Details

analyze64.0ms (0.9%)

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)

sample59.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	37×	body	1024	valid
14.0ms	55×	body	512	valid
12.0ms	139×	body	128	valid
4.0ms	25×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify31.0ms (0.4%)

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

prune5.0ms (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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize23.0ms (0.3%)

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))
✓	2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series22.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

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

rewrite412.0ms (5.6%)

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)))
48.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
15.0ms	(/.f64 1 (+.f64 x 1))
9.0ms	(/.f64 1 (-.f64 x 1))

simplify655.0ms (8.9%)

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

prune1.6s (22.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	849	4	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	849	5	854

Error

0.1b

Counts

854 → 5

Alt Table

Status	Error	Program
	29.0b	(+.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)))))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	26.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))
	28.9b	(/.f64 (fma.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))
	28.3b	(/.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 33743 to 26249 computations (22.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 x 1))
	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	1.3b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))
	2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))

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 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
452×	`fma-neg_binary64`
402×	`neg-mul-1_binary64`
281×	`times-frac_binary64`
280×	`cancel-sign-sub-inv_binary64`

Counts

23 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	537
1	152	486
2	424	480
3	1205	480
4	3448	480
5	4191	480
6	5081	480

prune1.1s (14.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	809	1	810
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	810	5	815

Error

0.1b

Counts

815 → 5

Alt Table

Status	Error	Program
✓	26.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	29.2b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))))
	28.9b	(/.f64 (fma.f64 (+.f64 x -1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))
▶	28.3b	(/.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 34319 to 27039 computations (21.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	20.0b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series10.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.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)))
3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
1.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
1.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite99.0ms (1.3%)

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:

25.0ms	(/.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)))
14.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
12.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify222.0ms (3%)

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

prune804.0ms (10.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	318	3	321
Fresh	1	1	2
Picked	1	0	1
Done	2	0	2
Total	322	4	326

Error

0.0b

Counts

326 → 4

Alt Table

Status	Error	Program
	28.3b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1)) (-.f64 (pow.f64 x 3) x))
	28.3b	(.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 (.f64 x x) (.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))
▶	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	29.2b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))))

Compiler

Compiled 16805 to 12493 computations (25.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite34.0ms (0.5%)

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:

18.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
9.0ms	(*.f64 (+.f64 x 1) x)

simplify129.0ms (1.7%)

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

prune183.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
	0.5b	(/.f64 (sqrt.f64 2) (/.f64 (fma.f64 x x -1) (/.f64 (sqrt.f64 2) x)))
	20.5b	(.f64 (sqrt.f64 (/.f64 2 (.f64 x (fma.f64 x x -1)))) (sqrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))))
	0.0b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
	0.1b	(/.f64 -2 (*.f64 x (neg.f64 (fma.f64 x x -1))))

Compiler

Compiled 3820 to 2806 computations (26.5% saved)

regimes332.0ms (4.5%)

Accuracy

Total 0.0b remaining (71.4%)

Threshold costs 0.0b (71.4%)

Counts

81 → 1

Compiler

Compiled 3330 to 2531 computations (24% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	13	14
2	14	14
3	12	14

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample1.5s (19.7%)

Algorithm

1×

intervals

Results

332.0ms	1328×	body	1024	valid
318.0ms	4475×	body	128	valid
284.0ms	1471×	body	512	valid
141.0ms	726×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 83 to 60 computations (27.7% 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

analyze64.0ms (0.9%)

sample59.0ms (0.8%)

simplify31.0ms (0.4%)

prune5.0ms (0.1%)

localize23.0ms (0.3%)

series22.0ms (0.3%)

rewrite412.0ms (5.6%)

simplify655.0ms (8.9%)

prune1.6s (22.3%)

localize12.0ms (0.2%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify77.0ms (1%)

prune1.1s (14.5%)

localize14.0ms (0.2%)

series10.0ms (0.1%)

rewrite99.0ms (1.3%)

simplify222.0ms (3%)

prune804.0ms (10.9%)

localize12.0ms (0.2%)

series10.0ms (0.1%)

rewrite34.0ms (0.5%)

simplify129.0ms (1.7%)

prune183.0ms (2.5%)

regimes332.0ms (4.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (19.7%)

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