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)

sample54.0ms (1.4%)

Algorithm

1×

intervals

Results

9.0ms	48×	body	1024	valid
7.0ms	145×	body	128	valid
6.0ms	47×	body	512	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify17.0ms (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

7.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.6b	(+.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(+.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))

rewrite173.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

714×	`*-un-lft-identity_binary64`
700×	`times-frac_binary64`
519×	`add-sqr-sqrt_binary64`
485×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

2 → 578

Calls

2 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))

simplify375.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
394×	`times-frac_binary64`
341×	`distribute-rgt-in_binary64`
252×	`cancel-sign-sub-inv_binary64`
217×	`fma-def_binary64`

Counts

602 → 723

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	358	17897
1	859	12377
2	2225	8575
3	4306	8575
4	4784	8575

prune773.0ms (19.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	720	3	723
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	720	4	724

Error

0.1b

Counts

724 → 4

Alt Table

Status	Error	Program
✓	7.6b	(+.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)))))
	33.6b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
▶	23.9b	(/.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 30921 to 23996 computations (22.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
✓	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 (+.f64 x 1) x) (-.f64 x 1))
✓	16.3b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series11.0ms (0.3%)

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))
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))

rewrite73.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`associate-*l/_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`

Counts

4 → 188

Calls

4 calls:

19.0ms	(/.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)))
13.0ms	(+.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))
4.0ms	(*.f64 (+.f64 x 1) x)

simplify204.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-r_binary64`
441×	`distribute-rgt-in_binary64`
419×	`distribute-lft-in_binary64`
360×	`*-commutative_binary64`
307×	`fma-def_binary64`

Counts

236 → 330

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	5937
1	1057	4948
2	4251	4897
3	4869	4897
4	4988	4897
5	4948	4897

prune424.0ms (10.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	368	2	370
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	371	3	374

Error

0.0b

Counts

374 → 3

Alt Table

Status	Error	Program
	33.6b	(+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5)))
	23.9b	(/.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))
▶	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 18462 to 13437 computations (27.2% 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 (+.f64 x 1) x) (-.f64 x 1))
✓	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

rewrite10.0ms (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:

8.0ms

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

simplify77.0ms (2%)

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

prune139.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	192	3	195

Error

0.0b

Counts

195 → 3

Alt Table

Status	Error	Program
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 2 (*.f64 (fma.f64 x x x) (-.f64 x 1)))
▶	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))

Compiler

Compiled 3821 to 2800 computations (26.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.2%)

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))

rewrite28.0ms (0.7%)

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:

10.0ms	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
2.0ms	(/.f64 2 (fma.f64 x x x))

simplify186.0ms (4.8%)

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

prune137.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	221	4	225

Error

Counts

225 → 4

Alt Table

Status	Error	Program
	1.5b	(/.f64 (/.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 (-.f64 x 1) (/.f64 (cbrt.f64 2) (cbrt.f64 (fma.f64 x x x)))))
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(/.f64 2 (*.f64 (fma.f64 x x x) (-.f64 x 1)))
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))

Compiler

Compiled 4694 to 2744 computations (41.5% saved)

regimes105.0ms (2.7%)

Accuracy

Total 0.1b remaining (76.2%)

Threshold costs 0.1b (76.2%)

Counts

52 → 1

Compiler

Compiled 1676 to 1244 computations (25.8% saved)

simplify2.0ms (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

end0.0ms (0%)

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

sample1.0s (26.5%)

Algorithm

1×

intervals

Results

252.0ms	1272×	body	1024	valid
238.0ms	4489×	body	128	valid
210.0ms	1474×	body	512	valid
81.0ms	765×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 90 to 59 computations (34.4% 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%)

sample54.0ms (1.4%)

simplify17.0ms (0.4%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series7.0ms (0.2%)

rewrite173.0ms (4.5%)

simplify375.0ms (9.7%)

prune773.0ms (19.9%)

localize14.0ms (0.4%)

series11.0ms (0.3%)

rewrite73.0ms (1.9%)

simplify204.0ms (5.3%)

prune424.0ms (10.9%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite10.0ms (0.3%)

simplify77.0ms (2%)

prune139.0ms (3.6%)

localize5.0ms (0.1%)

series7.0ms (0.2%)

rewrite28.0ms (0.7%)

simplify186.0ms (4.8%)

prune137.0ms (3.5%)

regimes105.0ms (2.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (26.5%)

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