Details

analyze47.0ms (1.2%)

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
50%	50%	0.1%	4
50%	50%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
87.4%	12.5%	0.1%	8
87.4%	12.5%	0.1%	9
93.7%	6.2%	0.1%	10
93.7%	6.2%	0.1%	11
96.8%	3.1%	0.1%	12
96.8%	3.1%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample60.0ms (1.5%)

Algorithm

1×

intervals

Results

7.0ms	245×	body	128	valid
1.0ms	6×	body	1024	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

254×	`fma-neg_binary64`
112×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
48×	`sub-neg_binary64`
40×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

prune3.0ms (0.1%)

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 (-.f64 x y) 1/2 x)

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(fma.f64 (-.f64 x y) 1/2 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 (-.f64 x y) 1/2 x)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

854×	`distribute-neg-out_binary64`
765×	`unsub-neg_binary64`
531×	`fma-def_binary64`
337×	`associate-l_binary64`
272×	`associate-r_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	331
1	35	278
2	68	278
3	169	278
4	658	278
5	2504	278
6	5244	278

prune34.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	3	23

Error

0.0b

Counts

23 → 3

Alt Table

Status	Error	Program
	34.6b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 313 to 185 computations (40.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

series61.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

28.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

27.0ms

(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

rewrite18.0ms (0.5%)

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:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

1.0ms

(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

simplify108.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
497×	`cancel-sign-sub-inv_binary64`
224×	`sub-neg_binary64`
213×	`unswap-sqr_binary64`
203×	`associate-r_binary64`

Counts

165 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	4501
1	895	4176
2	2910	3743
3	5249	3743

prune393.0ms (9.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	439	3	442
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	440	5	445

Error

0.0b

Counts

445 → 5

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.7b	(.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
	34.6b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 15821 to 9799 computations (38.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
	0.5b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))

series62.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

37.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))

25.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
6×	`associate-l_binary64`
6×	`add-cube-cbrt_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 39

Calls

2 calls:

6.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
495×	`cancel-sign-sub-inv_binary64`
222×	`sub-neg_binary64`
188×	`unswap-sqr_binary64`
168×	`associate-r_binary64`

Counts

87 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	3367
1	849	3203
2	2738	2950
3	4983	2950

prune653.0ms (16.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	627	0	627
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	627	5	632

Error

0.0b

Counts

632 → 5

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.7b	(.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
	34.6b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 33652 to 20518 computations (39% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
	0.5b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

series53.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
24.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

8.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

simplify129.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary64`
493×	`cancel-sign-sub-inv_binary64`
228×	`sub-neg_binary64`
208×	`associate-r_binary64`
183×	`unswap-sqr_binary64`

Counts

120 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	4786
1	924	4548
2	3066	4155
3	5281	4155

prune1.0s (25.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	811	0	811
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	811	5	816

Error

0.0b

Counts

816 → 5

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.7b	(.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 6))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
	34.6b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.0b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 47728 to 29590 computations (38% saved)

regimes533.0ms (13.4%)

Accuracy

Total 0.0b remaining (35.7%)

Threshold costs 0.0b (35.7%)

Counts

132 → 1

Compiler

Compiled 11250 to 6869 computations (38.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	15	10
3	17	10
4	18	10
5	18	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample557.0ms (14%)

Algorithm

1×

intervals

Results

209.0ms	7438×	body	128	valid
20.0ms	206×	body	1024	valid
19.0ms	161×	body	2048	valid
9.0ms	114×	body	512	valid
4.0ms	81×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 170 to 101 computations (40.6% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8

Details

analyze47.0ms (1.2%)

sample60.0ms (1.5%)

simplify25.0ms (0.6%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite1.0ms (0%)

simplify45.0ms (1.1%)

prune34.0ms (0.9%)

localize8.0ms (0.2%)

series61.0ms (1.5%)

rewrite18.0ms (0.5%)

simplify108.0ms (2.7%)

prune393.0ms (9.9%)

localize12.0ms (0.3%)

series62.0ms (1.6%)

rewrite14.0ms (0.3%)

simplify91.0ms (2.3%)

prune653.0ms (16.4%)

localize12.0ms (0.3%)

series53.0ms (1.3%)

rewrite16.0ms (0.4%)

simplify129.0ms (3.3%)

prune1.0s (25.9%)

regimes533.0ms (13.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample557.0ms (14%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	79	10
5	146	10
6	244	10
7	348	8
8	442	8
9	595	8
10	650	8
11	590	8