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)

sample748.0ms (45.6%)

Results

721.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify7.0ms (0.4%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify50.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

822×	`distribute-rgt-in_binary64`
507×	`associate-/l*_binary64`
396×	`associate-/l/_binary64`
383×	`fma-def_binary64`
343×	`times-frac_binary64`

Counts

41 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	533
1	103	499
2	216	499
3	434	499
4	1114	499
5	3350	499
6	4886	499

prune27.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Error

0.3b

Counts

40 → 4

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)
	17.4b	-1/2
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)
	47.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

Compiler

Compiled 521 to 388 computations (25.5% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

simplify46.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5148	197

prune10.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	16	4	20

Error

0.3b

Counts

20 → 4

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	17.4b	-1/2
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)
	47.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

Compiler

Compiled 194 to 127 computations (34.5% saved)

localize0.0ms (0%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.3b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	17.4b	-1/2
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)
▶	47.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

Compiler

Compiled 44 to 32 computations (27.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 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))))
✓	0.2b	(sqrt.f64 (fma.f64 x x -3))

series6.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(sqrt.f64 (fma.f64 x x -3))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

rewrite33.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
141×	`add-sqr-sqrt_binary64`
140×	`*-un-lft-identity_binary64`
140×	`add-cube-cbrt_binary64`
135×	`sqrt-prod_binary64`

Counts

2 → 192

Calls

2 calls:

8.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
1.0ms	(sqrt.f64 (fma.f64 x x -3))

simplify249.0ms (15.2%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
685×	`associate-/r/_binary64`
427×	`associate-/r*_binary64`
404×	`associate-l_binary64`
322×	`associate-r_binary64`

Counts

216 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	7416
1	561	6615
2	1739	6103
3	3644	5907
4	4719	5907
5	4927	5907

prune242.0ms (14.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	277	5	282

Error

0.2b

Counts

282 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	17.4b	-1/2
✓	0.3b	(/.f64 (fma.f64 x x -3) 6)
✓	47.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	47.1b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 1/6 (sqrt.f64 (fma.f64 x x -3))))

Compiler

Compiled 7012 to 5312 computations (24.2% saved)

regimes126.0ms (7.7%)

Accuracy

Total 0.1b remaining (52.7%)

Threshold costs 0.1b (52.7%)

Counts

35 → 1

Compiler

Compiled 2295 to 1727 computations (24.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end61.0ms (3.7%)

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

Details

analyze4.0ms (0.2%)

sample748.0ms (45.6%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite4.0ms (0.3%)

simplify50.0ms (3.1%)

prune27.0ms (1.6%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0%)

simplify46.0ms (2.8%)

prune10.0ms (0.6%)

localize0.0ms (0%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series6.0ms (0.4%)

rewrite33.0ms (2%)

simplify249.0ms (15.2%)

prune242.0ms (14.8%)

regimes126.0ms (7.7%)

simplify2.0ms (0.1%)

end61.0ms (3.7%)

Profiling