4%)

localize16.0ms (0.6%)

series12.0ms (0.5%)

rewrite1.0ms (0.1%)

simplify76.0ms (3%)

prune43.0ms (1.7%)

localize14.0ms (0.6%)

series118.0ms (4.7%)

rewrite55.0ms (2.2%)

simplify169.0ms (6.7%)

prune445.0ms (17.6%)

regimes66.0ms (2.6%)

simplify4.0ms (0.2%)

end311.0ms (12.3%)

Profiling