Details

analyze10.0ms (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)

sample1.9s (33.7%)

Results

649.0ms	1382×	body	1024	valid
546.0ms	4537×	body	128	valid
534.0ms	1608×	body	512	valid
142.0ms	729×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify15.0ms (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

prune4.0ms (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

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(+.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 (0.1%)

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))
✓	2.3b	(+.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 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite191.0ms (3.4%)

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:

49.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
5.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 x 1))

simplify421.0ms (7.4%)

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

prune1.1s (18.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	850	3	853
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	851	3	854

Error

0.2b

Counts

854 → 3

Alt Table

Status	Error	Program
	30.3b	(+.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)))))
▶	27.0b	(/.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)))
	33.9b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))

Compiler

Compiled 33677 to 26202 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 1 x) (.f64 (+.f64 x 1) 2))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	17.2b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series11.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(*.f64 (+.f64 x 1) x)
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))

rewrite46.0ms (0.8%)

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:

14.0ms	(+.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))
6.0ms	(*.f64 (+.f64 x 1) x)
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify111.0ms (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	3792
1	791	3063
2	3278	2739
3	5428	2739

prune312.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	295	3	298

Error

0.2b

Counts

298 → 3

Alt Table

Status	Error	Program
	30.3b	(+.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)))))
✓	27.0b	(/.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)))
▶	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 13286 to 9721 computations (26.8% saved)

localize6.0ms (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)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite10.0ms (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:

8.0ms

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

simplify82.0ms (1.4%)

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

prune192.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	190	5	195

Error

0.0b

Counts

195 → 5

Alt Table

Status	Error	Program
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	3.5b	(/.f64 2 (/.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x -1)) (+.f64 x 1)))
	28.1b	(.f64 (/.f64 2 (.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)) x) (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1))) (+.f64 x 1)))
▶	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))

Compiler

Compiled 3919 to 2873 computations (26.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 x 1))
✓	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
✓	0.7b	(/.f64 1 (fma.f64 x x x))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite33.0ms (0.6%)

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:

17.0ms	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
4.0ms	(/.f64 2 (-.f64 x 1))
2.0ms	(/.f64 1 (fma.f64 x x x))

simplify130.0ms (2.3%)

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

prune234.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	259	5	264

Error

Counts

264 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (cbrt.f64 (pow.f64 (/.f64 2 (+.f64 x -1)) 3)))
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 (/.f64 2 (+.f64 x -1)) (fma.f64 x x x))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	28.1b	(.f64 (/.f64 2 (.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 1 3)) x) (-.f64 (.f64 x x) (.f64 1 1)))) (.f64 (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (*.f64 x 1))) (+.f64 x 1)))

Compiler

Compiled 5159 to 3352 computations (35% saved)

regimes772.0ms (13.6%)

Accuracy

Total 0.1b remaining (89.2%)

Threshold costs 0.1b (89.2%)

Counts

336 → 1

Compiler

Compiled 14314 to 11323 computations (20.9% saved)

simplify2.0ms (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

end77.0ms (1.4%)

Compiler: Compiled 101 to 73 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

analyze10.0ms (0.2%)

sample1.9s (33.7%)

simplify15.0ms (0.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series11.0ms (0.2%)

rewrite191.0ms (3.4%)

simplify421.0ms (7.4%)

prune1.1s (18.5%)

localize12.0ms (0.2%)

series11.0ms (0.2%)

rewrite46.0ms (0.8%)

simplify111.0ms (2%)

prune312.0ms (5.5%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify82.0ms (1.4%)

prune192.0ms (3.4%)

localize7.0ms (0.1%)

series9.0ms (0.2%)

rewrite33.0ms (0.6%)

simplify130.0ms (2.3%)

prune234.0ms (4.1%)

regimes772.0ms (13.6%)

simplify2.0ms (0%)

end77.0ms (1.4%)

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