Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify22.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	20	12
3	22	12
done	22	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
34.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite152.0ms

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:

16.0ms	(+ (* x x) (* y y))
61.0ms	(+ (+ (* x x) (* y y)) (* z z))
74.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series300.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* x x) (* y y))
80.0ms	(+ (+ (* x x) (* y y)) (* z z))
169.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.5s

Counts

48 → 48

Iterations

Useful iterations: 3 (706.0ms)

Iter	Nodes	Cost
0	74	742
1	203	681
2	653	621
3	2437	605
done	5001	605

prune177.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.1b

localize15.0ms

Local error

Found 4 expressions with local error:

34.0b	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

205.0ms	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
22.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
17.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (* (* (cbrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
132.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
140.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
139.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.9s

Counts

101 → 101

Iterations

Useful iterations: 3 (367.0ms)

Iter	Nodes	Cost
0	171	4335
1	297	3955
2	554	3310
3	1344	3038
4	4534	3038
done	5001	3038

prune414.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.1b

localize38.0ms

Local error

Found 4 expressions with local error:

35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

31.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
29.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
31.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series803.0ms

Counts

4 → 12

Calls

4 calls:

388.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
124.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
130.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
161.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.0s

Counts

64 → 64

Iterations

Useful iterations: 3 (332.0ms)

Iter	Nodes	Cost
0	58	1352
1	139	1324
2	386	1204
3	1170	1124
4	4161	1124
done	5000	1124

prune351.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 20.1b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 20.1b

regimes313.0ms

Accuracy

63.1% (7.3b remaining)

Error of 25.5b against oracle of 18.2b and baseline of 38.1b

bsearch70.0ms

Steps

Iters	Range		Point
8	9.20494146023971e+137	7.045427827826125e+140	1.9453302589220937e+138
9	-1.9215371086303872e+109	-1.5895300252882697e+103	-1.8843851882908976e+109

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	18	23
done	18	23

end0.0ms

sample813.0ms

Algorithm

intervals

Results

514.0ms

8000×

body

valid