Details

analyze100.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample20.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 29 to 19 computations (34.5% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`
1×	`distribute-lft-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	13
2	24	13
3	24	13
4	24	13

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 59 to 37 computations (37.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x 2) (.f64 x x))
0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
2×	`+-commutative_binary64`
2×	`flip-+_binary64`
2×	`*-un-lft-identity_binary64`

Counts

2 → 25

Calls

2 calls:

4.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
2.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 521 to 236 computations (54.7% saved)

series33.0ms (1.5%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

20.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
7.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 380 to 277 computations (27.1% saved)

simplify88.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

465×	`cancel-sign-sub-inv_binary64`
410×	`distribute-rgt-out_binary64`
328×	`associate-l_binary64`
285×	`distribute-rgt-in_binary64`
284×	`distribute-lft-out_binary64`

Counts

46 → 39

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	601
1	196	550
2	616	541
3	2298	541
4	4422	541
5	4907	541
6	4973	541

prune22.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
	32.3b	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
	10.6b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))

Compiler

Compiled 447 to 252 computations (43.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.0b	(*.f64 x (+.f64 x 2))

rewrite35.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 36

Calls

2 calls:

5.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
4.0ms	(*.f64 x (+.f64 x 2))

Compiler

Compiled 552 to 295 computations (46.6% saved)

series30.0ms (1.3%)

Error

Counts

2 → 21

Calls

2 calls:

17.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
9.0ms	(*.f64 x (+.f64 x 2))

Compiler

Compiled 380 to 277 computations (27.1% saved)

simplify76.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

445×	`distribute-rgt-in_binary64`
434×	`distribute-lft-in_binary64`
398×	`associate-l_binary64`
361×	`cancel-sign-sub-inv_binary64`
322×	`associate-r_binary64`

Counts

57 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	656
1	203	620
2	641	611
3	2393	611
4	4118	611
5	4997	611

prune18.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
	32.3b	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
▶	10.6b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))

Compiler

Compiled 539 to 302 computations (44% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))
0.0b	(*.f64 x (+.f64 2 x))
0.0b	(*.f64 x (+.f64 2 x))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))

rewrite106.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
20×	`*-un-lft-identity_binary64`
18×	`sqrt-prod_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 118

Calls

4 calls:

9.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
4.0ms	(*.f64 x (+.f64 2 x))
4.0ms	(*.f64 x (+.f64 2 x))
3.0ms	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))

Compiler

Compiled 3165 to 1757 computations (44.5% saved)

series68.0ms (3%)

Error

Counts

4 → 42

Calls

4 calls:

20.0ms	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))
18.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
10.0ms	(*.f64 x (+.f64 2 x))
7.0ms	(*.f64 x (+.f64 2 x))

Compiler

Compiled 1358 to 922 computations (32.1% saved)

simplify171.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

611×	`distribute-rgt-in_binary64`
603×	`distribute-lft-in_binary64`
362×	`unswap-sqr_binary64`
244×	`associate--l+_binary64`
232×	`*-commutative_binary64`

Counts

160 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	2556
1	271	2341
2	927	2283
3	3095	2185
4	4480	2185
5	4882	2185
6	4980	2185
7	4899	2185

prune51.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	143	3	146

Error

Counts

146 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
▶	32.3b	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
✓	10.6b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))

Compiler

Compiled 1983 to 1125 computations (43.3% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x))))
0.1b	(.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))
1.2b	(-.f64 (.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4))
30.8b	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))

rewrite149.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

28×	`associate-*r/_binary64`
28×	`distribute-lft-in_binary64`
28×	`distribute-rgt-in_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 126

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
11.0ms	(-.f64 (.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4))
10.0ms	(.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x))))
8.0ms	(.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))

Compiler

Compiled 4647 to 2914 computations (37.3% saved)

series123.0ms (5.4%)

Error

Counts

4 → 51

Calls

4 calls:

53.0ms	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
31.0ms	(-.f64 (.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4))
14.0ms	(.f64 x (.f64 x (*.f64 (+.f64 2 x) (+.f64 2 x))))
12.0ms	(.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))

Compiler

Compiled 2142 to 1556 computations (27.4% saved)

simplify141.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

546×	`associate-/r*_binary64`
238×	`associate-/l/_binary64`
225×	`associate-/r/_binary64`
223×	`associate-l_binary64`
220×	`associate-r_binary64`

Counts

177 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3999
1	612	3679
2	2503	3416
3	4983	3416
4	4977	3416

prune65.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
	32.3b	(/.f64 (-.f64 (.f64 x (.f64 x (.f64 (+.f64 2 x) (+.f64 2 x)))) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 2 x)) (*.f64 y y)))
	10.6b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))

Compiler

Compiled 2865 to 1804 computations (37% saved)

regimes370.0ms (16.4%)

Accuracy

Total 0.0b remaining (50.6%)

Threshold costs 0.0b (50.6%)

Compiler

Compiled 6646 to 4444 computations (33.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16
2	12	16

end0.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample521.0ms (23.1%)

Algorithm

1×

intervals

Results

284.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 90 to 60 computations (33.3% saved)

Details

analyze100.0ms (4.4%)

sample20.0ms (0.9%)

simplify9.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

rewrite23.0ms (1%)

series33.0ms (1.5%)

simplify88.0ms (3.9%)

prune22.0ms (1%)

localize5.0ms (0.2%)

rewrite35.0ms (1.5%)

series30.0ms (1.3%)

simplify76.0ms (3.4%)

prune18.0ms (0.8%)

localize11.0ms (0.5%)

rewrite106.0ms (4.7%)

series68.0ms (3%)

simplify171.0ms (7.6%)

prune51.0ms (2.3%)

localize12.0ms (0.5%)

rewrite149.0ms (6.6%)

series123.0ms (5.4%)

simplify141.0ms (6.2%)

prune65.0ms (2.9%)

regimes370.0ms (16.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample521.0ms (23.1%)

Profiling