Details

analyze43.0ms (1.4%)

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)

sample58.0ms (1.9%)

Algorithm

1×

intervals

Results

6.0ms	232×	body	128	valid
1.0ms	11×	body	1024	valid
0.0ms	6×	body	512	valid
0.0ms	3×	body	2048	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify22.0ms (0.7%)

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

prune4.0ms (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)

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)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(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)

simplify43.0ms (1.4%)

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

prune15.0ms (0.5%)

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

0.1b

Counts

23 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
▶	1.2b	(.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)))
	34.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))

Compiler

Compiled 313 to 185 computations (40.9% saved)

localize7.0ms (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))

series54.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

25.0ms

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

22.0ms

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

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)))

rewrite19.0ms (0.6%)

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:

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)))

4.0ms

(*.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))

simplify115.0ms (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

prune402.0ms (13.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	433	9	442
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	435	10	445

Error

0.0b

Counts

445 → 10

Alt Table

Status	Error	Program
	34.8b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (.f64 (sqrt.f64 (cbrt.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)))
	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)))))
	2.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
	34.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))
	31.2b	(.f64 (cbrt.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.8b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))) (cbrt.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)))
▶	1.2b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	42.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 y (*.f64 3/2 x)) 3))))

Compiler

Compiled 16171 to 10011 computations (38.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
	0.5b	(cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)

series938.0ms (31%)

Counts

1 → 24

Calls

1 calls:

938.0ms

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

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

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

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-def_binary64`
509×	`associate-l_binary64`
492×	`associate-r_binary64`
327×	`log-prod_binary64`
261×	`exp-prod_binary64`

Counts

56 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1254
1	273	1130
2	779	1069
3	3260	749
4	4760	749
5	5002	749

prune113.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	154	3	157
Fresh	7	1	8
Picked	0	1	1
Done	0	1	1
Total	161	6	167

Error

Counts

167 → 6

Alt Table

Status	Error	Program
	2.5b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 4)) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))
	9.7b	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
▶	0.7b	(*.f64 (cbrt.f64 27/8) (fma.f64 y -1/3 x))
	29.8b	(/.f64 -3/2 (/.f64 -1 x))
✓	1.2b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)

Compiler

Compiled 3216 to 2324 computations (27.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 27/8) (fma.f64 y -1/3 x))
✓	0.2b	(fma.f64 y -1/3 x)
✓	1.0b	(cbrt.f64 27/8)

series8.0ms (0.3%)

Counts

3 → 48

Calls

3 calls:

5.0ms	(*.f64 (cbrt.f64 27/8) (fma.f64 y -1/3 x))
4.0ms	(fma.f64 y -1/3 x)
0.0ms	(cbrt.f64 27/8)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 49

Calls

3 calls:

4.0ms	(*.f64 (cbrt.f64 27/8) (fma.f64 y -1/3 x))
1.0ms	(cbrt.f64 27/8)
0.0ms	(fma.f64 y -1/3 x)

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-def_binary64`
667×	`distribute-rgt-neg-out_binary64`
554×	`distribute-lft-in_binary64`
552×	`distribute-rgt-in_binary64`
259×	`unsub-neg_binary64`

Counts

97 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	900
1	112	775
2	277	771
3	765	771
4	2508	771
5	4959	771

prune38.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	3	0	3
Picked	1	0	1
Done	2	0	2
Total	80	1	81

Error

Counts

81 → 1

Alt Table

Status	Error	Program
	0b	(fma.f64 x 3/2 (*.f64 y -1/2))

Compiler

Compiled 839 to 654 computations (22.1% saved)

regimes469.0ms (15.5%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 9009 to 5531 computations (38.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
2	8	8

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample489.0ms (16.2%)

Algorithm

1×

intervals

Results

212.0ms	7373×	body	128	valid
21.0ms	163×	body	2048	valid
19.0ms	210×	body	1024	valid
15.0ms	171×	body	512	valid
4.0ms	83×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 28 to 21 computations (25% 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

analyze43.0ms (1.4%)

sample58.0ms (1.9%)

simplify22.0ms (0.7%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify43.0ms (1.4%)

prune15.0ms (0.5%)

localize7.0ms (0.2%)

series54.0ms (1.8%)

rewrite19.0ms (0.6%)

simplify115.0ms (3.8%)

prune402.0ms (13.3%)

localize11.0ms (0.4%)

series938.0ms (31%)

rewrite8.0ms (0.3%)

simplify85.0ms (2.8%)

prune113.0ms (3.7%)

localize7.0ms (0.2%)

series8.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify55.0ms (1.8%)

prune38.0ms (1.2%)

regimes469.0ms (15.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample489.0ms (16.2%)

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