Details

analyze703.0ms (17.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
43.7%	56.2%	0%	6
46.9%	53.1%	0%	7
48.4%	51.5%	0%	8
48.4%	51.5%	0%	9
48.4%	51.5%	0%	10
48.6%	51.3%	0%	11
48.6%	51.3%	0%	12
48.7%	51.3%	0%	13
48.7%	51.3%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (49.7%)

Results

1.2s	2639×	body	8192	exit
756.0ms	8256×	body	128	valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify9.0ms (0.2%)

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

0.1b

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)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (0.1%)

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)

simplify52.0ms (1.3%)

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

prune30.0ms (0.7%)

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
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
▶	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	42.3b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	42.3b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 593 to 440 computations (25.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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)

simplify47.0ms (1.2%)

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

prune12.0ms (0.3%)

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
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
▶	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	42.3b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	42.3b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 266 to 179 computations (32.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.2b	(cbrt.f64 (/.f64 (fma.f64 x x -3) 6))
✓	0.8b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))

series59.0ms (1.5%)

Counts

3 → 36

Calls

3 calls:

30.0ms

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

17.0ms

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

12.0ms

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

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

11.0ms

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

11.0ms

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

2.0ms

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

simplify152.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

556×	`times-frac_binary64`
505×	`fma-def_binary64`
343×	`cancel-sign-sub-inv_binary64`
266×	`associate-r_binary64`
257×	`associate-l_binary64`

Counts

196 → 275

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	5193
1	569	4860
2	1787	4430
3	4463	4369
4	5358	4369

prune407.0ms (10.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	498	5	503

Error

Counts

503 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	42.3b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
▶	42.3b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 15552 to 12032 computations (22.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 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))

series7.0ms (0.2%)

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))

rewrite21.0ms (0.5%)

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:

8.0ms	(*.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)

simplify98.0ms (2.4%)

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

prune92.0ms (2.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	149	5	154

Error

Counts

154 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.1b	(fma.f64 1/6 (*.f64 x x) -1/2)
	42.3b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	42.3b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 3166 to 2376 computations (25% saved)

regimes176.0ms (4.4%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

48 → 1

Compiler

Compiled 2876 to 2186 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end80.0ms (2%)

Compiler: Compiled 80 to 58 computations (27.5% saved)

Details

analyze703.0ms (17.5%)

sample2.0s (49.7%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify52.0ms (1.3%)

prune30.0ms (0.7%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify47.0ms (1.2%)

prune12.0ms (0.3%)

localize7.0ms (0.2%)

series59.0ms (1.5%)

rewrite40.0ms (1%)

simplify152.0ms (3.8%)

prune407.0ms (10.1%)

localize8.0ms (0.2%)

series7.0ms (0.2%)

rewrite21.0ms (0.5%)

simplify98.0ms (2.4%)

prune92.0ms (2.3%)

regimes176.0ms (4.4%)

simplify2.0ms (0%)

end80.0ms (2%)

Profiling