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)

sample70.0ms (1.5%)

Algorithm

1×

intervals

Results

15.0ms	53×	body	512	valid
12.0ms	141×	body	128	valid
7.0ms	38×	body	1024	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify16.0ms (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

7.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize9.0ms (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))
✓	1.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series15.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

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

rewrite196.0ms (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:

50.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
23.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify468.0ms (10.3%)

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

prune869.0ms (19.1%)

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

0.5b

Counts

854 → 4

Alt Table

Status	Error	Program
✓	7.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	26.2b	(/.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)))
	32.5b	(+.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)))))
	26.8b	(/.f64 (.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))

Compiler

Compiled 33741 to 26255 computations (22.2% saved)

localize12.0ms (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 x 1) x)
✓	0.0b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	19.5b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series13.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(*.f64 (+.f64 x 1) x)
1.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite59.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
54×	`prod-diff_binary64`
51×	`add-cube-cbrt_binary64`
48×	`associate-*l/_binary64`

Counts

4 → 195

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))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
9.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
6.0ms	(*.f64 (+.f64 x 1) x)

simplify126.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-l_binary64`
626×	`associate-+l+_binary64`
466×	`associate-r_binary64`
366×	`distribute-rgt-in_binary64`
348×	`distribute-lft-in_binary64`

Counts

243 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	4962
1	814	4219
2	3340	4103
3	5575	4103

prune344.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	353	3	356

Error

0.5b

Counts

356 → 3

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	32.5b	(+.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)))))
✓	7.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 16383 to 12065 computations (26.4% saved)

localize7.0ms (0.2%)

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))
✓	0.5b	(/.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)))

rewrite11.0ms (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)))

simplify78.0ms (1.7%)

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

prune300.0ms (6.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	192	3	195

Error

0.0b

Counts

195 → 3

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	0.5b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	27.4b	(.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 3859 to 2832 computations (26.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`

Counts

2 → 125

Calls

2 calls:

12.0ms	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
5.0ms	(/.f64 2 (*.f64 (+.f64 x 1) x))

simplify126.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

425×	`associate-/l/_binary64`
408×	`fma-def_binary64`
325×	`times-frac_binary64`
297×	`distribute-rgt-in_binary64`
276×	`fma-neg_binary64`

Counts

149 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	3590
1	599	3247
2	1752	3054
3	4511	3050
4	5044	3050

prune268.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	237	4	241

Error

Counts

241 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	0.5b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	16.2b	(/.f64 (*.f64 (sqrt.f64 (/.f64 2 (fma.f64 x x x))) (sqrt.f64 (/.f64 2 (fma.f64 x x x)))) (-.f64 x 1))
	27.4b	(.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 4573 to 3299 computations (27.9% saved)

regimes353.0ms (7.8%)

Accuracy

Total 0.1b remaining (82%)

Threshold costs 0.1b (82%)

Counts

149 → 1

Compiler

Compiled 5404 to 4106 computations (24% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16
2	17	16
3	15	16

end0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample1.1s (25.2%)

Algorithm

1×

intervals

Results

293.0ms	1378×	body	1024	valid
272.0ms	4343×	body	128	valid
249.0ms	1503×	body	512	valid
73.0ms	776×	body	256	valid

Compiler

Compiled 99 to 72 computations (27.3% 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%)

sample70.0ms (1.5%)

simplify16.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series15.0ms (0.3%)

rewrite196.0ms (4.3%)

simplify468.0ms (10.3%)

prune869.0ms (19.1%)

localize12.0ms (0.3%)

series13.0ms (0.3%)

rewrite59.0ms (1.3%)

simplify126.0ms (2.8%)

prune344.0ms (7.6%)

localize7.0ms (0.2%)

series4.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify78.0ms (1.7%)

prune300.0ms (6.6%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite28.0ms (0.6%)

simplify126.0ms (2.8%)

prune268.0ms (5.9%)

regimes353.0ms (7.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (25.2%)

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