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)

sample507.0ms (25.3%)

Infinites

26% of outputs are infinite.

Results

458.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (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

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.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
✓	0.0b	(/.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)

rewrite3.0ms (0.2%)

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)

simplify66.0ms (3.3%)

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

prune37.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	4	40

Error

Counts

40 → 4

Alt Table

Status	Error	Program
	31.8b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (sqrt.f64 6)) (/.f64 (cbrt.f64 (fma.f64 x x -3)) (sqrt.f64 6)))
▶	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	0.7b	(/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 6))

Compiler

Compiled 580 to 433 computations (25.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(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)

simplify55.0ms (2.7%)

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

prune14.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

Counts

20 → 4

Alt Table

Status	Error	Program
	31.8b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (sqrt.f64 6)) (/.f64 (cbrt.f64 (fma.f64 x x -3)) (sqrt.f64 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	0.7b	(/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 6))

Compiler

Compiled 253 to 172 computations (32% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 6))
✓	0.6b	(/.f64 (fma.f64 x x -3) (sqrt.f64 6))

series35.0ms (1.7%)

Counts

2 → 24

Calls

2 calls:

28.0ms	(/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 6))
7.0ms	(/.f64 (fma.f64 x x -3) (sqrt.f64 6))

rewrite39.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
154×	`add-sqr-sqrt_binary64`
154×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

2 → 218

Calls

2 calls:

8.0ms	(/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 6))
3.0ms	(/.f64 (fma.f64 x x -3) (sqrt.f64 6))

simplify380.0ms (19%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/l/_binary64`
488×	`distribute-rgt-in_binary64`
480×	`distribute-lft-in_binary64`
392×	`fma-def_binary64`
308×	`times-frac_binary64`

Counts

242 → 257

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	222	6570
1	466	6364
2	869	6082
3	1902	5899
4	2663	5824
5	4748	5824
6	4983	5824
7	4999	5824
8	4894	5824

prune325.0ms (16.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	258	3	261

Error

Counts

261 → 3

Alt Table

Status	Error	Program
	0.6b	(/.f64 (/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 (sqrt.f64 6))) (sqrt.f64 (sqrt.f64 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
▶	0.0b	(fma.f64 x (/.f64 x 6) -1/2)

Compiler

Compiled 5631 to 4711 computations (16.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (/.f64 x 6) -1/2)

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

simplify56.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
610×	`associate-l_binary64`
471×	`associate-+l+_binary64`
452×	`associate-r_binary64`
423×	`associate-/r*_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	214
1	35	197
2	67	197
3	166	197
4	586	197
5	2881	197
6	5257	197

prune14.0ms (0.7%)

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

Counts

19 → 3

Alt Table

Status	Error	Program
	0.6b	(/.f64 (/.f64 (/.f64 (fma.f64 x x -3) (sqrt.f64 6)) (sqrt.f64 (sqrt.f64 6))) (sqrt.f64 (sqrt.f64 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.0b	(fma.f64 x (/.f64 x 6) -1/2)

Compiler

Compiled 178 to 133 computations (25.3% saved)

regimes342.0ms (17.1%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

61 → 1

Compiler

Compiled 3541 to 2927 computations (17.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end80.0ms (4%)

Compiler: Compiled 44 to 34 computations (22.7% saved)

Details

analyze1.0ms (0%)

sample507.0ms (25.3%)

simplify10.0ms (0.5%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify66.0ms (3.3%)

prune37.0ms (1.8%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite1.0ms (0%)

simplify55.0ms (2.7%)

prune14.0ms (0.7%)

localize6.0ms (0.3%)

series35.0ms (1.7%)

rewrite39.0ms (2%)

simplify380.0ms (19%)

prune325.0ms (16.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0%)

simplify56.0ms (2.8%)

prune14.0ms (0.7%)

regimes342.0ms (17.1%)

simplify3.0ms (0.2%)

end80.0ms (4%)

Profiling