Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample612.0ms (24.9%)

Results

557.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify16.0ms (0.6%)

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

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

0.1b

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)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

rewrite7.0ms (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:

5.0ms

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

simplify91.0ms (3.7%)

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

prune46.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

Counts

40 → 5

Alt Table

Status	Error	Program
	35.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
▶	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	35.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	35.1b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 577 to 428 computations (25.8% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite1.0ms (0.1%)

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:

1.0ms

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

simplify81.0ms (3.3%)

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

prune24.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	16	5	21

Error

Counts

21 → 5

Alt Table

Status	Error	Program
▶	35.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	35.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	35.1b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 250 to 167 computations (33.2% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 6 (sqrt.f64 (fma.f64 x x -3)))
✓	0.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	11.7b	(sqrt.f64 (fma.f64 x x -3))

series26.0ms (1%)

Counts

3 → 36

Calls

3 calls:

12.0ms	(/.f64 6 (sqrt.f64 (fma.f64 x x -3)))
7.0ms	(sqrt.f64 (fma.f64 x x -3))
6.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))

rewrite87.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 233

Calls

3 calls:

17.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
10.0ms	(/.f64 6 (sqrt.f64 (fma.f64 x x -3)))
2.0ms	(sqrt.f64 (fma.f64 x x -3))

simplify225.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-/r/_binary64`
560×	`fma-def_binary64`
525×	`associate-/r*_binary64`
406×	`associate-r_binary64`
277×	`fma-neg_binary64`

Counts

269 → 320

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	8501
1	724	7591
2	2268	7120
3	4678	7114
4	5083	7114

prune305.0ms (12.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	358	0	358
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	358	5	363

Error

Counts

363 → 5

Alt Table

Status	Error	Program
✓	35.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	35.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	35.1b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 9102 to 6906 computations (24.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) 6)
✓	0.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	11.7b	(sqrt.f64 (fma.f64 x x -3))

series14.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) 6)
6.0ms	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

rewrite44.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

2 → 91

Calls

2 calls:

20.0ms	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
6.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) 6)

simplify164.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

573×	`fma-def_binary64`
349×	`associate-/l*_binary64`
303×	`distribute-rgt-in_binary64`
228×	`associate-l_binary64`
207×	`associate-r_binary64`

Counts

115 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2191
1	347	1939
2	993	1881
3	2968	1881
4	4730	1881
5	4941	1881

prune280.0ms (11.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	225	5	230

Error

Counts

230 → 5

Alt Table

Status	Error	Program
✓	35.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	35.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	35.1b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)) (sqrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 4660 to 3509 computations (24.7% saved)

regimes254.0ms (10.3%)

Accuracy

Total 0.1b remaining (85.6%)

Threshold costs 0.1b (85.6%)

Counts

40 → 1

Compiler

Compiled 2095 to 1551 computations (26% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end131.0ms (5.3%)

Compiler: Compiled 72 to 52 computations (27.8% saved)

Details

analyze1.0ms (0%)

sample612.0ms (24.9%)

simplify16.0ms (0.6%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

series6.0ms (0.2%)

rewrite7.0ms (0.3%)

simplify91.0ms (3.7%)

prune46.0ms (1.9%)

localize7.0ms (0.3%)

series5.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify81.0ms (3.3%)

prune24.0ms (1%)

localize11.0ms (0.4%)

series26.0ms (1%)

rewrite87.0ms (3.5%)

simplify225.0ms (9.1%)

prune305.0ms (12.4%)

localize11.0ms (0.4%)

series14.0ms (0.6%)

rewrite44.0ms (1.8%)

simplify164.0ms (6.6%)

prune280.0ms (11.4%)

regimes254.0ms (10.3%)

simplify4.0ms (0.2%)

end131.0ms (5.3%)

Profiling