Details

analyze53.0ms (1.8%)

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)

sample876.0ms (29.7%)

Results

669.0ms	7668×	body	128	valid
59.0ms	217×	body	1024	valid
57.0ms	166×	body	2048	valid
25.0ms	131×	body	512	valid
10.0ms	74×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% 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

prune2.0ms (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 (1.5%)

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

prune22.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	5	23

Error

0.0b

Counts

23 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	31.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
▶	1.4b	(.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)))
	41.4b	(cbrt.f64 (pow.f64 (fma.f64 -1/2 y (*.f64 3/2 x)) 3))
	41.4b	(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)))

Compiler

Compiled 381 to 227 computations (40.4% saved)

localize8.0ms (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)))
✓	0.6b	(*.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))

series52.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

26.0ms

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

21.0ms

(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)))

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)))

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))

simplify103.0ms (3.5%)

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

prune341.0ms (11.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	439	3	442
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	440	7	447

Error

0.0b

Counts

447 → 7

Alt Table

Status	Error	Program
▶	1.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
	31.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	41.4b	(cbrt.f64 (pow.f64 (fma.f64 -1/2 y (*.f64 3/2 x)) 3))
	41.4b	(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)))
	4.5b	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (-.f64 x y) x))) 6))) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))
	31.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))

Compiler

Compiled 15777 to 9785 computations (38% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 x y) 1/2 x)
	0.6b	(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)

series890.0ms (30.2%)

Counts

1 → 24

Calls

1 calls:

890.0ms

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

rewrite3.0ms (0.1%)

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)

simplify87.0ms (2.9%)

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

prune105.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	5	0	5
Picked	0	1	1
Done	0	1	1
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
✓	1.4b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)
✓	0.1b	(fma.f64 (-.f64 x y) 1/2 x)
▶	11.9b	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
	31.1b	(/.f64 -3/2 (/.f64 -1 x))

Compiler

Compiled 3134 to 2268 computations (27.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
✓	13.6b	(/.f64 (.f64 x (.f64 y -1/2)) y)

series7.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

4.0ms	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))
3.0ms	(/.f64 (.f64 x (.f64 y -1/2)) y)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

6.0ms	(/.f64 (.f64 x (.f64 y -1/2)) y)
0.0ms	(fma.f64 (/.f64 (.f64 x (.f64 y -1/2)) y) -3 (*.f64 y -1/2))

simplify69.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

887×	`times-frac_binary64`
779×	`associate-/l*_binary64`
519×	`associate-l_binary64`
305×	`associate-/r*_binary64`
263×	`associate-*l/_binary64`

Counts

83 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	926
1	193	595
2	773	565
3	4141	565
4	4985	565
5	4925	565

prune37.0ms (1.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	0	1
Picked	1	0	1
Done	2	0	2
Total	68	1	69

Error

Counts

69 → 1

Alt Table

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

Compiler

Compiled 990 to 667 computations (32.6% saved)

regimes138.0ms (4.7%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

40 → 1

Compiler

Compiled 2082 to 1367 computations (34.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end40.0ms (1.4%)

Compiler: Compiled 30 to 24 computations (20% 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

analyze53.0ms (1.8%)

sample876.0ms (29.7%)

simplify22.0ms (0.7%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify43.0ms (1.5%)

prune22.0ms (0.7%)

localize8.0ms (0.3%)

series52.0ms (1.8%)

rewrite19.0ms (0.6%)

simplify103.0ms (3.5%)

prune341.0ms (11.6%)

localize7.0ms (0.2%)

series890.0ms (30.2%)

rewrite3.0ms (0.1%)

simplify87.0ms (2.9%)

prune105.0ms (3.6%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify69.0ms (2.3%)

prune37.0ms (1.3%)

regimes138.0ms (4.7%)

simplify4.0ms (0.1%)

end40.0ms (1.4%)

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