Details

analyze131.0ms (7.1%)

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

5.0ms	256×	body	128	valid
0.0ms	3×	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-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

prune1.0ms (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)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

rewrite24.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`
6×	`swap-sqr_binary64`

Counts

1 → 40

Calls

1 calls:

6.0ms

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

Compiler

Compiled 517 to 121 computations (76.6% saved)

series25.0ms (1.4%)

Error

0.0b

Counts

1 → 18

Calls

1 calls:

20.0ms

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

Compiler

Compiled 315 to 229 computations (27.3% saved)

simplify76.0ms (4.2%)

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	66	914
1	192	766
2	689	729
3	2167	630
4	4973	630
5	4955	630

prune16.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Error

0.0b

Counts

55 → 3

Alt Table

Status	Error	Program
	43.5b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (-.f64 x y)))
▶	33.5b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))

Compiler

Compiled 393 to 166 computations (57.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 y x))
0.4b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`*-un-lft-identity_binary64`
8×	`sqrt-prod_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`unpow-prod-down_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
3.0ms	(sqrt.f64 (+.f64 y x))

Compiler

Compiled 418 to 197 computations (52.9% saved)

series42.0ms (2.3%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

28.0ms	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)
10.0ms	(sqrt.f64 (+.f64 y x))

Compiler

Compiled 489 to 379 computations (22.5% saved)

simplify98.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

365×	`exp-prod_binary64`
321×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`
283×	`*-commutative_binary64`
252×	`unswap-sqr_binary64`

Counts

58 → 41

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	83	650
1	169	539
2	346	521
3	984	516
4	2584	498
5	4404	484
6	4932	484
7	4840	484

prune17.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
▶	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
	1.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
✓	33.5b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)

Compiler

Compiled 358 to 200 computations (44.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite30.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 35

Calls

2 calls:

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

Compiler

Compiled 670 to 354 computations (47.2% saved)

series45.0ms (2.4%)

Error

Counts

2 → 30

Calls

2 calls:

23.0ms	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
18.0ms	(.f64 x (+.f64 x (.f64 2 y)))

Compiler

Compiled 584 to 401 computations (31.3% saved)

simplify90.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

459×	`sub-neg_binary64`
414×	`distribute-rgt-in_binary64`
400×	`distribute-lft-in_binary64`
297×	`+-commutative_binary64`
211×	`*-commutative_binary64`

Counts

65 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	928
1	230	853
2	768	841
3	2383	841
4	3724	841
5	4980	841
6	4936	841

prune20.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	56	4	60

Error

Counts

60 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
▶	1.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
✓	33.5b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)

Compiler

Compiled 603 to 331 computations (45.1% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
8.5b	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
8.5b	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
8.5b	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

rewrite113.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

107×	`cbrt-prod_binary64`
52×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
42×	`unpow-prod-down_binary64`
25×	`unswap-sqr_binary64`

Counts

4 → 132

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
3.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
3.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
3.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

Compiler

Compiled 3467 to 1950 computations (43.8% saved)

series180.0ms (9.8%)

Error

Counts

4 → 60

Calls

4 calls:

45.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
43.0ms	(*.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
39.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))
39.0ms	(cbrt.f64 (pow.f64 (+.f64 x y) 2))

Compiler

Compiled 3376 to 2563 computations (24.1% saved)

simplify193.0ms (10.5%)

Algorithm

1×	egg-herbie

Rules

424×	`distribute-rgt-in_binary64`
421×	`distribute-lft-in_binary64`
354×	`associate-l_binary64`
305×	`associate-r_binary64`
209×	`exp-prod_binary64`

Counts

192 → 179

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	3538
1	237	3338
2	543	3122
3	1663	3083
4	3621	2578
5	4311	2578
6	4740	2578
7	4930	2578

prune41.0ms (2.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	179	4	183

Error

Counts

183 → 4

Alt Table

Status	Error	Program
	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
	0.0b	(+.f64 (.f64 x (+.f64 x (.f64 2 y))) (*.f64 y y))
	1.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 x y) 2)) (cbrt.f64 (pow.f64 (+.f64 x y) 2))) (cbrt.f64 (pow.f64 (+.f64 x y) 2)))
	33.5b	(pow.f64 (sqrt.f64 (+.f64 y x)) 4)

Compiler

Compiled 1449 to 806 computations (44.4% saved)

regimes186.0ms (10.1%)

Accuracy

Total 0.0b remaining (68.4%)

Threshold costs 0.0b (68.4%)

Compiler

Compiled 2801 to 1594 computations (43.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	14	19
2	14	19

end9.0ms (0.5%)

Remove: (sort x y)
Compiler: Compiled 45 to 33 computations (26.7% saved)

sample422.0ms (23%)

Algorithm

1×

intervals

Results

162.0ms	8000×	body	128	valid
2.0ms	89×	body	128	invalid

Compiler

Compiled 79 to 50 computations (36.7% saved)

Details

analyze131.0ms (7.1%)

sample18.0ms (1%)

simplify10.0ms (0.5%)

prune1.0ms (0.1%)

localize7.0ms (0.4%)

rewrite24.0ms (1.3%)

series25.0ms (1.4%)

simplify76.0ms (4.2%)

prune16.0ms (0.9%)

localize4.0ms (0.2%)

rewrite22.0ms (1.2%)

series42.0ms (2.3%)

simplify98.0ms (5.3%)

prune17.0ms (0.9%)

localize6.0ms (0.3%)

rewrite30.0ms (1.6%)

series45.0ms (2.4%)

simplify90.0ms (4.9%)

prune20.0ms (1.1%)

localize8.0ms (0.4%)

rewrite113.0ms (6.1%)

series180.0ms (9.8%)

simplify193.0ms (10.5%)

prune41.0ms (2.2%)

regimes186.0ms (10.1%)

simplify3.0ms (0.2%)

end9.0ms (0.5%)

sample422.0ms (23%)

Profiling