Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.5s (28.7%)

Results

1.1s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify335.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
✓	0.0b	(*.f64 6 (-.f64 x 1))
✓	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

series58.0ms (1.1%)

Counts

3 → 18

Calls

3 calls:

44.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
10.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
3.0ms	(*.f64 6 (-.f64 x 1))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 98

Calls

3 calls:

21.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
11.0ms	(*.f64 6 (-.f64 x 1))
9.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

simplify166.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

431×	`distribute-rgt-in_binary64`
407×	`times-frac_binary64`
393×	`associate-l_binary64`
389×	`fma-def_binary64`
383×	`distribute-lft-in_binary64`

Counts

116 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1561
1	341	1205
2	1073	1190
3	4684	1190
4	4933	1190

prune275.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	148	3	151

Error

Counts

151 → 3

Alt Table

Status	Error	Program
	18.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 6 6) 6) (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1))) (.f64 (.f64 (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x)))) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))))
✓	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 3508 to 2629 computations (25.1% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.1b	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series78.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

40.0ms	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
29.0ms	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
8.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

3 → 104

Calls

3 calls:

12.0ms	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
9.0ms	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

simplify152.0ms (3%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
413×	`associate-/r/_binary64`
378×	`associate-+r+_binary64`
357×	`associate-+l+_binary64`
326×	`associate-/r*_binary64`

Counts

113 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	2657
1	255	2462
2	706	2406
3	2159	2396
4	4947	2396

prune222.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
▶	18.7b	(cbrt.f64 (.f64 (.f64 (.f64 6 6) 6) (/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 3943 to 2806 computations (28.8% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1))
✓	0.1b	(*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.9b	(cbrt.f64 (.f64 (.f64 (.f64 6 6) 6) (/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	17.5b	(/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series146.0ms (2.8%)

Counts

4 → 21

Calls

4 calls:

86.0ms	(cbrt.f64 (.f64 (.f64 (.f64 6 6) 6) (/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
28.0ms	(/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
27.0ms	(*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
5.0ms	(.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1))

rewrite147.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`frac-times_binary64`
54×	`flip--_binary64`
54×	`flip3--_binary64`
50×	`add-cbrt-cube_binary64`
47×	`add-exp-log_binary64`

Counts

4 → 187

Calls

4 calls:

34.0ms	(/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
28.0ms	(cbrt.f64 (.f64 (.f64 (.f64 6 6) 6) (/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
27.0ms	(.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1))
11.0ms	(*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

simplify284.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
390×	`associate-*l/_binary64`
302×	`associate-*r/_binary64`
280×	`associate-l_binary64`
230×	`distribute-rgt-in_binary64`

Counts

208 → 281

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	8067
1	528	4122
2	2150	3767
3	4877	3766
4	5124	3766

prune579.0ms (11.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	281	3	284

Error

Counts

284 → 3

Alt Table

Status	Error	Program
✓	18.7b	(cbrt.f64 (.f64 (.f64 (.f64 6 6) 6) (/.f64 (.f64 (.f64 (-.f64 x 1) (-.f64 x 1)) (-.f64 x 1)) (.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 14696 to 10688 computations (27.3% saved)

regimes905.0ms (17.6%)

Accuracy

Total 0.0b remaining (53.7%)

Threshold costs 0.0b (53.7%)

Counts

194 → 1

Compiler

Compiled 11174 to 8597 computations (23.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	18	19
2	19	19
3	17	19

end149.0ms (2.9%)

Compiler: Compiled 100 to 77 computations (23% saved)

Details

analyze4.0ms (0.1%)

sample1.5s (28.7%)

simplify335.0ms (6.5%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

series58.0ms (1.1%)

rewrite52.0ms (1%)

simplify166.0ms (3.2%)

prune275.0ms (5.4%)

localize15.0ms (0.3%)

series78.0ms (1.5%)

rewrite42.0ms (0.8%)

simplify152.0ms (3%)

prune222.0ms (4.3%)

localize25.0ms (0.5%)

series146.0ms (2.8%)

rewrite147.0ms (2.9%)

simplify284.0ms (5.5%)

prune579.0ms (11.3%)

regimes905.0ms (17.6%)

simplify6.0ms (0.1%)

end149.0ms (2.9%)

Profiling