Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	297×	body	80	valid
5.0ms	95×	body	80	nan

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	180	18
4	432	18
5	1221	18
6	4692	18
done	5000	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.7b	(/ (* M D) (* 2.0 d))
9.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 121

Calls

4 calls:

18.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
9.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

446.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
392.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms	(/ (* M D) (* 2.0 d))
703.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify964.0ms

Counts

133 → 133

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	244	2427
1	598	2198
2	2296	2040
done	5002	2040

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.5b

localize15.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
3.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.7b	(/ (* M D) (* 2.0 d))
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

24.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
12.0ms	(/ (* M D) (* 2.0 d))
43.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

series1.9s

Counts

4 → 12

Calls

4 calls:

757.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
402.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
28.0ms	(/ (* M D) (* 2.0 d))
723.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))

simplify985.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (390.0ms)

Iter	Nodes	Cost
0	277	2631
1	668	2190
2	2514	1982
done	5001	1982

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize24.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* M D) (* 2.0 d))
4.7b	(/ (* M D) (* 2.0 d))
5.5b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

1402×	`add-exp-log`
907×	`prod-exp`
366×	`div-exp`
305×	`pow-exp`
61×	`pow-to-exp`
57×	`rec-exp` `1-exp`
51×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 340

Calls

4 calls:

12.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(/ (* M D) (* 2.0 d))
121.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
24.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.6s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(/ (* M D) (* 2.0 d))
724.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
762.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.1s

Counts

352 → 352

Iterations

Useful iterations: 2 (463.0ms)

Iter	Nodes	Cost
0	447	10610
1	918	6194
2	2990	5718
done	5000	5718

prune441.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize21.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* 2.0 d) (* M D))
4.7b	(/ (* M D) (* 2.0 d))
5.5b	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

3834×	`add-exp-log`
2351×	`prod-exp`
1294×	`div-exp`
877×	`pow-exp`
305×	`rec-exp` `1-exp`
105×	`pow-to-exp`
51×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 692

Calls

4 calls:

12.0ms	(/ (* 2.0 d) (* M D))
12.0ms	(/ (* M D) (* 2.0 d))
143.0ms	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
24.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.7s

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (* 2.0 d) (* M D))
27.0ms	(/ (* M D) (* 2.0 d))
936.0ms	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
739.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify1.9s

Counts

704 → 704

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	892	24296
1	1502	19840
2	4167	17643
done	5000	17062

prune501.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

regimes737.0ms

Accuracy

43% (1.2b remaining)

Error of 8.3b against oracle of 7.1b and baseline of 9.2b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	78
1	43	78
done	43	78

end0.0ms

sample1.2s

Algorithm

intervals

Results

463.0ms	9337×	body	80	valid
167.0ms	3102×	body	80	nan