Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	6
1	20	6
2	22	6
3	22	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 38.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
35.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(+ (+ (* x x) (* y y)) (* z z))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (* x x) (* y y)) (* z z))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	209	340
1	959	320
2	3316	316
3	5001	315

prune99.0ms

Filtered

48 candidates to 37 candidates (77.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 18.5b

Counts

49 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

33.5b	(cbrt (+ (* x x) (* y y)))
33.5b	(cbrt (+ (* x x) (* y y)))
33.5b	(cbrt (+ (* x x) (* y y)))
35.6b	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
21.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (* x x) (* y y)))
423.0ms	(cbrt (+ (* x x) (* y y)))
94.0ms	(cbrt (+ (* x x) (* y y)))
104.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	201	739
1	622	690
2	2121	690
3	5003	689

prune180.0ms

Filtered

66 candidates to 57 candidates (86.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	66	6	72

Merged error: 18.5b

Counts

72 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
0.3b	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
36.8b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
36.8b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

5.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
10.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
140.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
107.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
109.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	320	1178
1	1304	1101
2	5001	1084

prune249.0ms

Filtered

86 candidates to 75 candidates (87.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	86	6	92

Merged error: 18.5b

Counts

92 → 6

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Merged error: 18.5b

Counts

6 → 6

regimes315.0ms

Accuracy

63.4% (7.2b remaining)

Error of 24.9b against oracle of 17.7b and baseline of 37.4b

bsearch55.0ms

Steps

Iters	Range		Point
10	1.7826190976464906e+97	7.552700620960131e+107	1.3566371815103393e+105
5	-1.7575017886047935e+118	-4.9561533689906815e+117	-1.6174687293654252e+118

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

sample432.0ms

Algorithm

intervals

Results

255.0ms

8000×

body

valid