Details

analyze110.0ms (6.1%)

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%	56.2%	18.8%	6
25%	40.6%	34.4%	7
31.2%	31.2%	37.6%	8
39%	21.1%	39.9%	9
42.9%	16%	41.1%	10
47.2%	10.7%	42%	11
49.4%	8.1%	42.5%	12
51.6%	5.4%	43%	13
52.7%	4.1%	43.2%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample18.0ms (1%)

Algorithm

1×

intervals

Results

4.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 21 to 11 computations (47.6% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`
6×	`distribute-rgt-out_binary64` `distribute-lft-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	24	10
3	36	10
4	53	10
5	63	10
6	68	10
7	70	10
8	70	10

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

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

Compiler

Compiled 18 to 8 computations (55.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite34.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`flip3-+_binary64` `flip-+_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 40

Calls

1 calls:

9.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

Compiler

Compiled 517 to 121 computations (76.6% saved)

series33.0ms (1.8%)

Error

0.0b

Counts

1 → 18

Calls

1 calls:

25.0ms

(*.f64 (+.f64 x y) (+.f64 x y))

Compiler

Compiled 315 to 229 computations (27.3% saved)

simplify78.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-+l+_binary64`
594×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
187×	`*-commutative_binary64`

Counts

58 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	914
1	192	766
2	689	729
3	2167	630
4	4973	630
5	4955	630

prune24.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	6	55

Error

Counts

55 → 6

Alt Table

Status	Error	Program
	35.0b	(/.f64 (.f64 (+.f64 y x) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y))))
▶	0.0b	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
	28.7b	(.f64 x (+.f64 (.f64 y 2) x))
	31.3b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
	27.8b	(.f64 y (+.f64 y (.f64 2 x)))

Compiler

Compiled 443 to 200 computations (54.9% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

rewrite75.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`associate-*r/_binary64`
11×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `flip3-+_binary64` `flip-+_binary64`
6×	`associate-l_binary64`

Counts

3 → 66

Calls

3 calls:

8.0ms	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
7.0ms	(*.f64 y (+.f64 y x))
6.0ms	(*.f64 x (+.f64 y x))

Compiler

Compiled 1223 to 243 computations (80.1% saved)

series82.0ms (4.5%)

Error

Counts

3 → 42

Calls

3 calls:

36.0ms	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
19.0ms	(*.f64 x (+.f64 y x))
19.0ms	(*.f64 y (+.f64 y x))

Compiler

Compiled 869 to 542 computations (37.6% saved)

simplify104.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

379×	`cancel-sign-sub-inv_binary64`
372×	`associate-+l+_binary64`
360×	`associate-+r+_binary64` `*-commutative_binary64`
348×	`distribute-rgt-out_binary64`
277×	`unswap-sqr_binary64`

Counts

108 → 86

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	1341
1	351	1242
2	1364	1188
3	3036	1146
4	4462	1110
5	4738	1110

prune43.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	87	5	92

Error

Counts

92 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
▶	14.3b	(+.f64 (.f64 x (+.f64 y x)) (.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (.f64 y (+.f64 x y)))))
	28.7b	(.f64 x (+.f64 (.f64 y 2) x))
	31.3b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
	27.8b	(.f64 y (+.f64 y (.f64 2 x)))

Compiler

Compiled 920 to 268 computations (70.9% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (+.f64 x y))
0.1b	(.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (*.f64 y (+.f64 x y))))
8.1b	(sqrt.f64 (*.f64 y (+.f64 x y)))
8.1b	(sqrt.f64 (*.f64 y (+.f64 x y)))

rewrite107.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

61×	`pow1_binary64`
32×	`sqrt-pow1_binary64`
23×	`pow-prod-down_binary64`
20×	`associate-*r/_binary64`
16×	`sqrt-div_binary64`

Counts

4 → 106

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (*.f64 y (+.f64 x y))))
7.0ms	(*.f64 y (+.f64 x y))
4.0ms	(sqrt.f64 (*.f64 y (+.f64 x y)))
4.0ms	(sqrt.f64 (*.f64 y (+.f64 x y)))

Compiler

Compiled 2278 to 428 computations (81.2% saved)

series104.0ms (5.7%)

Error

Counts

4 → 48

Calls

4 calls:

23.0ms	(*.f64 y (+.f64 x y))
22.0ms	(.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (*.f64 y (+.f64 x y))))
22.0ms	(sqrt.f64 (*.f64 y (+.f64 x y)))
19.0ms	(sqrt.f64 (*.f64 y (+.f64 x y)))

Compiler

Compiled 1762 to 1014 computations (42.5% saved)

simplify117.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-/l*_binary64`
346×	`associate-/r*_binary64`
335×	`distribute-rgt-in_binary64`
333×	`distribute-lft-in_binary64`
279×	`associate-*l/_binary64`

Counts

154 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	1763
1	247	1675
2	910	1643
3	2568	1568
4	4540	1469
5	5044	1469

prune48.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	104	5	109

Error

Counts

109 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
✓	14.3b	(+.f64 (.f64 x (+.f64 y x)) (.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (.f64 y (+.f64 x y)))))
	28.7b	(.f64 x (+.f64 (.f64 y 2) x))
	31.3b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
▶	27.8b	(.f64 y (+.f64 y (.f64 2 x)))

Compiler

Compiled 1190 to 322 computations (72.9% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite23.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

5×	`add-sqr-sqrt_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l_binary64` `associate-r*_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

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

Compiler

Compiled 302 to 188 computations (37.7% saved)

series24.0ms (1.3%)

Error

Counts

1 → 12

Calls

1 calls:

22.0ms

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

Compiler

Compiled 187 to 135 computations (27.8% saved)

simplify78.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

512×	`unswap-sqr_binary64` `distribute-rgt-out_binary64`
429×	`associate-l_binary64`
341×	`associate-+l+_binary64`
319×	`associate-r_binary64`
256×	`associate-+r+_binary64`

Counts

34 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	421
1	145	379
2	509	379
3	1617	379
4	3216	379
5	4901	379
6	4943	379

prune15.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	28	5	33

Error

Counts

33 → 5

Alt Table

Status	Error	Program
	0.0b	(+.f64 (.f64 x (+.f64 y x)) (.f64 y (+.f64 y x)))
	14.3b	(+.f64 (.f64 x (+.f64 y x)) (.f64 (sqrt.f64 (.f64 y (+.f64 x y))) (sqrt.f64 (.f64 y (+.f64 x y)))))
	28.7b	(.f64 x (+.f64 (.f64 y 2) x))
	31.3b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
	27.8b	(.f64 y (+.f64 y (.f64 2 x)))

Compiler

Compiled 304 to 115 computations (62.2% saved)

regimes197.0ms (10.9%)

Accuracy

Total 0.0b remaining (52.9%)

Threshold costs 0.0b (52.9%)

Compiler

Compiled 2210 to 1257 computations (43.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	11	16
2	11	16

end6.0ms (0.3%)

Remove: (sort x y)
Compiler: Compiled 39 to 18 computations (53.8% saved)

sample450.0ms (24.8%)

Algorithm

1×

intervals

Results

143.0ms	8000×	body	128	valid
1.0ms	86×	body	128	invalid

Compiler

Compiled 85 to 46 computations (45.9% saved)

Details

analyze110.0ms (6.1%)

sample18.0ms (1%)

simplify10.0ms (0.5%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

rewrite34.0ms (1.9%)

series33.0ms (1.8%)

simplify78.0ms (4.3%)

prune24.0ms (1.3%)

localize9.0ms (0.5%)

rewrite75.0ms (4.1%)

series82.0ms (4.5%)

simplify104.0ms (5.8%)

prune43.0ms (2.4%)

localize9.0ms (0.5%)

rewrite107.0ms (5.9%)

series104.0ms (5.7%)

simplify117.0ms (6.5%)

prune48.0ms (2.7%)

localize4.0ms (0.2%)

rewrite23.0ms (1.3%)

series24.0ms (1.3%)

simplify78.0ms (4.3%)

prune15.0ms (0.8%)

regimes197.0ms (10.9%)

simplify3.0ms (0.2%)

end6.0ms (0.3%)

sample450.0ms (24.8%)

Profiling