Details

analyze9.0ms (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 (35%)

Results

511.0ms	4611×	body	128	valid
495.0ms	1353×	body	1024	valid
414.0ms	1519×	body	512	valid
152.0ms	773×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify18.0ms (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

prune3.0ms (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

9.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.2b	(+.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 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series14.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite202.0ms (4.4%)

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:

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))

simplify427.0ms (9.3%)

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

prune852.0ms (18.5%)

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

0.3b

Counts

854 → 4

Alt Table

Status	Error	Program
	31.6b	(/.f64 2 (pow.f64 x 3))
	32.6b	(fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x))
✓	9.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	25.7b	(/.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 33647 to 26177 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	17.7b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series9.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

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

rewrite55.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
55×	`prod-diff_binary64`
55×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
46×	`associate-*l/_binary64`

Counts

4 → 188

Calls

4 calls:

12.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
10.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
8.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify151.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
626×	`associate-l_binary64`
459×	`associate-r_binary64`
377×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`

Counts

236 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5247
1	827	4042
2	3405	3411
3	4686	3405
4	5206	3405

prune298.0ms (6.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	304	3	307

Error

0.3b

Counts

307 → 3

Alt Table

Status	Error	Program
	31.6b	(/.f64 2 (pow.f64 x 3))
▶	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	9.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 14301 to 10632 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.3b	(/.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 (0.3%)

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)))

simplify72.0ms (1.6%)

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

prune213.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	26.7b	(.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 3249 to 2422 computations (25.5% saved)

localize8.0ms (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)))
✓	0.2b	(/.f64 1 (fma.f64 x x x))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(*.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))

rewrite32.0ms (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:

15.0ms	(*.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))

simplify133.0ms (2.9%)

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

prune250.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	259	3	262

Error

Counts

262 → 3

Alt Table

Status	Error	Program
	0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	26.7b	(.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 5133 to 3333 computations (35.1% saved)

regimes134.0ms (2.9%)

Accuracy

Total 0.0b remaining (73.6%)

Threshold costs 0.0b (73.6%)

Counts

72 → 1

Compiler

Compiled 2328 to 1762 computations (24.3% 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

end63.0ms (1.4%)

Compiler: Compiled 75 to 54 computations (28% 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

analyze9.0ms (0.2%)

sample1.6s (35%)

simplify18.0ms (0.4%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series14.0ms (0.3%)

rewrite202.0ms (4.4%)

simplify427.0ms (9.3%)

prune852.0ms (18.5%)

localize13.0ms (0.3%)

series9.0ms (0.2%)

rewrite55.0ms (1.2%)

simplify151.0ms (3.3%)

prune298.0ms (6.5%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite12.0ms (0.3%)

simplify72.0ms (1.6%)

prune213.0ms (4.6%)

localize8.0ms (0.2%)

series9.0ms (0.2%)

rewrite32.0ms (0.7%)

simplify133.0ms (2.9%)

prune250.0ms (5.4%)

regimes134.0ms (2.9%)

simplify2.0ms (0%)

end63.0ms (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