Details

analyze815.0ms (15.9%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	199×	body	128	valid
7.0ms	26×	body	2048	valid
4.0ms	256×	pre	128	true
4.0ms	19×	body	1024	valid
3.0ms	8×	body	4096	valid
0.0ms	3×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 45 to 34 computations (24.4% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-/l*_binary64` `+-commutative_binary64`
1×	`1-exp_binary64` `associate-/r/_binary64` `associate-l/_binary64` `associate-r/_binary64` `associate-l_binary64` `associate-r_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

prune3.0ms (0.1%)

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

11.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.9b	(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)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
16.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite213.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

11.8b

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 81

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
5.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2276 to 1437 computations (36.9% saved)

series195.0ms (3.8%)

Error

3.8b

Counts

4 → 53

Calls

4 calls:

54.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
37.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
33.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
32.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2038 to 1706 computations (16.3% saved)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

835×	`times-frac_binary64`
560×	`associate-/l*_binary64`
435×	`associate-/r*_binary64`
271×	`associate-*l/_binary64`
166×	`associate-/r/_binary64`

Counts

134 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	3104
1	490	2941
2	1404	2920
3	4978	2920
4	4947	2920

prune88.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

2.7b

Counts

102 → 5

Alt Table

Status	Error	Program
▶	29.8b	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
	53.4b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
	55.3b	(-.f64 (.f64 3 (.f64 (pow.f64 (/.f64 p x) 3) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
	54.6b	(/.f64 (.f64 p (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (neg.f64 x))
✓	11.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 2160 to 1404 computations (35% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
0.2b	(.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)))
0.4b	(*.f64 (/.f64 x p) (sqrt.f64 1/2))

rewrite78.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

23×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-l_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`times-frac_binary64`

Counts

3 → 69

Calls

3 calls:

8.0ms	(.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)))
8.0ms	(*.f64 (/.f64 x p) (sqrt.f64 1/2))
4.0ms	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))

Compiler

Compiled 1187 to 850 computations (28.4% saved)

series83.0ms (1.6%)

Error

2.7b

Counts

3 → 24

Calls

3 calls:

34.0ms	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
24.0ms	(.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)))
22.0ms	(*.f64 (/.f64 x p) (sqrt.f64 1/2))

Compiler

Compiled 533 to 451 computations (15.4% saved)

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

638×	`times-frac_binary64`
472×	`associate-*r/_binary64`
470×	`associate-*l/_binary64`
248×	`*-commutative_binary64`
224×	`distribute-neg-frac_binary64`

Counts

93 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1359
1	294	1252
2	876	1239
3	3149	1236
4	4656	1236
5	5031	1236

prune43.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	69	5	74

Error

2.7b

Counts

74 → 5

Alt Table

Status	Error	Program
✓	29.8b	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
▶	53.4b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
	55.3b	(-.f64 (.f64 3 (.f64 (pow.f64 (/.f64 p x) 3) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (/.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 x p)))
	54.6b	(/.f64 (.f64 p (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (neg.f64 x))
✓	11.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 878 to 653 computations (25.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
0.2b	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
24.2b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite103.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

2.6b

Rules

38×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
36×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
15×	`pow1_binary64`
12×	`prod-exp_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
7.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
6.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
4.0ms	(/.f64 (*.f64 x x) p)

Compiler

Compiled 2028 to 897 computations (55.8% saved)

series76.0ms (1.5%)

Error

Counts

4 → 24

Calls

4 calls:

22.0ms	(.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p))))
20.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
17.0ms	(/.f64 (*.f64 x x) p)
12.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 566 to 446 computations (21.2% saved)

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-/l*_binary64`
571×	`associate-/r/_binary64`
473×	`associate-/r*_binary64`
446×	`associate-/l/_binary64`
301×	`*-commutative_binary64`

Counts

131 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2098
1	346	1636
2	1140	1478
3	3746	1446
4	4725	1446
5	4950	1446

prune44.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	108	6	114

Error

0.0b

Counts

114 → 6

Alt Table

Status	Error	Program
✓	29.8b	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
▶	47.4b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
✓	11.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
	47.6b	(.f64 (.f64 (cbrt.f64 (fabs.f64 (/.f64 p x))) (cbrt.f64 (fabs.f64 (/.f64 p x)))) (cbrt.f64 (fabs.f64 (/.f64 p x))))
	53.4b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
	54.5b	(neg.f64 (/.f64 p x))

Compiler

Compiled 1159 to 494 computations (57.4% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
7.4b	(sqrt.f64 (fabs.f64 (/.f64 p x)))
7.4b	(sqrt.f64 (fabs.f64 (/.f64 p x)))

rewrite148.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

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:

24.0ms	(*.f64 (sqrt.f64 (fabs.f64 (/.f64 p x))) (sqrt.f64 (fabs.f64 (/.f64 p x))))
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))
4.0ms	(sqrt.f64 (fabs.f64 (/.f64 p x)))

Compiler

Compiled 3757 to 653 computations (82.6% saved)

series31.0ms (0.6%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

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

Compiler

Compiled 401 to 198 computations (50.6% saved)

simplify228.0ms (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

prune50.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
	29.8b	(+.f64 (sqrt.f64 1/2) (.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2))))
	53.9b	(pow.f64 (/.f64 p x) 1)
	11.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
	54.5b	(neg.f64 (/.f64 p x))

Compiler

Compiled 1358 to 366 computations (73% saved)

regimes1.1s (22.2%)

Accuracy

Total 0.1b remaining (52.5%)

Threshold costs 0.1b (52.5%)

Compiler

Compiled 16502 to 11522 computations (30.2% saved)

bsearch3.0ms (0.1%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`unpow1_binary64` `1-exp_binary64` `fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	58
1	36	58
2	34	58

end1.0ms (0%)

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

sample1.4s (26.8%)

Algorithm

1×

intervals

Results

320.0ms	6087×	body	128	valid
212.0ms	796×	body	2048	valid
155.0ms	8000×	pre	128	true
103.0ms	487×	body	1024	valid
97.0ms	273×	body	4096	valid
37.0ms	242×	body	512	valid
12.0ms	115×	body	256	valid

Compiler

Compiled 111 to 81 computations (27% saved)

Details

analyze815.0ms (15.9%)

sample41.0ms (0.8%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize15.0ms (0.3%)

rewrite213.0ms (4.2%)

series195.0ms (3.8%)

simplify116.0ms (2.3%)

prune88.0ms (1.7%)

localize7.0ms (0.1%)

rewrite78.0ms (1.5%)

series83.0ms (1.6%)

simplify92.0ms (1.8%)

prune43.0ms (0.8%)

localize8.0ms (0.2%)

rewrite103.0ms (2%)

series76.0ms (1.5%)

simplify111.0ms (2.2%)

prune44.0ms (0.9%)

localize5.0ms (0.1%)

rewrite148.0ms (2.9%)

series31.0ms (0.6%)

simplify228.0ms (4.4%)

prune50.0ms (1%)

regimes1.1s (22.2%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.4s (26.8%)

Profiling