Details

analyze423.0ms

Algorithm

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

sample22.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	12
1	43	12

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 36.6b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
33.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sum-log` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

2 → 28

Calls

2 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ (+ (* x x) (* y y)) (* z z))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	474
1	4923	474

prune59.0ms

Filtered

27 candidates to 34 candidates (-25.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	5	35

Merged error: 15.2b

Counts

35 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (* y y) (* z z))
13.1b	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
33.9b	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))))
43.3b	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity` `difference-of-squares`
24×	`sqrt-prod`
8×	`unpow-prod-down` `add-log-exp` `sqr-pow`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1`
4×	`associate-/r/`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `associate--l+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 108

Calls

4 calls:

4.0ms	(- (* y y) (* z z))
12.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
15.0ms	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))))
20.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* y y) (* z z))
32.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
50.0ms	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z)))))
32.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (+ (* x x) (- (* y y) (* z z))))

simplify73.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4937	3929
1	4937	3929

prune216.0ms

Filtered

93 candidates to 120 candidates (-29.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Merged error: 15.2b

Counts

125 → 5

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Merged error: 15.2b

Counts

5 → 5

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	3	3
Total	5	5

Merged error: 15.2b

Counts

5 → 5

regimes633.0ms

Accuracy

58.3% (8.3b remaining)

Error of 26.3b against oracle of 18.0b and baseline of 37.9b

bsearch91.0ms

Steps

Iters	Range		Point
9	1.757658448603172e+147	8.303001601395945e+154	3.196595555888106e+148
9	8.520592458011397e-276	8.83160276300271e-270	2.0921178682604062e-275
8	-4.077446708901963e-283	-1.7447803066861568e-286	-2.171932746604494e-286
5	-1.5122602458701182e-54	-3.864851903432938e-55	-1.472003350999863e-54
6	-5.614409803750604e-37	-4.5891674206509886e-38	-4.654197057473422e-38
11	-7.750808825680552e+172	-6.86892579199904e+149	-8.4611892877849e+149

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	65
1	104	65

end0.0ms

sample514.0ms

Algorithm

intervals

Results

332.0ms

8000×

body

valid

Details

analyze423.0ms

sample22.0ms

simplify4.0ms

prune7.0ms

localize7.0ms

rewrite12.0ms

series28.0ms

simplify47.0ms

prune59.0ms

localize14.0ms

rewrite54.0ms

series120.0ms

simplify73.0ms

prune216.0ms

localize1.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune6.0ms

localize1.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune0.0ms

regimes633.0ms

bsearch91.0ms

simplify3.0ms

end0.0ms

sample514.0ms

Profiling