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
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample784.0ms (33.8%)

Results

567.0ms	7484×	body	128	valid
101.0ms	436×	body	1024	valid
39.0ms	214×	body	512	valid
16.0ms	122×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify40.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
127×	`cancel-sign-sub-inv_binary64`
85×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
▶	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 50 to 38 computations (24% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -9 6)
✓	0.1b	(*.f64 x (fma.f64 x -9 6))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(*.f64 x (fma.f64 x -9 6))
1.0ms	(fma.f64 x -9 6)

rewrite75.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`log1p-udef_binary64`
506×	`log1p-expm1-u_binary64`
506×	`expm1-log1p-u_binary64`
285×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`

Counts

2 → 56

Calls

2 calls:

74.0ms	(fma.f64 x -9 6)
74.0ms	(*.f64 x (fma.f64 x -9 6))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1306	13
3	4959	13
4	6551	13

simplify129.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1613×	`fma-def_binary64`
1033×	`distribute-rgt-in_binary64`
753×	`fma-neg_binary64`
486×	`distribute-rgt-neg-in_binary64`
451×	`cancel-sign-sub-inv_binary64`

Counts

80 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	32	189
2	54	144
3	123	144
4	324	144
5	926	144
6	1625	144
7	2459	144
8	3649	144
9	4122	144
10	3387	144
11	3645	144
12	4440	144
13	5540	144

prune48.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	9	68

Error

0.0b

Counts

68 → 9

Alt Table

Status	Error	Program
	1.4b	(*.f64 x (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 3))
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	41.9b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	39.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	1.4b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	9.7b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	1.4b	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -9 6)) (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 2)))

Compiler

Compiled 872 to 678 computations (22.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series5.0ms (0.2%)

Counts

2 → 3

Calls

2 calls:

3.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
2.0ms	(*.f64 9 (pow.f64 x 2))

rewrite52.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
92×	`add-log-exp_binary64`
91×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

50.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
50.0ms	(*.f64 9 (pow.f64 x 2))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	204	18
2	2269	18
3	5265	18

simplify149.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1127×	`sqr-pow_binary64`
577×	`fabs-mul_binary64`
564×	`cube-prod_binary64`
541×	`pow-sqr_binary64`
523×	`associate-l_binary64`

Counts

67 → 67

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	25	18
3	48	18
4	103	18
5	258	18
6	799	18
7	1202	18
8	1307	18
9	1463	18
10	1643	18
11	1824	18
12	2047	18
13	2214	18
14	2633	18
15	3198	18
16	3884	18
17	4102	18
18	4346	18
19	4428	18
20	4461	18
21	4482	18
22	5051	18

prune48.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Error

0.0b

Counts

76 → 8

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 6 x) (pow.f64 (.f64 x 3) 2))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	39.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	9.7b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	1.4b	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -9 6)) (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 2)))
▶	0.2b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	9.4b	(-.f64 (.f64 6 x) (sqrt.f64 (.f64 81 (pow.f64 x 4))))

Compiler

Compiled 1377 to 838 computations (39.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
✓	0.2b	(.f64 (.f64 x x) -9)

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(.f64 (.f64 x x) -9)
3.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))

rewrite73.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log1p-expm1-u_binary64`
577×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
123×	`prod-diff_binary64`
120×	`expm1-udef_binary64`

Counts

2 → 47

Calls

2 calls:

72.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))
72.0ms	(.f64 (.f64 x x) -9)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	144	17
2	1508	17
3	4992	17
4	4900	17

simplify134.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

1661×	`fma-def_binary64`
724×	`fma-neg_binary64`
531×	`unsub-neg_binary64`
521×	`distribute-rgt-neg-in_binary64`
420×	`distribute-lft-neg-in_binary64`

Counts

71 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	219
1	24	201
2	45	192
3	110	174
4	284	174
5	809	174
6	1430	174
7	2365	174
8	3740	174
9	3984	174
10	3359	174
11	3616	174
12	3797	174
13	4899	174
14	4770	174

prune41.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	53	8	61

Error

0.0b

Counts

61 → 8

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 6 x) (pow.f64 (.f64 x 3) 2))
	39.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	9.7b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	1.4b	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -9 6)) (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 2)))
▶	0.2b	(*.f64 x (fma.f64 -9 x 6))
✓	0.2b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	9.4b	(-.f64 (.f64 6 x) (sqrt.f64 (.f64 81 (pow.f64 x 4))))

Compiler

Compiled 797 to 577 computations (27.6% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -9 x 6)
✓	0.1b	(*.f64 x (fma.f64 -9 x 6))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(*.f64 x (fma.f64 -9 x 6))
1.0ms	(fma.f64 -9 x 6)

rewrite221.0ms (9.5%)

Algorithm

1×	batch-egg-rewrite

Rules

967×	`log1p-udef_binary64`
506×	`log1p-expm1-u_binary64`
506×	`expm1-log1p-u_binary64`
285×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`

Counts

2 → 56

Calls

2 calls:

220.0ms	(fma.f64 -9 x 6)
220.0ms	(*.f64 x (fma.f64 -9 x 6))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1307	13
3	4960	13
4	6551	13

simplify129.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1613×	`fma-def_binary64`
1033×	`distribute-rgt-in_binary64`
753×	`fma-neg_binary64`
486×	`distribute-rgt-neg-in_binary64`
451×	`cancel-sign-sub-inv_binary64`

Counts

80 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	32	189
2	54	144
3	123	144
4	324	144
5	926	144
6	1625	144
7	2459	144
8	3649	144
9	4122	144
10	3387	144
11	3645	144
12	4440	144
13	5540	144

prune35.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	66	8	74

Error

0.0b

Counts

74 → 8

Alt Table

Status	Error	Program
	0.3b	(-.f64 (.f64 6 x) (pow.f64 (.f64 x 3) 2))
	39.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	9.7b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	1.4b	(.f64 x (.f64 (cbrt.f64 (fma.f64 x -9 6)) (pow.f64 (cbrt.f64 (fma.f64 x -9 6)) 2)))
✓	0.2b	(*.f64 x (fma.f64 -9 x 6))
✓	0.2b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
	9.4b	(-.f64 (.f64 6 x) (sqrt.f64 (.f64 81 (pow.f64 x 4))))

Compiler

Compiled 763 to 589 computations (22.8% saved)

regimes194.0ms (8.3%)

Accuracy

Total 0.1b remaining (81%)

Threshold costs 0.1b (81%)

Counts

31 → 1

Compiler

Compiled 620 to 482 computations (22.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end121.0ms (5.2%)

Compiler: Compiled 101 to 77 computations (23.8% saved)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8

Details

analyze4.0ms (0.2%)

sample784.0ms (33.8%)

simplify40.0ms (1.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite75.0ms (3.2%)

simplify129.0ms (5.6%)

prune48.0ms (2.1%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite52.0ms (2.2%)

simplify149.0ms (6.4%)

prune48.0ms (2.1%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite73.0ms (3.1%)

simplify134.0ms (5.8%)

prune41.0ms (1.8%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite221.0ms (9.5%)

simplify129.0ms (5.5%)

prune35.0ms (1.5%)

regimes194.0ms (8.3%)

simplify2.0ms (0.1%)

end121.0ms (5.2%)

Profiling

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	92	8
4	173	8
5	259	8
6	365	8
7	561	8
8	580	8
9	675	8
10	798	8
11	821	8
12	918	8
13	922	8
14	922	8
15	803	8