Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.4%	13
66.6%	0%	33.4%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample861.0ms (46.1%)

Results

677.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify164.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

1514×	`fma-def_binary64`
1229×	`fma-neg_binary64`
587×	`distribute-rgt-neg-in_binary64`
552×	`cancel-sign-sub-inv_binary64`
522×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	42	11
3	96	11
4	169	11
5	224	11
6	343	11
7	549	11
8	728	11
9	1208	11
10	1666	11
11	2306	11
12	2905	11
13	3028	11
14	3233	11
15	3418	11
16	4282	11
17	3230	11
18	3595	11
19	4713	11
20	4755	11

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

Compiler

Compiled 36 to 23 computations (36.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

(*.f64 (*.f64 x x) (fma.f64 x -2 3))

simplify83.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1057×	`fma-def_binary64`
450×	`associate-l_binary64`
439×	`times-frac_binary64`
381×	`exp-prod_binary64`
334×	`associate-r_binary64`

Counts

35 → 37

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	539
1	122	424
2	381	424
3	1373	424
4	2370	424
5	3834	424
6	5293	424

prune34.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	6	38

Error

0.0b

Counts

38 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	9.1b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
	0.6b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 3)))
	9.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 649 to 429 computations (33.9% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.0b	(*.f64 2 (pow.f64 x 3))
✓	0.2b	(*.f64 3 (pow.f64 x 2))

series10.0ms (0.5%)

Counts

3 → 3

Calls

3 calls:

4.0ms	(*.f64 2 (pow.f64 x 3))
4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
2.0ms	(*.f64 3 (pow.f64 x 2))

rewrite14.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

4.0ms	(*.f64 2 (pow.f64 x 3))
4.0ms	(*.f64 3 (pow.f64 x 2))
3.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify111.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
465×	`fma-neg_binary64`
389×	`exp-prod_binary64`
316×	`distribute-rgt-neg-in_binary64`
308×	`distribute-lft-neg-in_binary64`

Counts

81 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1015
1	257	861
2	724	817
3	1848	788
4	3852	780
5	4761	780
6	4994	780
7	4715	780

prune102.0ms (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	114	6	120

Error

0.0b

Counts

120 → 6

Alt Table

Status	Error	Program
	35.6b	(-.f64 (.f64 (.f64 3 x) (pow.f64 (sqrt.f64 x) 2)) (*.f64 2 (pow.f64 x 3)))
	0.6b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 3)))
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	9.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
▶	0.1b	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

Compiler

Compiled 2044 to 1609 computations (21.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -2 (pow.f64 x 3))
✓	0.1b	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

series6.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))
3.0ms	(*.f64 -2 (pow.f64 x 3))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(*.f64 -2 (pow.f64 x 3))
0.0ms	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

simplify64.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-l_binary64`
588×	`associate-r_binary64`
413×	`log-prod_binary64`
376×	`fma-def_binary64`
278×	`exp-prod_binary64`

Counts

55 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	700
1	133	631
2	369	612
3	2245	550
4	4854	550
5	4937	550

prune52.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
	35.6b	(-.f64 (.f64 (.f64 3 x) (pow.f64 (sqrt.f64 x) 2)) (*.f64 2 (pow.f64 x 3)))
	0.6b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 3)))
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
▶	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	9.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
✓	0.1b	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

Compiler

Compiled 1153 to 896 computations (22.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x -2 3))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

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

simplify70.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
444×	`unswap-sqr_binary64`
444×	`times-frac_binary64`
351×	`*-commutative_binary64`
216×	`exp-prod_binary64`

Counts

70 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	970
1	152	752
2	484	752
3	1374	750
4	2163	750
5	4334	750
6	5493	750

prune64.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
	35.6b	(-.f64 (.f64 (.f64 3 x) (pow.f64 (sqrt.f64 x) 2)) (*.f64 2 (pow.f64 x 3)))
	0.6b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (cbrt.f64 (fma.f64 x -2 3)))
✓	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
✓	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))
	35.7b	(.f64 x (.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (fma.f64 x -2 3))))
	9.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
✓	0.1b	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

Compiler

Compiled 994 to 641 computations (35.5% saved)

regimes76.0ms (4.1%)

Accuracy

Total 0.1b remaining (90.7%)

Threshold costs 0.1b (90.7%)

Counts

41 → 1

Compiler

Compiled 1138 to 846 computations (25.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	10	14
2	10	14

end99.0ms (5.3%)

Compiler: Compiled 117 to 88 computations (24.8% saved)

Details

analyze4.0ms (0.2%)

sample861.0ms (46.1%)

simplify164.0ms (8.8%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify83.0ms (4.5%)

prune34.0ms (1.8%)

localize6.0ms (0.3%)

series10.0ms (0.5%)

rewrite14.0ms (0.8%)

simplify111.0ms (5.9%)

prune102.0ms (5.5%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite6.0ms (0.3%)

simplify64.0ms (3.4%)

prune52.0ms (2.8%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite8.0ms (0.4%)

simplify70.0ms (3.7%)

prune64.0ms (3.4%)

regimes76.0ms (4.1%)

simplify2.0ms (0.1%)

end99.0ms (5.3%)

Profiling