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)

sample689.0ms (31%)

Results

649.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (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

0.1b

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 (0.2%)

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)

simplify54.0ms (2.4%)

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

prune33.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

Counts

40 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
	1.2b	(.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)))
	16.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x -3) 6) 3))
▶	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	41.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	41.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 653 to 484 computations (25.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(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)

simplify48.0ms (2.2%)

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

prune15.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	16	7	23

Error

Counts

23 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
	1.2b	(.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)))
	16.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x -3) 6) 3))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	41.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	41.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
▶	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 326 to 223 computations (31.6% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series26.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(/.f64 (cbrt.f64 (fma.f64 x x -3)) 6)
8.0ms	(cbrt.f64 (fma.f64 x x -3))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3)))
3.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))

rewrite30.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 143

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))
7.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3)))
3.0ms	(/.f64 (cbrt.f64 (fma.f64 x x -3)) 6)
1.0ms	(cbrt.f64 (fma.f64 x x -3))

simplify151.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

439×	`fma-def_binary64`
372×	`fma-neg_binary64`
342×	`associate-/l/_binary64`
272×	`cancel-sign-sub-inv_binary64`
267×	`associate-l_binary64`

Counts

191 → 250

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	3845
1	602	3574
2	2120	3312
3	4516	3259
4	4984	3259
5	4950	3259

prune246.0ms (11%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	314	7	321

Error

Counts

321 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
▶	1.2b	(.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)))
	16.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x -3) 6) 3))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	41.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	41.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 8470 to 6274 computations (25.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
	0.1b	(/.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)))

series50.0ms (2.2%)

Counts

3 → 36

Calls

3 calls:

25.0ms

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

14.0ms

(*.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)))

12.0ms

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

rewrite42.0ms (1.9%)

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 (*.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)))

10.0ms

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

4.0ms

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

simplify148.0ms (6.6%)

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

prune384.0ms (17.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	498	7	505

Error

Counts

505 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	1.2b	(.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)))
	16.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x -3) 6) 3))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	41.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	41.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 (cbrt.f64 (fma.f64 x x -3)) 6))

Compiler

Compiled 15554 to 12034 computations (22.6% saved)

regimes171.0ms (7.7%)

Accuracy

Total 0.1b remaining (60.5%)

Threshold costs 0.1b (60.5%)

Counts

47 → 1

Compiler

Compiled 3037 to 2315 computations (23.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end92.0ms (4.1%)

Compiler: Compiled 110 to 80 computations (27.3% saved)

Details

analyze4.0ms (0.2%)

sample689.0ms (31%)

simplify8.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify54.0ms (2.4%)

prune33.0ms (1.5%)

localize3.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0%)

simplify48.0ms (2.2%)

prune15.0ms (0.7%)

localize7.0ms (0.3%)

series26.0ms (1.2%)

rewrite30.0ms (1.3%)

simplify151.0ms (6.8%)

prune246.0ms (11%)

localize10.0ms (0.4%)

series50.0ms (2.2%)

rewrite42.0ms (1.9%)

simplify148.0ms (6.6%)

prune384.0ms (17.2%)

regimes171.0ms (7.7%)

simplify2.0ms (0.1%)

end92.0ms (4.1%)

Profiling