Details

analyze36.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample37.0ms (1%)

Algorithm

1×

intervals

Results

7.0ms	54×	body	512	valid
7.0ms	38×	body	1024	valid
7.0ms	138×	body	128	valid
2.0ms	26×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	1.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite170.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

50.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

series14.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

simplify442.0ms (11.7%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 1385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune790.0ms (20.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	1384	1	1385
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1384	2	1386

Error

0.3b

Counts

1386 → 2

Alt Table

Status	Error	Program
▶	33.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	10.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 33592 to 26138 computations (22.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (pow.f64 x 7))
✓	0.3b	(/.f64 2 (pow.f64 x 3))
✓	0.6b	(/.f64 2 (pow.f64 x 5))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
36×	`unpow-prod-down_binary64`

Counts

3 → 161

Calls

3 calls:

4.0ms	(/.f64 2 (pow.f64 x 3))
3.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(/.f64 2 (pow.f64 x 7))

series55.0ms (1.5%)

Counts

3 → 0

Calls

3 calls:

22.0ms	(/.f64 2 (pow.f64 x 7))
18.0ms	(/.f64 2 (pow.f64 x 5))
14.0ms	(/.f64 2 (pow.f64 x 3))

simplify137.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
483×	`associate-l_binary64`
363×	`associate-r_binary64`
354×	`fma-def_binary64`
332×	`associate-/l/_binary64`

Counts

161 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	2314
1	369	2224
2	1086	2140
3	4048	2140
4	4948	2140
5	4981	2140

prune146.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	250	4	254

Error

Counts

254 → 4

Alt Table

Status	Error	Program
✓	33.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 7))))
	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x)) (/.f64 2 (pow.f64 x 7))))
✓	10.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 4473 to 3664 computations (18.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (pow.f64 x 7))
✓	0.1b	(/.f64 (/.f64 2 (*.f64 x x)) x)
✓	0.2b	(/.f64 2 (*.f64 x x))
	0.6b	(/.f64 2 (pow.f64 x 5))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
3.0ms	(/.f64 2 (*.f64 x x))

series25.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(/.f64 (/.f64 2 (*.f64 x x)) x)
10.0ms	(/.f64 2 (*.f64 x x))

simplify132.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
514×	`fma-def_binary64`
311×	`div-sub_binary64`
272×	`*-commutative_binary64`
270×	`cancel-sign-sub-inv_binary64`

Counts

97 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1258
1	240	1147
2	571	1138
3	1725	1111
4	2300	1099
5	3261	1099
6	4474	1099
7	4981	1099
8	4848	1099

prune161.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	289	4	293

Error

Counts

293 → 4

Alt Table

Status	Error	Program
✓	33.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 7))))
▶	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x)) (/.f64 2 (pow.f64 x 7))))
✓	10.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 5484 to 3939 computations (28.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (pow.f64 x 7))
✓	0.1b	(.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x))
✓	0.2b	(/.f64 1 (*.f64 x x))
	0.6b	(/.f64 2 (pow.f64 x 5))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
28×	`add-cbrt-cube_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`prod-exp_binary64`
22×	`times-frac_binary64`

Counts

2 → 94

Calls

2 calls:

11.0ms	(.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x))
3.0ms	(/.f64 1 (*.f64 x x))

series21.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x))
7.0ms	(/.f64 1 (*.f64 x x))

simplify121.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

655×	`times-frac_binary64`
564×	`fma-neg_binary64`
501×	`associate-*l/_binary64`
348×	`associate-/l*_binary64`
320×	`associate-*r/_binary64`

Counts

118 → 212

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1480
1	271	1160
2	907	1097
3	2955	1082
4	3585	992
5	4632	992
6	4883	992

prune223.0ms (5.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	488	0	488
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	488	4	492

Error

Counts

492 → 4

Alt Table

Status	Error	Program
✓	33.1b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) x) (/.f64 2 (pow.f64 x 7))))
✓	32.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (.f64 (/.f64 1 (.f64 x x)) (/.f64 2 x)) (/.f64 2 (pow.f64 x 7))))
✓	10.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 6462 to 4746 computations (26.6% saved)

regimes125.0ms (3.3%)

Accuracy

Total 0.4b remaining (91.8%)

Threshold costs 0.4b (91.8%)

Compiler

Compiled 1344 to 1088 computations (19% saved)

bsearch1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	123
1	52	123
2	63	123
3	70	123
4	74	123
5	75	123
6	72	123

end2.0ms (0%)

Compiler: Compiled 84 to 68 computations (19% saved)

sample1.0s (27%)

Algorithm

1×

intervals

Results

248.0ms	1312×	body	1024	valid
217.0ms	4472×	body	128	valid
207.0ms	1520×	body	512	valid
65.0ms	696×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 178 to 143 computations (19.7% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze36.0ms (1%)

sample37.0ms (1%)

simplify19.0ms (0.5%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite170.0ms (4.5%)

series14.0ms (0.4%)

simplify442.0ms (11.7%)

prune790.0ms (20.9%)

localize10.0ms (0.3%)

rewrite19.0ms (0.5%)

series55.0ms (1.5%)

simplify137.0ms (3.6%)

prune146.0ms (3.9%)

localize12.0ms (0.3%)

rewrite12.0ms (0.3%)

series25.0ms (0.7%)

simplify132.0ms (3.5%)

prune161.0ms (4.3%)

localize12.0ms (0.3%)

rewrite19.0ms (0.5%)

series21.0ms (0.5%)

simplify121.0ms (3.2%)

prune223.0ms (5.9%)

regimes125.0ms (3.3%)

bsearch1.0ms (0%)

simplify6.0ms (0.2%)

end2.0ms (0%)

sample1.0s (27%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22