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)

sample1.7s (33.4%)

Results

528.0ms	1349×	body	1024	valid
514.0ms	4604×	body	128	valid
456.0ms	1547×	body	512	valid
151.0ms	756×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify16.0ms (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

9.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.9b	(+.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 3 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))
✓	2.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite202.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

739×	`*-un-lft-identity_binary64`
721×	`times-frac_binary64`
548×	`add-sqr-sqrt_binary64`
498×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

3 → 629

Calls

3 calls:

52.0ms	(+.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))
5.0ms	(/.f64 1 (-.f64 x 1))

simplify520.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

885×	`fma-neg_binary64`
394×	`times-frac_binary64`
267×	`cancel-sign-sub-inv_binary64`
226×	`fma-def_binary64`
176×	`exp-prod_binary64`

Counts

665 → 800

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	18730
1	936	13173
2	2405	9307
3	4121	9307
4	4989	9307
5	4989	9307
6	4766	9307

prune876.0ms (17.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	798	2	800
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	798	3	801

Error

0.2b

Counts

801 → 3

Alt Table

Status	Error	Program
▶	24.9b	(/.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)))
	32.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 32538 to 25286 computations (22.3% saved)

localize14.0ms (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))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	16.5b	(+.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))

rewrite58.0ms (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:

14.0ms	(+.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))
9.0ms	(.f64 (-.f64 (.f64 1 x) (*.f64 (+.f64 x 1) 2)) (-.f64 x 1))
5.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

simplify155.0ms (3.1%)

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

prune316.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	303	3	306

Error

0.2b

Counts

306 → 3

Alt Table

Status	Error	Program
	32.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
▶	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	9.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 14325 to 10652 computations (25.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`associate-*l/_binary64`
8×	`associate-/r/_binary64`
8×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

9.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
5.0ms	(*.f64 (+.f64 x 1) x)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/r*_binary64`
506×	`distribute-rgt-in_binary64`
466×	`distribute-lft-in_binary64`
324×	`fma-def_binary64`
187×	`times-frac_binary64`

Counts

80 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1295
1	365	957
2	1226	936
3	4668	936
4	4964	936
5	4951	936

prune182.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	188	6	194

Error

Counts

194 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 2 (.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 (+.f64 x 1)) x)) (-.f64 x 1)))
	18.5b	(.f64 (/.f64 2 (.f64 x (.f64 (fma.f64 x x -1) (fma.f64 x x -1)))) (.f64 (-.f64 x 1) (+.f64 x 1)))
▶	0.1b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	0.6b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)) (sqrt.f64 2)))
	32.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
	1.1b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 3982 to 2915 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)
✓	0.0b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
✓	0.4b	(/.f64 2 (*.f64 (+.f64 x 1) x))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite27.0ms (0.5%)

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:

10.0ms	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
6.0ms	(/.f64 2 (*.f64 (+.f64 x 1) x))

simplify150.0ms (3%)

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

prune277.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Error

Counts

243 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (*.f64 (+.f64 x 1) x)) (-.f64 x 1))
	16.4b	(.f64 (/.f64 2 (+.f64 x (pow.f64 x 4))) (-.f64 (/.f64 (.f64 x x) (-.f64 x 1)) 1))
	0.2b	(/.f64 (/.f64 (/.f64 2 (fma.f64 x x x)) (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (cbrt.f64 (-.f64 x 1)))
	0.2b	(*.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x)) 1)
	1.1b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))

Compiler

Compiled 4566 to 3298 computations (27.8% saved)

regimes315.0ms (6.2%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

148 → 1

Compiler

Compiled 4726 to 3524 computations (25.4% saved)

simplify2.0ms (0%)

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

end80.0ms (1.6%)

Compiler: Compiled 106 to 79 computations (25.5% 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%)

sample1.7s (33.4%)

simplify16.0ms (0.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series9.0ms (0.2%)

rewrite202.0ms (4%)

simplify520.0ms (10.3%)

prune876.0ms (17.4%)

localize14.0ms (0.3%)

series9.0ms (0.2%)

rewrite58.0ms (1.2%)

simplify155.0ms (3.1%)

prune316.0ms (6.3%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite19.0ms (0.4%)

simplify81.0ms (1.6%)

prune182.0ms (3.6%)

localize6.0ms (0.1%)

series7.0ms (0.1%)

rewrite27.0ms (0.5%)

simplify150.0ms (3%)

prune277.0ms (5.5%)

regimes315.0ms (6.2%)

simplify2.0ms (0%)

end80.0ms (1.6%)

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