Details

analyze141.0ms (7%)

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)

sample18.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 29 to 19 computations (34.5% saved)

simplify10.0ms (0.5%)

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 (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 37 to 23 computations (37.8% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`add-log-exp_binary64`
3×	`sum-log_binary64`
1×	`+-commutative_binary64`
1×	`associate-+l+_binary64`
1×	`flip-+_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

Compiler

Compiled 290 to 129 computations (55.5% saved)

series26.0ms (1.3%)

Error

0.0b

Counts

1 → 15

Calls

1 calls:

22.0ms

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

Compiler

Compiled 250 to 192 computations (23.2% saved)

simplify105.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

667×	`unswap-sqr_binary64`
419×	`*-commutative_binary64`
336×	`cancel-sign-sub-inv_binary64`
327×	`sub-neg_binary64`
271×	`distribute-rgt-in_binary64`

Counts

28 → 25

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	416
1	124	380
2	421	371
3	1714	371
4	3079	371
5	4977	371
6	4976	371
7	4990	371

prune12.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

Counts

26 → 3

Alt Table

Status	Error	Program
▶	13.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x (+.f64 2 x)))))
	40.4b	(cbrt.f64 (pow.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x))) 3))
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 270 to 155 computations (42.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite107.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`
14×	`sqrt-div_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 100

Calls

4 calls:

28.0ms	(.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 (.f64 y y) (.f64 x (+.f64 2 x)))
4.0ms	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))
3.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x))))

Compiler

Compiled 2918 to 1604 computations (45% saved)

series121.0ms (6%)

Error

Counts

4 → 61

Calls

4 calls:

29.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x (+.f64 2 x))))
26.0ms	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))
26.0ms	(+.f64 (.f64 y y) (.f64 x (+.f64 2 x)))
23.0ms	(.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 2389 to 1687 computations (29.4% saved)

simplify157.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
671×	`distribute-lft-in_binary64`
198×	`cancel-sign-sub-inv_binary64`
185×	`times-frac_binary64`
149×	`associate-r_binary64`

Counts

161 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3790
1	391	3425
2	1555	3318
3	4736	3293
4	4968	3293

prune48.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	146	2	148

Error

Counts

148 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
▶	38.6b	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4))

Compiler

Compiled 1916 to 1089 computations (43.2% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.1b	(pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4)
24.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4))

rewrite67.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`unpow-prod-down_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
6.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4)
5.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))

Compiler

Compiled 1571 to 1001 computations (36.3% saved)

series197.0ms (9.7%)

Error

Counts

4 → 70

Calls

4 calls:

83.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4)
37.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))
26.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
25.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4))

Compiler

Compiled 2412 to 1920 computations (20.4% saved)

simplify119.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-in_binary64`
484×	`distribute-lft-in_binary64`
198×	`cancel-sign-sub-inv_binary64`
166×	`exp-sum_binary64`
162×	`times-frac_binary64`

Counts

144 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	226	3096
1	523	2784
2	1635	2549
3	4575	2543
4	4974	2543

prune40.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
✓	38.6b	(sqrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) 4))

Compiler

Compiled 1270 to 758 computations (40.3% saved)

regimes277.0ms (13.7%)

Accuracy

Total 0.0b remaining (33.1%)

Threshold costs 0.0b (33.1%)

Compiler

Compiled 2866 to 2027 computations (29.3% saved)

simplify3.0ms (0.2%)

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 8 computations (38.5% saved)

sample537.0ms (26.5%)

Algorithm

1×

intervals

Results

278.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 57 to 38 computations (33.3% saved)

Details

analyze141.0ms (7%)

sample18.0ms (0.9%)

simplify10.0ms (0.5%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

rewrite12.0ms (0.6%)

series26.0ms (1.3%)

simplify105.0ms (5.2%)

prune12.0ms (0.6%)

localize8.0ms (0.4%)

rewrite107.0ms (5.3%)

series121.0ms (6%)

simplify157.0ms (7.7%)

prune48.0ms (2.4%)

localize9.0ms (0.4%)

rewrite67.0ms (3.3%)

series197.0ms (9.7%)

simplify119.0ms (5.9%)

prune40.0ms (2%)

regimes277.0ms (13.7%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample537.0ms (26.5%)

Profiling