Details

analyze56.0ms (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
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)

sample847.0ms (15.7%)

Results

704.0ms	7935×	body	128	valid
43.0ms	120×	body	1024	valid
29.0ms	94×	body	2048	valid
17.0ms	69×	body	512	valid
11.0ms	38×	body	256	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify16.0ms (0.3%)

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

prune2.0ms (0%)

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)

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(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)

simplify75.0ms (1.4%)

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

prune11.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

0.0b

Counts

22 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	13.9b	(*.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)))

Compiler

Compiled 345 to 162 computations (53% saved)

localize8.0ms (0.1%)

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))

series916.0ms (16.9%)

Counts

3 → 72

Calls

3 calls:

494.0ms

(*.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)))

414.0ms

(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)))

rewrite23.0ms (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:

12.0ms

(*.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))

simplify117.0ms (2.2%)

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

prune234.0ms (4.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	331	7	338

Error

0.0b

Counts

338 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)
	14.8b	(.f64 (.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))) (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)))
	29.9b	(*.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)))
	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (.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)))) (cbrt.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)))
	13.9b	(*.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)))
	14.2b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 11983 to 5929 computations (50.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	0.6b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

series1.0s (19.1%)

Counts

1 → 24

Calls

1 calls:

1.0s	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 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 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-in_binary64`
431×	`distribute-lft-in_binary64`
409×	`associate-l_binary64`
352×	`exp-prod_binary64`
347×	`log-prod_binary64`

Counts

56 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	967
1	151	870
2	407	825
3	1831	747
4	4498	747
5	4961	747
6	4888	747

prune72.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	118	7	125

Error

0.0b

Counts

125 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)
	14.8b	(.f64 (.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))) (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)))
	29.9b	(*.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)))
▶	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (.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)))) (cbrt.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)))
	13.9b	(*.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)))
	14.2b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 2572 to 1480 computations (42.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series962.0ms (17.8%)

Counts

2 → 48

Calls

2 calls:

574.0ms	(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))))
388.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

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

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

603×	`associate-r_binary64`
572×	`associate-l_binary64`
446×	`fma-def_binary64`
334×	`fma-neg_binary64`
218×	`times-frac_binary64`

Counts

75 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2193
1	430	2169
2	1224	1985
3	4850	1983
4	5053	1983

prune423.0ms (7.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	403	1	404
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	403	8	411

Error

0.0b

Counts

411 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)
	14.8b	(.f64 (.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))) (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)))
	29.9b	(*.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)))
	14.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (.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 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.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)))
✓	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (.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)))) (cbrt.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)))
	13.9b	(*.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)))
	14.2b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 23985 to 12211 computations (49.1% saved)

regimes253.0ms (4.7%)

Accuracy

Total 0.0b remaining (57.9%)

Threshold costs 0.0b (57.9%)

Counts

64 → 1

Compiler

Compiled 6512 to 3643 computations (44.1% saved)

simplify5.0ms (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

end147.0ms (2.7%)

Compiler: Compiled 266 to 151 computations (43.2% 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

analyze56.0ms (1%)

sample847.0ms (15.7%)

simplify16.0ms (0.3%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify75.0ms (1.4%)

prune11.0ms (0.2%)

localize8.0ms (0.1%)

series916.0ms (16.9%)

rewrite23.0ms (0.4%)

simplify117.0ms (2.2%)

prune234.0ms (4.3%)

localize7.0ms (0.1%)

series1.0s (19.1%)

rewrite3.0ms (0.1%)

simplify83.0ms (1.5%)

prune72.0ms (1.3%)

localize12.0ms (0.2%)

series962.0ms (17.8%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.6%)

prune423.0ms (7.8%)

regimes253.0ms (4.7%)

simplify5.0ms (0.1%)

end147.0ms (2.7%)

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