Details

sample253.0ms

Algorithm

intervals

Results

114.0ms	1236×	body	80	nan
56.0ms	420×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	720	17
3	5001	17
done	5001	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize32.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.1b	(pow (/ d h) (/ 1.0 2.0))
11.4b	(pow (/ d l) (/ 1.0 2.0))
13.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

Calls

4 calls:

64.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
8.0ms	(pow (/ d h) (/ 1.0 2.0))
8.0ms	(pow (/ d l) (/ 1.0 2.0))
55.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.8s

Counts

4 → 12

Calls

4 calls:

681.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
67.0ms	(pow (/ d h) (/ 1.0 2.0))
64.0ms	(pow (/ d l) (/ 1.0 2.0))
974.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify50.0ms

Counts

202 → 202

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5002	2125
done	5002	2125

prune765.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.7b

localize46.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
5.8b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.4b	(pow (/ d l) (/ 1.0 2.0))
13.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
487×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 274

Calls

4 calls:

12.0ms	(/ (* M D) (* 2.0 d))
339.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0ms	(pow (/ d l) (/ 1.0 2.0))
52.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* M D) (* 2.0 d))
709.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
68.0ms	(pow (/ d l) (/ 1.0 2.0))
779.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify69.0ms

Counts

286 → 286

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717
done	5001	5717

prune893.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.7b

localize54.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* M D) (* 2.0 d))
5.8b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.8b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
11.4b	(pow (/ d l) (/ 1.0 2.0))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

1038×	`add-exp-log`
658×	`prod-exp`
261×	`div-exp`
246×	`pow-exp`
84×	`pow-to-exp`
70×	`add-cbrt-cube`
47×	`cbrt-unprod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`cbrt-undiv`
20×	`times-frac`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1`
8×	`associate-r`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 320

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
334.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
79.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
8.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2.0 d))
712.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
604.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
69.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify96.0ms

Counts

332 → 332

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	2014	9035
1	5002	8345
done	5002	8345

prune1.0s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.0b

localize60.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (/ (cbrt d) l) (/ 1.0 2.0))
4.8b	(/ (* M D) (* 2.0 d))
5.8b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.8b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite767.0ms

Algorithm

rewrite-expression-head

Rules

5773×	`add-exp-log`
4252×	`prod-exp`
2024×	`pow-exp`
1474×	`div-exp`
649×	`pow-to-exp`
232×	`1-exp`
79×	`add-cbrt-cube`
54×	`cbrt-unprod`
29×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-down`
21×	`cbrt-undiv`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-prod`
8×	`associate-r`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1057

Calls

4 calls:

10.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
12.0ms	(/ (* M D) (* 2.0 d))
494.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
78.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.9s

Counts

4 → 12

Calls

4 calls:

179.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
30.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
620.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify334.0ms

Counts

1069 → 1069

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	4620	44787
1	5001	43733
done	5001	43733

prune1.2s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.6b

regimes1.4s

Accuracy

0% (4.9b remaining)

Error of 15.6b against oracle of 10.8b and baseline of 15.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	47
1	48	47
done	48	47

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.6s	38413×	body	80	nan
1.7s	12883×	body	80	valid