Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify14.0ms

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: 40.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
37.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite86.0ms

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:

34.0ms	(+ (+ (* x x) (* y y)) (* z z))
51.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (+ (* x x) (* y y)) (* z z))
114.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify488.0ms

Counts

34 → 34

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	58	576
1	162	535
2	804	490
done	5001	490

prune161.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
37.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.8b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

42.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
231.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
39.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
43.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
125.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
137.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
148.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts

146 → 146

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	130	4100
1	290	2689
2	1472	2489
done	5000	2442

prune370.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.8b

localize24.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (+ (* x x) (* y y)) (* z z))
11.8b	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
37.8b	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z))))
42.1b	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
49×	`times-frac`
44×	`difference-of-squares`
30×	`sqrt-prod`
27×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-log-exp`
10×	`unpow-prod-down` `sqr-pow`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `flip3--` `flip--`
4×	`associate-/r*` `associate-/r/`
3×	`diff-log` `associate--l+`
2×	`sub-neg` `rem-sqrt-square` `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` `sum-log`

Counts

4 → 125

Calls

4 calls:

60.0ms	(- (+ (* x x) (* y y)) (* z z))
40.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
71.0ms	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z))))
123.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z)))

series815.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (+ (* x x) (* y y)) (* z z))
274.0ms	(- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4))
285.0ms	(sqrt (/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z))))
184.0ms	(/ (- (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (pow z 4)) (- (+ (* x x) (* y y)) (* z z)))

simplify1.7s

Counts

137 → 137

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	230	5433
1	569	5261
2	2931	4935
done	5001	4898

prune517.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.8b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 19.8b

regimes377.0ms

Accuracy

57.8% (8.2b remaining)

Error of 26.8b against oracle of 18.6b and baseline of 38.0b

bsearch120.0ms

Steps

Iters	Range		Point
8	1.9445145714521144e+92	6.598426988503463e+95	2.9682675892586475e+95
7	6.123354719305387e-149	4.8857590053090926e-147	6.220903762266977e-149
9	8.975843869006682e-209	1.807242467643983e-199	5.393455774424304e-203
8	-1.6504271973040736e+100	-3.113286269135709e+96	-1.629188860154807e+100

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	44
1	24	44
done	24	44

end0.0ms

sample1.2s

Algorithm

intervals

Results

812.0ms

8000×

body

valid