Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.9s (22.5%)

Results

644.0ms	4572×	body	128	valid
561.0ms	1370×	body	1024	valid
521.0ms	1562×	body	512	valid
167.0ms	752×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify20.0ms (0.2%)

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

prune7.0ms (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

7.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.2b	(+.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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	1.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series13.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.0ms	(/.f64 1 (+.f64 x 1))

rewrite368.0ms (4.3%)

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:

108.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
40.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
8.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))

simplify797.0ms (9.2%)

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 → 853

Iterations

Useful iterations: 2 (0.0ms)

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

prune2.0s (23.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	850	4	854

Error

0.1b

Counts

854 → 4

Alt Table

Status	Error	Program
✓	7.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	35.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	28.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
▶	20.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 33683 to 26207 computations (22.2% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	14.5b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series18.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
5.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
2.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite140.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`associate-*l/_binary64`
39×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

41.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
30.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
16.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
6.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify310.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-r_binary64`
442×	`distribute-rgt-in_binary64`
409×	`distribute-lft-in_binary64`
342×	`*-commutative_binary64`
307×	`fma-def_binary64`

Counts

229 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6234
1	1064	4993
2	4286	4902
3	4952	4894
4	4946	4894

prune661.0ms (7.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	321	4	325

Error

0.1b

Counts

325 → 4

Alt Table

Status	Error	Program
	20.8b	(.f64 (/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)) x) (-.f64 x 1))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1))))
✓	7.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	35.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
▶	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 16801 to 12494 computations (25.6% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series11.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
4.0ms	(*.f64 (+.f64 x 1) x)

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`associate-*l/_binary64`
8×	`associate-/r/_binary64`
8×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

27.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
22.0ms	(*.f64 (+.f64 x 1) x)

simplify159.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/r*_binary64`
506×	`distribute-rgt-in_binary64`
466×	`distribute-lft-in_binary64`
324×	`fma-def_binary64`
187×	`times-frac_binary64`

Counts

80 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1295
1	365	957
2	1226	936
3	4668	936
4	4964	936
5	4951	936

prune405.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	191	4	195

Error

0.0b

Counts

195 → 4

Alt Table

Status	Error	Program
	2.0b	(.f64 (/.f64 2 (.f64 (fma.f64 x x x) (fma.f64 x x -1))) (+.f64 x 1))
✓	7.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	35.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
▶	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))

Compiler

Compiled 3888 to 2859 computations (26.5% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 x 1))
✓	0.0b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
✓	0.3b	(/.f64 1 (fma.f64 x x x))

series16.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
5.0ms	(/.f64 1 (fma.f64 x x x))
4.0ms	(/.f64 2 (-.f64 x 1))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 152

Calls

3 calls:

28.0ms	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
5.0ms	(/.f64 2 (-.f64 x 1))
4.0ms	(/.f64 1 (fma.f64 x x x))

simplify222.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-neg_binary64`
367×	`fma-def_binary64`
342×	`associate-/l*_binary64`
317×	`associate-*l/_binary64`
297×	`times-frac_binary64`

Counts

188 → 259

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3239
1	549	2947
2	1579	2831
3	4279	2828
4	4762	2828
5	4925	2828

prune418.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	258	5	263

Error

Counts

263 → 5

Alt Table

Status	Error	Program
	2.0b	(.f64 (/.f64 2 (.f64 (fma.f64 x x x) (fma.f64 x x -1))) (+.f64 x 1))
✓	7.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	35.0b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (cbrt.f64 (pow.f64 (/.f64 2 (+.f64 x -1)) 3)))
✓	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))

Compiler

Compiled 5161 to 3355 computations (35% saved)

regimes762.0ms (8.8%)

Accuracy

Total 0.1b remaining (76.5%)

Threshold costs 0.1b (76.5%)

Counts

225 → 1

Compiler

Compiled 8358 to 6298 computations (24.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	11
1	14	11
2	11	11

end150.0ms (1.7%)

Compiler: Compiled 103 to 76 computations (26.2% 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

analyze5.0ms (0.1%)

sample1.9s (22.5%)

simplify20.0ms (0.2%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

series13.0ms (0.2%)

rewrite368.0ms (4.3%)

simplify797.0ms (9.2%)

prune2.0s (23.4%)

localize26.0ms (0.3%)

series18.0ms (0.2%)

rewrite140.0ms (1.6%)

simplify310.0ms (3.6%)

prune661.0ms (7.7%)

localize12.0ms (0.1%)

series11.0ms (0.1%)

rewrite56.0ms (0.6%)

simplify159.0ms (1.8%)

prune405.0ms (4.7%)

localize14.0ms (0.2%)

series16.0ms (0.2%)

rewrite59.0ms (0.7%)

simplify222.0ms (2.6%)

prune418.0ms (4.9%)

regimes762.0ms (8.8%)

simplify4.0ms (0%)

end150.0ms (1.7%)

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