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)

sample857.0ms (43.8%)

Results

667.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify166.0ms (8.5%)

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))

series5.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(*.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))

simplify60.0ms (3.1%)

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

prune37.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	5	38

Error

0.0b

Counts

38 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	0.5b	(.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)))
	6.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
	24.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (fma.f64 x -2 3) (fma.f64 x -2 3)) (fma.f64 x -2 3))))
▶	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 664 to 433 computations (34.8% 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))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))
2.0ms	(*.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)))
2.0ms	(*.f64 x (fma.f64 x -2 3))

simplify73.0ms (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

prune58.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	69	6	75

Error

Counts

75 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 x (fma.f64 x -2 3))))
	0.5b	(.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)))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	15.4b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
	6.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 1064 to 691 computations (35.1% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series9.0ms (0.5%)

Counts

3 → 3

Calls

3 calls:

4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
3.0ms	(*.f64 2 (pow.f64 x 3))
2.0ms	(*.f64 3 (pow.f64 x 2))

rewrite14.0ms (0.7%)

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:

5.0ms	(*.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)))

simplify102.0ms (5.2%)

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	258	861
2	724	817
3	1848	788
4	3852	780
5	4761	780
6	4994	780
7	4715	780

prune98.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

Counts

120 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	15.4b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
▶	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2))) (*.f64 2 (pow.f64 x 3)))
	0.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 x (fma.f64 x -2 3))))
	6.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 2030 to 1595 computations (21.4% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series22.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2))) (*.f64 2 (pow.f64 x 3)))
7.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2)))
4.0ms	(*.f64 (sqrt.f64 3) (pow.f64 x 2))

rewrite21.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 76

Calls

3 calls:

7.0ms	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2))) (*.f64 2 (pow.f64 x 3)))
6.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2)))
5.0ms	(*.f64 (sqrt.f64 3) (pow.f64 x 2))

simplify77.0ms (4%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
424×	`unswap-sqr_binary64`
353×	`fma-neg_binary64`
297×	`times-frac_binary64`
274×	`*-commutative_binary64`

Counts

100 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	1318
1	248	1217
2	833	1178
3	1858	1107
4	4286	1069
5	5162	1069

prune147.0ms (7.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	155	6	161

Error

Counts

161 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	15.4b	(.f64 x (cbrt.f64 (pow.f64 (.f64 x (fma.f64 x -2 3)) 3)))
✓	0.3b	(-.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (pow.f64 x 2))) (*.f64 2 (pow.f64 x 3)))
	0.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (.f64 x (fma.f64 x -2 3))))
	6.1b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 3229 to 2680 computations (17% saved)

regimes71.0ms (3.7%)

Accuracy

Total 0.1b remaining (86.9%)

Threshold costs 0.1b (86.9%)

Counts

45 → 1

Compiler

Compiled 1226 to 890 computations (27.4% 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

end85.0ms (4.3%)

Compiler: Compiled 103 to 78 computations (24.3% saved)

Details

analyze4.0ms (0.2%)

sample857.0ms (43.8%)

simplify166.0ms (8.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite5.0ms (0.3%)

simplify60.0ms (3.1%)

prune37.0ms (1.9%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite8.0ms (0.4%)

simplify73.0ms (3.7%)

prune58.0ms (3%)

localize6.0ms (0.3%)

series9.0ms (0.5%)

rewrite14.0ms (0.7%)

simplify102.0ms (5.2%)

prune98.0ms (5%)

localize11.0ms (0.5%)

series22.0ms (1.2%)

rewrite21.0ms (1.1%)

simplify77.0ms (4%)

prune147.0ms (7.5%)

regimes71.0ms (3.7%)

simplify2.0ms (0.1%)

end85.0ms (4.3%)

Profiling