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
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample667.0ms (38.9%)

Results

639.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8
6	24	8

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 x x -3) 6)

rewrite38.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

540×	`log1p-expm1-u_binary64`
540×	`expm1-log1p-u_binary64`
265×	`unpow-prod-down_binary64`
237×	`log-prod_binary64`
152×	`pow2_binary64`

Counts

1 → 43

Calls

1 calls:

37.0ms

(/.f64 (fma.f64 x x -3) 6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	129	8
2	1414	8
3	4957	8
0	0	0
1	0	0

simplify146.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

55 → 48

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	29	87
3	50	87
4	99	87
5	236	87
6	716	87
7	1141	87
8	1143	87
9	1291	87
10	1461	87
11	1643	87
12	1866	87
13	2151	87
14	2570	87
15	3135	87
16	3821	87
17	4039	87
18	4283	87
19	4365	87
20	4398	87
21	4419	87
22	4987	87

prune35.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Error

0.0b

Counts

49 → 5

Alt Table

Status	Error	Program
	45.2b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) 2)
	45.1b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
	0.1b	(*.f64 1/6 (pow.f64 (/.f64 1 (fma.f64 x x -3)) -1))
▶	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

Compiler

Compiled 658 to 507 computations (22.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 6 (fma.f64 x x -3))
✓	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)
3.0ms	(/.f64 6 (fma.f64 x x -3))

rewrite47.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
304×	`log-prod_binary64`
137×	`expm1-udef_binary64`
137×	`log1p-udef_binary64`

Counts

2 → 58

Calls

2 calls:

46.0ms	(/.f64 6 (fma.f64 x x -3))
46.0ms	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	170	16
2	1805	16
3	5240	16
0	0	0
1	0	0

simplify85.0ms (5%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary64`
414×	`unswap-sqr_binary64`
382×	`fma-def_binary64`
358×	`distribute-rgt-neg-in_binary64`
353×	`associate-l_binary64`

Counts

82 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	49	309
1	125	305
2	314	299
3	831	299
4	2517	299
5	4705	299
6	4912	299
7	4930	299

prune50.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	78	5	83

Error

0.0b

Counts

83 → 5

Alt Table

Status	Error	Program
	45.1b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
	45.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
▶	0.1b	(*.f64 (fma.f64 x x -3) 1/6)
✓	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

Compiler

Compiled 1046 to 819 computations (21.7% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 x x -3) 1/6)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (fma.f64 x x -3) 1/6)

rewrite76.0ms (4.4%)

Algorithm

2×	batch-egg-rewrite

Rules

923×	`log1p-udef_binary64`
486×	`log1p-expm1-u_binary64`
486×	`expm1-log1p-u_binary64`
265×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`

Counts

1 → 21

Calls

1 calls:

75.0ms

(*.f64 (fma.f64 x x -3) 1/6)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	121	8
2	1270	8
3	4911	8
4	6392	8
0	0	0
1	0	0

simplify147.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

33 → 25

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	29	87
3	50	87
4	99	87
5	236	87
6	716	87
7	1141	87
8	1143	87
9	1291	87
10	1461	87
11	1643	87
12	1866	87
13	2151	87
14	2570	87
15	3135	87
16	3821	87
17	4039	87
18	4283	87
19	4365	87
20	4398	87
21	4419	87
22	4987	87

prune15.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	25	5	30

Error

0.0b

Counts

30 → 5

Alt Table

Status	Error	Program
	45.1b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))
▶	45.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(*.f64 (fma.f64 x x -3) 1/6)
✓	0.1b	(pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)

Compiler

Compiled 298 to 222 computations (25.5% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

rewrite57.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

778×	`log1p-expm1-u_binary64`
778×	`expm1-log1p-u_binary64`
145×	`log1p-udef_binary64`
83×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`

Counts

1 → 41

Calls

1 calls:

56.0ms

(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	173	8
2	2051	8
3	5026	8
0	0	0
1	0	0

simplify146.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

53 → 46

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	29	87
3	50	87
4	99	87
5	236	87
6	716	87
7	1141	87
8	1143	87
9	1291	87
10	1461	87
11	1643	87
12	1866	87
13	2151	87
14	2570	87
15	3135	87
16	3821	87
17	4039	87
18	4283	87
19	4365	87
20	4398	87
21	4419	87
22	4987	87

prune24.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	1	0	1
Picked	0	1	1
Done	1	2	3
Total	47	4	51

Error

Counts

51 → 4

Alt Table

Status	Error	Program
✓	45.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(*.f64 (fma.f64 x x -3) 1/6)
	45.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 687 to 506 computations (26.3% saved)

regimes80.0ms (4.7%)

Accuracy

Total 0.1b remaining (51.8%)

Threshold costs 0.1b (51.8%)

Counts

29 → 1

Compiler

Compiled 1196 to 930 computations (22.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	11	10
3	10	10

end54.0ms (3.1%)

Compiler: Compiled 58 to 42 computations (27.6% saved)

Details

analyze4.0ms (0.2%)

sample667.0ms (38.9%)

simplify8.0ms (0.5%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite38.0ms (2.2%)

simplify146.0ms (8.5%)

prune35.0ms (2%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite47.0ms (2.7%)

simplify85.0ms (5%)

prune50.0ms (2.9%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite76.0ms (4.4%)

simplify147.0ms (8.6%)

prune15.0ms (0.9%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite57.0ms (3.3%)

simplify146.0ms (8.5%)

prune24.0ms (1.4%)

regimes80.0ms (4.7%)

simplify2.0ms (0.1%)

end54.0ms (3.1%)

Profiling