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)

sample956.0ms (47.2%)

Results

760.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify166.0ms (8.2%)

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

prune4.0ms (0.2%)

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)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite11.0ms (0.6%)

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:

10.0ms

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

simplify69.0ms (3.4%)

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

prune41.0ms (2%)

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
	8.4b	(.f64 (.f64 x (*.f64 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)))
	0.7b	(.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)))
	8.4b	(.f64 (.f64 x (sqrt.f64 (fma.f64 x -2 3))) (*.f64 x (sqrt.f64 (fma.f64 x -2 3))))
	0.2b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 640 to 423 computations (33.9% 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 (0.4%)

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))

rewrite66.0ms (3.3%)

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:

55.0ms	(*.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 (5.5%)

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

prune99.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Error

0.0b

Counts

119 → 4

Alt Table

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

Compiler

Compiled 1985 to 1565 computations (21.2% saved)

localize9.0ms (0.4%)

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)))

series10.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

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

rewrite10.0ms (0.5%)

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:

7.0ms	(*.f64 -2 (pow.f64 x 3))
1.0ms	(fma.f64 3 (pow.f64 x 2) (*.f64 -2 (pow.f64 x 3)))

simplify72.0ms (3.6%)

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

prune49.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	68	4	72

Error

0.0b

Counts

72 → 4

Alt Table

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

Compiler

Compiled 1094 to 852 computations (22.1% 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 (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite16.0ms (0.8%)

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:

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

simplify79.0ms (3.9%)

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

prune56.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

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

Compiler

Compiled 953 to 613 computations (35.7% saved)

regimes76.0ms (3.8%)

Accuracy

Total 0.1b remaining (85.2%)

Threshold costs 0.1b (85.2%)

Counts

38 → 1

Compiler

Compiled 1050 to 778 computations (25.9% 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

end83.0ms (4.1%)

Compiler: Compiled 76 to 60 computations (21.1% saved)

Details

analyze4.0ms (0.2%)

sample956.0ms (47.2%)

simplify166.0ms (8.2%)

prune4.0ms (0.2%)

localize6.0ms (0.3%)

series5.0ms (0.2%)

rewrite11.0ms (0.6%)

simplify69.0ms (3.4%)

prune41.0ms (2%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite66.0ms (3.3%)

simplify111.0ms (5.5%)

prune99.0ms (4.9%)

localize9.0ms (0.4%)

series10.0ms (0.5%)

rewrite10.0ms (0.5%)

simplify72.0ms (3.6%)

prune49.0ms (2.4%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite16.0ms (0.8%)

simplify79.0ms (3.9%)

prune56.0ms (2.8%)

regimes76.0ms (3.8%)

simplify2.0ms (0.1%)

end83.0ms (4.1%)

Profiling