Details

analyze158.0ms (2.9%)

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)

sample31.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	242×	body	128	valid
1.0ms	5×	body	1024	valid
0.0ms	2×	body	2048	valid
0.0ms	3×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify32.0ms (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

prune5.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 31 to 18 computations (41.9% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(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:

1.0ms

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

simplify72.0ms (1.3%)

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

prune29.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Error

0.0b

Counts

23 → 4

Alt Table

Status	Error	Program
	32.1b	(*.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)))
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x)) (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 359 to 209 computations (41.8% saved)

localize14.0ms (0.3%)

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)))
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

series104.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

47.0ms

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

46.0ms

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

9.0ms

(*.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)))

rewrite88.0ms (1.6%)

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:

66.0ms

(*.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)))

8.0ms

(*.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))

simplify207.0ms (3.8%)

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

prune690.0ms (12.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	438	4	442
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	440	6	446

Error

0.0b

Counts

446 → 6

Alt Table

Status	Error	Program
	32.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x)))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x)) (fma.f64 (-.f64 x y) 1/2 x)))
	49.7b	(.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 9/4) (*.f64 2 (log.f64 (/.f64 -1 x)))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	32.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
▶	32.0b	(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 15827 to 9821 computations (37.9% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.6b	(cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)
✓	30.3b	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6))

series598.0ms (11%)

Counts

3 → 72

Calls

3 calls:

505.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)
51.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6))
42.0ms	(cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64`
12×	`unpow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 56

Calls

3 calls:

3.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6))
3.0ms	(pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)
1.0ms	(cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))

simplify248.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

376×	`fma-neg_binary64`
303×	`unswap-sqr_binary64`
246×	`sub-neg_binary64`
231×	`associate-r_binary64`
167×	`*-commutative_binary64`

Counts

128 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	4732
1	1083	4504
2	3517	4211
3	4999	4211
4	5160	4211

prune432.0ms (7.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	270	6	276

Error

0.0b

Counts

276 → 6

Alt Table

Status	Error	Program
▶	32.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x)))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x)) (fma.f64 (-.f64 x y) 1/2 x)))
	49.7b	(.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 9/4) (*.f64 2 (log.f64 (/.f64 -1 x)))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	32.5b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	32.0b	(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 9761 to 6820 computations (30.1% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))))
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (.f64 (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))))))
✓	0.3b	(cbrt.f64 (.f64 (sqrt.f64 (fma.f64 -1/2 y (.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x)))))
	0.6b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))

series107.0ms (2%)

Counts

3 → 72

Calls

3 calls:

53.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))))))

45.0ms

(cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x)))))

8.0ms

(*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))))

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
20×	`pow1_binary64`
18×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

29.0ms

(*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))))

9.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))))))

6.0ms

(cbrt.f64 (*.f64 (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x))) (sqrt.f64 (fma.f64 -1/2 y (*.f64 3/2 x)))))

simplify263.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
289×	`fma-neg_binary64`
242×	`unswap-sqr_binary64`
226×	`associate-r_binary64`
224×	`sub-neg_binary64`

Counts

164 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	359	4430
1	928	4117
2	3048	3863
3	4920	3863
4	5051	3863

prune756.0ms (13.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	376	5	381

Error

0.0b

Counts

381 → 5

Alt Table

Status	Error	Program
✓	32.0b	(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)) 6)) (cbrt.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 3/2 x (*.f64 y -1/2)))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x)) (fma.f64 (-.f64 x y) 1/2 x)))
	1.3b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 3/2 x (.f64 y -1/2))) (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x)))) (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 3/2 x (.f64 y -1/2))) (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 16462 to 11280 computations (31.5% saved)

regimes375.0ms (6.9%)

Accuracy

Total 0.0b remaining (30.7%)

Threshold costs 0.0b (30.7%)

Counts

48 → 1

Compiler

Compiled 3414 to 2246 computations (34.2% saved)

simplify5.0ms (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

end1.0ms (0%)

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

sample1.1s (19.8%)

Algorithm

1×

intervals

Results

417.0ms	7437×	body	128	valid
43.0ms	213×	body	1024	valid
38.0ms	162×	body	2048	valid
18.0ms	122×	body	512	valid
6.0ms	66×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 140 to 89 computations (36.4% 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

analyze158.0ms (2.9%)

sample31.0ms (0.6%)

simplify32.0ms (0.6%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify72.0ms (1.3%)

prune29.0ms (0.5%)

localize14.0ms (0.3%)

series104.0ms (1.9%)

rewrite88.0ms (1.6%)

simplify207.0ms (3.8%)

prune690.0ms (12.7%)

localize26.0ms (0.5%)

series598.0ms (11%)

rewrite14.0ms (0.3%)

simplify248.0ms (4.6%)

prune432.0ms (7.9%)

localize29.0ms (0.5%)

series107.0ms (2%)

rewrite58.0ms (1.1%)

simplify263.0ms (4.8%)

prune756.0ms (13.9%)

regimes375.0ms (6.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (19.8%)

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