Details

analyze6.0ms (0.3%)

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)

sample183.0ms (8.1%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify160.0ms (7.1%)

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 (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite5.0ms (0.2%)

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))

simplify64.0ms (2.9%)

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 (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
	0.2b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
▶	0.2b	(.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)))

Compiler

Compiled 608 to 399 computations (34.4% saved)

localize5.0ms (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)))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite10.0ms (0.5%)

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:

5.0ms	(*.f64 x (fma.f64 x -2 3))
4.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))

simplify73.0ms (3.2%)

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

prune51.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
▶	0.2b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(.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)))

Compiler

Compiled 1008 to 655 computations (35% 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))

series13.0ms (0.6%)

Counts

3 → 3

Calls

3 calls:

6.0ms	(*.f64 2 (pow.f64 x 3))
4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
3.0ms	(*.f64 3 (pow.f64 x 2))

rewrite17.0ms (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:

5.0ms	(*.f64 2 (pow.f64 x 3))
4.0ms	(*.f64 3 (pow.f64 x 2))
4.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

simplify106.0ms (4.7%)

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

prune97.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Error

0.0b

Counts

118 → 5

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
✓	0.2b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
✓	0.2b	(.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)))
	0.7b	(-.f64 (.f64 (.f64 3 (.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2))) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 2032 to 1603 computations (21.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))
✓	0.1b	(cbrt.f64 (fma.f64 x -2 3))
✓	0.2b	(.f64 (.f64 x x) (*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3))))
✓	0.2b	(.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)))

series21.0ms (0.9%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(.f64 (.f64 x x) (*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3))))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))
5.0ms	(cbrt.f64 (fma.f64 x -2 3))
4.0ms	(.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)))

rewrite37.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`pow1_binary64`
36×	`add-exp-log_binary64`
29×	`pow-prod-down_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`

Counts

4 → 118

Calls

4 calls:

15.0ms	(.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)))
8.0ms	(.f64 (.f64 x x) (*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3))))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))
1.0ms	(cbrt.f64 (fma.f64 x -2 3))

simplify148.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-def_binary64`
412×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
293×	`unswap-sqr_binary64`
286×	`associate-l_binary64`

Counts

166 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	246	4075
1	635	3458
2	2264	3136
3	4848	3134
4	5043	3134

prune424.0ms (18.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	303	5	308

Error

Counts

308 → 5

Alt Table

Status	Error	Program
	5.7b	(.f64 (.f64 (*.f64 x x) (sqrt.f64 (fma.f64 x -2 3))) (sqrt.f64 (fma.f64 x -2 3)))
✓	0.2b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	5.8b	(.f64 (.f64 (.f64 x x) (.f64 (cbrt.f64 (fma.f64 x -2 3)) (cbrt.f64 (fma.f64 x -2 3)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3))) (cbrt.f64 (sqrt.f64 (fma.f64 x -2 3)))))
✓	0.2b	(.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)))

Compiler

Compiled 9614 to 7365 computations (23.4% saved)

regimes244.0ms (10.8%)

Accuracy

Total 0.1b remaining (92.7%)

Threshold costs 0.1b (92.7%)

Counts

83 → 1

Compiler

Compiled 2636 to 2010 computations (23.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	26	16
3	30	16
4	33	16
5	34	16
6	33	16

end1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample513.0ms (22.8%)

Algorithm

1×

intervals

Results

244.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 113 to 87 computations (23% saved)

Details

analyze6.0ms (0.3%)

sample183.0ms (8.1%)

simplify160.0ms (7.1%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify64.0ms (2.9%)

prune37.0ms (1.6%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite10.0ms (0.5%)

simplify73.0ms (3.2%)

prune51.0ms (2.3%)

localize6.0ms (0.3%)

series13.0ms (0.6%)

rewrite17.0ms (0.8%)

simplify106.0ms (4.7%)

prune97.0ms (4.3%)

localize9.0ms (0.4%)

series21.0ms (0.9%)

rewrite37.0ms (1.7%)

simplify148.0ms (6.6%)

prune424.0ms (18.8%)

regimes244.0ms (10.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample513.0ms (22.8%)

Profiling