Details

analyze17.0ms (1.6%)

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)

sample13.0ms (1.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify9.0ms (0.8%)

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 (0.2%)

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)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (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)

simplify53.0ms (5%)

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

prune26.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

0.0b

Counts

40 → 3

Alt Table

Status	Error	Program
	42.5b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
▶	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)

Compiler

Compiled 517 to 384 computations (25.7% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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:

0.0ms

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

simplify47.0ms (4.5%)

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

prune8.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
▶	42.5b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)

Compiler

Compiled 190 to 123 computations (35.3% saved)

localize5.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

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

rewrite19.0ms (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:

9.0ms	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 x x -3)) 6)

simplify103.0ms (9.8%)

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

prune82.0ms (7.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
✓	42.5b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	52.3b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 -1/6 x))

Compiler

Compiled 3148 to 2362 computations (25% saved)

localize5.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 -1/6 x))
✓	0.3b	(*.f64 -1/6 x)

series8.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 -1/6 x))
2.0ms	(*.f64 -1/6 x)

rewrite9.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`associate-l_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 -1/6 x))
3.0ms	(*.f64 -1/6 x)

simplify46.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
465×	`fma-neg_binary64`
462×	`associate-l_binary64`
370×	`associate-r_binary64`
303×	`cancel-sign-sub-inv_binary64`

Counts

55 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	763
1	271	706
2	736	696
3	2298	694
4	5031	694

prune36.0ms (3.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Status	Error	Program
✓	42.5b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	52.3b	(.f64 (sqrt.f64 (fma.f64 x x -3)) (.f64 -1/6 x))

Compiler

Compiled 1212 to 893 computations (26.3% saved)

regimes84.0ms (8%)

Accuracy

Total 0.1b remaining (53.6%)

Threshold costs 0.1b (53.6%)

Counts

23 → 1

Compiler

Compiled 1247 to 923 computations (26% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample458.0ms (43.4%)

Algorithm

1×

intervals

Results

236.0ms

8000×

body

128

valid

Compiler

Compiled 55 to 40 computations (27.3% saved)

Details

analyze17.0ms (1.6%)

sample13.0ms (1.3%)

simplify9.0ms (0.8%)

prune2.0ms (0.2%)

localize3.0ms (0.3%)

series3.0ms (0.3%)

rewrite3.0ms (0.3%)

simplify53.0ms (5%)

prune26.0ms (2.4%)

localize3.0ms (0.3%)

series3.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify47.0ms (4.5%)

prune8.0ms (0.8%)

localize5.0ms (0.5%)

series7.0ms (0.7%)

rewrite19.0ms (1.8%)

simplify103.0ms (9.8%)

prune82.0ms (7.7%)

localize5.0ms (0.5%)

series8.0ms (0.7%)

rewrite9.0ms (0.8%)

simplify46.0ms (4.4%)

prune36.0ms (3.4%)

regimes84.0ms (8%)

simplify2.0ms (0.2%)

end0.0ms (0%)

sample458.0ms (43.4%)

Profiling