Details

analyze49.0ms (2.1%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample902.0ms (39.4%)

Results

752.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify137.0ms (6%)

Algorithm

1×	egg-herbie

Rules

878×	`div-sub_binary64`
546×	`times-frac_binary64`
500×	`sub-neg_binary64`
408×	`fma-def_binary64`
395×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	16	13
2	40	13
3	81	13
4	153	13
5	248	13
6	435	11
7	1077	11
8	3029	11
9	3558	11
10	3959	11
11	4158	11
12	4377	11
13	4552	11
14	5083	11

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	11.7b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series18.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
7.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
0.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

simplify91.0ms (4%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
231×	`fma-def_binary64`
198×	`associate-/l*_binary64`
198×	`times-frac_binary64`

Counts

87 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1389
1	226	1308
2	679	1260
3	2411	1246
4	4577	1246
5	4993	1246
6	4941	1246

prune35.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	8.5b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))
	8.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
	33.7b	(*.f64 2 y)

Compiler

Compiled 1022 to 594 computations (41.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	3.0b	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x))
✓	4.7b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))

series188.0ms (8.2%)

Counts

4 → 72

Calls

4 calls:

103.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x))
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
34.0ms	(cbrt.f64 x)
14.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))

rewrite27.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
49×	`cbrt-prod_binary64`

Counts

4 → 162

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
4.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify159.0ms (7%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-neg_binary64`
513×	`*-commutative_binary64`
342×	`fma-def_binary64`
286×	`associate-/l*_binary64`
197×	`unswap-sqr_binary64`

Counts

234 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	4982
1	552	4123
2	2452	3939
3	3887	3848
4	4843	3848
5	4934	3848

prune127.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	300	4	304

Error

Counts

304 → 4

Alt Table

Status	Error	Program
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	8.5b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))
▶	8.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
	33.7b	(*.f64 2 y)

Compiler

Compiled 6778 to 3104 computations (54.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	3.2b	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
✓	4.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))

series57.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
20.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 88

Calls

2 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
2.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))

simplify89.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-/r*_binary64`
302×	`associate-/l/_binary64`
246×	`associate-l_binary64`
214×	`associate-r_binary64`
195×	`associate-/r/_binary64`

Counts

136 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	3522
1	629	3114
2	2467	3024
3	5309	3024

prune123.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	276	4	280

Error

Counts

280 → 4

Alt Table

Status	Error	Program
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	8.5b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))
✓	8.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
▶	33.7b	(*.f64 2 y)

Compiler

Compiled 6416 to 3046 computations (52.5% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	7.3b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	8.5b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) (cbrt.f64 x)))
✓	8.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	33.7b	(*.f64 2 y)

Compiler

Compiled 49 to 31 computations (36.7% saved)

regimes107.0ms (4.7%)

Accuracy

Total 1.0b remaining (98.7%)

Threshold costs 1.0b (98.7%)

Counts

14 → 5

Compiler

Compiled 565 to 376 computations (33.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	131
1	30	131
2	34	131
3	36	131
4	37	131
5	37	131

end123.0ms (5.4%)

Compiler: Compiled 233 to 135 computations (42.1% saved)

Details

analyze49.0ms (2.1%)

sample902.0ms (39.4%)

simplify137.0ms (6%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series18.0ms (0.8%)

rewrite4.0ms (0.2%)

simplify91.0ms (4%)

prune35.0ms (1.5%)

localize10.0ms (0.4%)

series188.0ms (8.2%)

rewrite27.0ms (1.2%)

simplify159.0ms (7%)

prune127.0ms (5.5%)

localize8.0ms (0.4%)

series57.0ms (2.5%)

rewrite19.0ms (0.8%)

simplify89.0ms (3.9%)

prune123.0ms (5.4%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

regimes107.0ms (4.7%)

bsearch1.0ms (0%)

simplify5.0ms (0.2%)

end123.0ms (5.4%)

Profiling