Details

analyze1.1s (23.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample48.0ms (1%)

Algorithm

1×

intervals

Results

15.0ms	197×	body	128	valid
6.0ms	19×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	8×	body	4096	valid
3.0ms	12×	body	1024	valid
3.0ms	13×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 45 to 34 computations (24.4% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	30	26
2	35	26
3	38	26
4	40	26
5	41	26
6	38	26

prune2.0ms (0%)

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

12.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 57 to 42 computations (26.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
17.7b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite110.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

Rules

8×	`add-log-exp_binary64`
8×	`pow1_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

4 → 51

Calls

4 calls:

11.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
10.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
4.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 1457 to 937 computations (35.7% saved)

series150.0ms (3.1%)

Error

2.8b

Counts

4 → 51

Calls

4 calls:

55.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
27.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
22.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
22.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

Compiler

Compiled 2010 to 1691 computations (15.9% saved)

simplify102.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

596×	`associate-/l*_binary64`
541×	`associate-/r*_binary64`
255×	`associate-*l/_binary64`
245×	`associate-*r/_binary64`
155×	`cancel-sign-sub-inv_binary64`

Counts

102 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2139
1	461	1991
2	1502	1917
3	4842	1917
4	4968	1917

prune56.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Error

1.8b

Counts

74 → 5

Alt Table

Status	Error	Program
▶	51.3b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
✓	12.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
	53.6b	(-.f64 (.f64 3 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (pow.f64 (/.f64 p x) 3))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
	56.2b	(sqrt.f64 (.f64 1/2 (+.f64 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))) (*.f64 20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
	55.0b	(sqrt.f64 (.f64 1/2 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))

Compiler

Compiled 1544 to 990 computations (35.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
21.9b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite81.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

38×	`add-cbrt-cube_binary64`
38×	`add-exp-log_binary64`
36×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
6.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
5.0ms	(/.f64 (*.f64 x x) p)
5.0ms	(/.f64 p (/.f64 (*.f64 x x) p))

Compiler

Compiled 2028 to 897 computations (55.8% saved)

series51.0ms (1.1%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

15.0ms	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
13.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
13.0ms	(/.f64 (*.f64 x x) p)
8.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 566 to 446 computations (21.2% saved)

simplify107.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-/l*_binary64`
571×	`associate-/r/_binary64`
473×	`associate-/r*_binary64`
442×	`associate-/l/_binary64`
300×	`*-commutative_binary64`

Counts

131 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1936
1	346	1636
2	1140	1478
3	3746	1446
4	4725	1446
5	4950	1446

prune41.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	106	8	114

Error

0.0b

Counts

114 → 8

Alt Table

Status	Error	Program
	46.5b	(.f64 (.f64 (cbrt.f64 (fabs.f64 (/.f64 p x))) (cbrt.f64 (fabs.f64 (/.f64 p x)))) (cbrt.f64 (fabs.f64 (/.f64 p x))))
	53.6b	(-.f64 (.f64 3 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (pow.f64 (/.f64 p x) 3))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
	52.9b	(neg.f64 (/.f64 p x))
	55.0b	(sqrt.f64 (.f64 1/2 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
	51.3b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
	56.2b	(sqrt.f64 (.f64 1/2 (+.f64 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))) (*.f64 20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
✓	12.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
▶	46.3b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))

Compiler

Compiled 1312 to 613 computations (53.3% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.4b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
8.9b	(sqrt.f64 (fabs.f64 (/.f64 p x)))
8.9b	(sqrt.f64 (fabs.f64 (/.f64 p x)))

rewrite115.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

271×	`add-sqr-sqrt_binary64`
170×	`sqrt-prod_binary64`
130×	`fabs-mul_binary64`
112×	`times-frac_binary64`
70×	`rem-sqrt-square_binary64`

Counts

3 → 225

Calls

3 calls:

18.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))

Compiler

Compiled 3757 to 653 computations (82.6% saved)

series26.0ms (0.5%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

11.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
8.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
5.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))

Compiler

Compiled 401 to 198 computations (50.6% saved)

simplify217.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/l*_binary64`
686×	`fabs-div_binary64`
432×	`log-div_binary64`
417×	`cube-div_binary64`
370×	`log-prod_binary64`

Counts

243 → 217

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	213	3232
1	305	2568
2	679	2495
3	1680	2393
4	3354	2235
5	3451	2232
6	4154	2232
7	4487	2226
8	5124	2226

prune41.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	219	6	225

Error

0.0b

Counts

225 → 6

Alt Table

Status	Error	Program
	56.2b	(sqrt.f64 (.f64 1/2 (+.f64 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))) (*.f64 20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
	54.4b	(pow.f64 (/.f64 p x) 1)
▶	52.9b	(neg.f64 (/.f64 p x))
	55.0b	(sqrt.f64 (.f64 1/2 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
	53.6b	(-.f64 (.f64 3 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (pow.f64 (/.f64 p x) 3))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
✓	12.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 1524 to 494 computations (67.6% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune7.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Error

0.0b

Counts

6 → 6

Alt Table

Status	Error	Program
	56.2b	(sqrt.f64 (.f64 1/2 (+.f64 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))) (*.f64 20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
	54.4b	(pow.f64 (/.f64 p x) 1)
	52.9b	(neg.f64 (/.f64 p x))
	55.0b	(sqrt.f64 (.f64 1/2 (-.f64 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
	53.6b	(-.f64 (.f64 3 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (pow.f64 (/.f64 p x) 3))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
	12.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 115 to 88 computations (23.5% saved)

regimes902.0ms (18.5%)

Accuracy

Total 0.1b remaining (60.6%)

Threshold costs 0.1b (60.6%)

Compiler

Compiled 12791 to 9222 computations (27.9% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	59
1	33	59
2	32	59

end1.0ms (0%)

Compiler: Compiled 40 to 27 computations (32.5% saved)

sample1.6s (33.2%)

Algorithm

1×

intervals

Results

431.0ms	6041×	body	128	valid
265.0ms	788×	body	2048	valid
161.0ms	8000×	pre	128	true
140.0ms	508×	body	1024	valid
131.0ms	285×	body	4096	valid
53.0ms	254×	body	512	valid
25.0ms	124×	body	256	valid

Compiler

Compiled 181 to 135 computations (25.4% saved)

Details

analyze1.1s (23.4%)

sample48.0ms (1%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize12.0ms (0.2%)

rewrite110.0ms (2.3%)

series150.0ms (3.1%)

simplify102.0ms (2.1%)

prune56.0ms (1.1%)

localize8.0ms (0.2%)

rewrite81.0ms (1.7%)

series51.0ms (1.1%)

simplify107.0ms (2.2%)

prune41.0ms (0.8%)

localize5.0ms (0.1%)

rewrite115.0ms (2.4%)

series26.0ms (0.5%)

simplify217.0ms (4.4%)

prune41.0ms (0.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.2%)

prune7.0ms (0.2%)

regimes902.0ms (18.5%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (33.2%)

Profiling