Details

analyze53.0ms (1.3%)

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
99.1%	0.8%	0.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample836.0ms (20.7%)

Results

723.0ms	7992×	body	128	valid
29.0ms	93×	body	1024	valid
21.0ms	66×	body	2048	valid
14.0ms	70×	body	512	valid
5.0ms	35×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-neg_binary64`
32×	`cancel-sign-sub-inv_binary64`
30×	`fma-def_binary64`
29×	`sub-neg_binary64`
17×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

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

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 35 to 21 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-neg-out_binary64`
515×	`neg-mul-1_binary64`
507×	`neg-sub0_binary64`
481×	`distribute-rgt-out_binary64`
469×	`*-commutative_binary64`

Counts

34 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	374
1	26	353
2	55	353
3	125	353
4	320	353
5	990	353
6	1892	353
7	2461	353
8	3898	353
9	5066	353

prune13.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	4	22

Error

0.0b

Counts

22 → 4

Alt Table

Status	Error	Program
	14.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	45.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 397 to 188 computations (52.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.6b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

series707.0ms (17.5%)

Counts

3 → 72

Calls

3 calls:

386.0ms

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

314.0ms

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

7.0ms

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

rewrite18.0ms (0.4%)

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

4.0ms

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

1.0ms

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

simplify118.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
393×	`*-commutative_binary64`
356×	`cancel-sign-sub-inv_binary64`
338×	`unswap-sqr_binary64`
309×	`fma-neg_binary64`

Counts

165 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3620
1	483	3205
2	1465	3016
3	3985	2880
4	5033	2880

prune227.0ms (5.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	332	3	335
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	332	7	339

Error

0.0b

Counts

339 → 7

Alt Table

Status	Error	Program
	14.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	35.1b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
▶	1.9b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 4)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	45.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	15.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 11945 to 5904 computations (50.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.6b	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
✓	0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 4)

series933.0ms (23.1%)

Counts

3 → 72

Calls

3 calls:

323.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 4)
315.0ms	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))
294.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 4)
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
1.0ms	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))

simplify112.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
614×	`times-frac_binary64`
295×	`unswap-sqr_binary64`
259×	`cancel-sign-sub-inv_binary64`
218×	`fma-neg_binary64`

Counts

127 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	3580
1	706	3459
2	2119	3232
3	4975	3232
4	4998	3232

prune354.0ms (8.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	286	8	294

Error

0.0b

Counts

294 → 8

Alt Table

Status	Error	Program
	15.9b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))) 4))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
▶	14.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	35.1b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	1.9b	(.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 4)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	45.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	15.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 15946 to 8686 computations (45.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	0.0b	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

series23.0ms (0.6%)

Counts

2 → 40

Calls

2 calls:

18.0ms	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
5.0ms	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.0ms	(sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify79.0ms (2%)

Algorithm

1×	egg-herbie

Rules

682×	`times-frac_binary64`
581×	`fma-def_binary64`
306×	`distribute-lft-in_binary64`
304×	`distribute-rgt-in_binary64`
283×	`fma-neg_binary64`

Counts

108 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1747
1	180	1580
2	499	1518
3	1804	1478
4	4926	1478
5	5056	1478

prune118.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	3	4
Picked	0	1	1
Done	1	2	3
Total	173	8	181

Error

0.0b

Counts

181 → 8

Alt Table

Status	Error	Program
✓	14.4b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	35.1b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x) 2)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	45.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	14.5b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	15.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	15.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 4296 to 2119 computations (50.7% saved)

regimes156.0ms (3.9%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Counts

41 → 1

Compiler

Compiled 3488 to 2122 computations (39.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	18	10
3	23	10
4	26	10
5	27	10
6	27	10

end138.0ms (3.4%)

Compiler: Compiled 230 to 130 computations (43.5% saved)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Details

analyze53.0ms (1.3%)

sample836.0ms (20.7%)

simplify16.0ms (0.4%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite1.0ms (0%)

simplify70.0ms (1.7%)

prune13.0ms (0.3%)

localize8.0ms (0.2%)

series707.0ms (17.5%)

rewrite18.0ms (0.4%)

simplify118.0ms (2.9%)

prune227.0ms (5.6%)

localize15.0ms (0.4%)

series933.0ms (23.1%)

rewrite6.0ms (0.2%)

simplify112.0ms (2.8%)

prune354.0ms (8.8%)

localize6.0ms (0.2%)

series23.0ms (0.6%)

rewrite10.0ms (0.3%)

simplify79.0ms (2%)

prune118.0ms (2.9%)

regimes156.0ms (3.9%)

simplify2.0ms (0.1%)

end138.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10