Details

analyze8.0ms (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
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)

sample1.6s (31.4%)

Results

511.0ms	4612×	body	128	valid
480.0ms	1368×	body	1024	valid
387.0ms	1484×	body	512	valid
150.0ms	792×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify17.0ms (0.3%)

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%)

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)

localize8.0ms (0.2%)

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))
✓	3.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series11.0ms (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)))
2.0ms	(/.f64 1 (+.f64 x 1))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite187.0ms (3.7%)

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:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify403.0ms (8.1%)

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

prune871.0ms (17.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	851	2	853
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	851	3	854

Error

0.4b

Counts

854 → 3

Alt Table

Status	Error	Program
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	22.1b	(/.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)))
	34.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 33649 to 26181 computations (22.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
✓	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	12.8b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series8.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(*.f64 (+.f64 x 1) x)
2.0ms	(-.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))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`associate-*l/_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 153

Calls

4 calls:

13.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
4.0ms	(*.f64 (+.f64 x 1) x)
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Rules

613×	`associate-+l+_binary64`
601×	`associate-l_binary64`
445×	`associate-r_binary64`
364×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`

Counts

201 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3868
1	791	3063
2	3278	2739
3	5428	2739

prune299.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	295	3	298

Error

0.4b

Counts

298 → 3

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	34.4b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 13258 to 9700 computations (26.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x 1) x)
	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.4b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(/.f64 2 (*.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`associate-/r/_binary64`
8×	`associate-*l/_binary64`
4×	`frac-times_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

(/.f64 2 (*.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

simplify104.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-l_binary64`
481×	`distribute-rgt-in_binary64`
462×	`associate-/r*_binary64`
437×	`distribute-lft-in_binary64`
371×	`fma-neg_binary64`

Counts

45 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	975
1	335	727
2	1109	699
3	4461	672
4	4853	671
5	4990	671

prune193.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	186	4	190
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	188	5	193

Error

0.0b

Counts

193 → 5

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
	23.0b	(.f64 (/.f64 2 (.f64 (+.f64 x (pow.f64 x 4)) (fma.f64 x x -1))) (.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (+.f64 x 1)))
✓	0.4b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	2.2b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))
	0.1b	(.f64 (/.f64 1 (.f64 (+.f64 x 1) x)) (/.f64 2 (-.f64 x 1)))

Compiler

Compiled 3912 to 2872 computations (26.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	0.3b	(/.f64 2 (fma.f64 x x x))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite101.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64`
136×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`

Counts

2 → 159

Calls

2 calls:

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

simplify172.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-neg_binary64`
414×	`associate-/r*_binary64`
384×	`associate-/l/_binary64`
300×	`fma-def_binary64`
235×	`times-frac_binary64`

Counts

183 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4872
1	618	4739
2	1619	4586
3	4340	4553
4	4701	4553
5	4955	4553

prune236.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	222	5	227

Error

Counts

227 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	2.2b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))
	0.1b	(.f64 (/.f64 1 (.f64 (+.f64 x 1) x)) (/.f64 2 (-.f64 x 1)))
	0.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x x))) (cbrt.f64 (/.f64 2 (fma.f64 x x x)))) (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (cbrt.f64 (/.f64 2 (fma.f64 x x x))) (cbrt.f64 (-.f64 x 1))))
	23.0b	(.f64 (/.f64 2 (.f64 (+.f64 x (pow.f64 x 4)) (fma.f64 x x -1))) (.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (+.f64 x 1)))

Compiler

Compiled 4747 to 2788 computations (41.3% saved)

regimes517.0ms (10.4%)

Accuracy

Total 0.0b remaining (73.7%)

Threshold costs 0.0b (73.7%)

Counts

227 → 1

Compiler

Compiled 8706 to 6186 computations (28.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	16	14
2	17	14
3	14	14

end92.0ms (1.8%)

Compiler: Compiled 136 to 95 computations (30.1% 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

analyze8.0ms (0.2%)

sample1.6s (31.4%)

simplify17.0ms (0.3%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series11.0ms (0.2%)

rewrite187.0ms (3.7%)

simplify403.0ms (8.1%)

prune871.0ms (17.4%)

localize12.0ms (0.2%)

series8.0ms (0.2%)

rewrite45.0ms (0.9%)

simplify98.0ms (2%)

prune299.0ms (6%)

localize7.0ms (0.1%)

series4.0ms (0.1%)

rewrite12.0ms (0.2%)

simplify104.0ms (2.1%)

prune193.0ms (3.9%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite101.0ms (2%)

simplify172.0ms (3.5%)

prune236.0ms (4.7%)

regimes517.0ms (10.4%)

simplify2.0ms (0%)

end92.0ms (1.8%)

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