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)

sample839.0ms (37.1%)

Results

660.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 23 computations (28.1% 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))

rewrite123.0ms (5.4%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
296×	`log-prod_binary64`
171×	`pow2_binary64`
120×	`pow1/3_binary64`

Counts

1 → 25

Calls

1 calls:

122.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	144	11
2	1532	11
3	4967	11
4	4888	11
0	0	0
1	0	0

simplify84.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-neg_binary64`
851×	`fma-def_binary64`
771×	`distribute-rgt-neg-in_binary64`
628×	`distribute-lft-neg-in_binary64`
439×	`neg-mul-1_binary64`

Counts

37 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	165
1	30	147
2	77	138
3	219	120
4	616	120
5	1129	120
6	2106	120
7	3386	120
8	4690	120
9	4971	120
10	4943	120

prune26.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	26	5	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
	23.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	10.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
▶	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 460 to 303 computations (34.1% 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 (0.4%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(-.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))

rewrite59.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

3 → 78

Calls

3 calls:

57.0ms	(*.f64 2 (pow.f64 x 3))
57.0ms	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
57.0ms	(*.f64 3 (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	206	28
2	2266	28
3	5276	28
0	0	0
1	0	0

simplify155.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

968×	`sqr-pow_binary64`
623×	`cube-prod_binary64`
608×	`fabs-mul_binary64`
562×	`pow-sqr_binary64`
538×	`unswap-sqr_binary64`

Counts

81 → 80

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	22	21
2	50	21
3	104	21
4	245	21
5	923	21
6	1516	21
7	1655	21
8	1879	21
9	2106	21
10	2437	21
11	2516	21
12	2827	21
13	3296	21
14	3593	21
15	3806	21
16	3930	21
17	3976	21
18	4003	21
19	4658	21
20	4764	21
21	4855	21

prune64.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

0.0b

Counts

85 → 5

Alt Table

Status	Error	Program
	23.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	10.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
	0.9b	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
▶	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 1629 to 1223 computations (24.9% 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)))

series5.0ms (0.2%)

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))

rewrite107.0ms (4.7%)

Algorithm

2×	batch-egg-rewrite

Rules

600×	`log1p-expm1-u_binary64`
600×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
124×	`pow1/3_binary64`
123×	`expm1-udef_binary64`

Counts

2 → 50

Calls

2 calls:

106.0ms	(*.f64 x (fma.f64 x -2 3))
106.0ms	(.f64 x (.f64 x (fma.f64 x -2 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	143	19
2	1570	19
3	4969	19
4	4912	19
0	0	0
1	0	0

simplify91.0ms (4%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-neg_binary64`
685×	`fma-def_binary64`
500×	`distribute-rgt-neg-in_binary64`
442×	`neg-mul-1_binary64`
438×	`neg-sub0_binary64`

Counts

74 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	300
1	41	264
2	92	246
3	253	210
4	693	210
5	1267	210
6	2302	210
7	3410	210
8	4539	210
9	4972	210
10	4803	210

prune39.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	60	5	65

Error

0.0b

Counts

65 → 5

Alt Table

Status	Error	Program
	23.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	10.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
▶	0.9b	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))

Compiler

Compiled 785 to 547 computations (30.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 x x) (fma.f64 x -2 3))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
✓	23.2b	(cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)))

series85.0ms (3.7%)

Counts

2 → 24

Calls

2 calls:

78.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
6.0ms	(cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)))

rewrite51.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

688×	`log1p-expm1-u_binary64`
688×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
134×	`expm1-udef_binary64`
134×	`log1p-udef_binary64`

Counts

2 → 74

Calls

2 calls:

50.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3))) 3)
50.0ms	(cbrt.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	171	24
2	1802	24
3	5216	24
0	0	0
1	0	0

simplify66.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
768×	`fma-neg_binary64`
243×	`fma-def_binary64`
197×	`associate-r_binary64`
187×	`sub-neg_binary64`

Counts

98 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1189
1	256	1121
2	721	793
3	2721	573
4	4910	573
5	5037	573

prune108.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	141	5	146

Error

0.0b

Counts

146 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (*.f64 x x) (pow.f64 (cbrt.f64 (fma.f64 x -2 3)) 2)) (cbrt.f64 (fma.f64 x -2 3)))
✓	0.1b	(-.f64 (.f64 3 (pow.f64 x 2)) (.f64 2 (pow.f64 x 3)))
	23.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 x x) (fma.f64 x -2 3)) 3))
	10.1b	(pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x -2 3))) 2)
✓	0.1b	(.f64 x (.f64 x (fma.f64 x -2 3)))

Compiler

Compiled 2641 to 1949 computations (26.2% saved)

regimes81.0ms (3.6%)

Accuracy

Total 0.1b remaining (88.1%)

Threshold costs 0.1b (88.1%)

Counts

47 → 1

Compiler

Compiled 1124 to 850 computations (24.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	17	16
2	25	16
3	29	16
4	32	16
5	33	16
6	32	16

end78.0ms (3.4%)

Compiler: Compiled 85 to 67 computations (21.2% saved)

Details

analyze4.0ms (0.2%)

sample839.0ms (37.1%)

simplify160.0ms (7.1%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite123.0ms (5.4%)

simplify84.0ms (3.7%)

prune26.0ms (1.1%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite59.0ms (2.6%)

simplify155.0ms (6.9%)

prune64.0ms (2.8%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite107.0ms (4.7%)

simplify91.0ms (4%)

prune39.0ms (1.7%)

localize7.0ms (0.3%)

series85.0ms (3.7%)

rewrite51.0ms (2.3%)

simplify66.0ms (2.9%)

prune108.0ms (4.7%)

regimes81.0ms (3.6%)

simplify4.0ms (0.2%)

end78.0ms (3.4%)

Profiling