Details

sample102.0ms

Algorithm

intervals

Results

42.0ms	308×	body	80	valid
12.0ms	115×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2638
4	446
3	177
2	81
1	36
0	17

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize45.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
6.0b	(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
6.5b	(/ (* M D) (* 2.0 d))
6.5b	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`pow-exp` `add-cube-cbrt`
9×	`associate-r`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `clear-num` `frac-2neg` `sqrt-div` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
16.0ms	(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
29.0ms	(/ (* M D) (* 2.0 d))
36.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

series2.4s

Counts

4 → 12

Calls

4 calls:

469.0ms	(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
883.0ms	(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
41.0ms	(/ (* M D) (* 2.0 d))
977.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	2601
1	552
0	222

prune850.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize54.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))
5.3b	(* (/ M 2.0) (/ D d))
6.0b	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
6.5b	(/ (* M D) (* 2.0 d))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

352×	`add-exp-log`
173×	`prod-exp`
125×	`div-exp`
75×	`pow-exp`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
26×	`times-frac`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
15×	`pow-to-exp`
13×	`associate-r` `associate-l`
11×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1`
5×	`sqrt-prod`
4×	`associate-/r*` `div-inv` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/l*`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 165

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))
18.0ms	(* (/ M 2.0) (/ D d))
45.0ms	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
10.0ms	(/ (* M D) (* 2.0 d))

series1.3s

Counts

4 → 12

Calls

4 calls:

399.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))
35.0ms	(* (/ M 2.0) (/ D d))
854.0ms	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
46.0ms	(/ (* M D) (* 2.0 d))

simplify521.0ms

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
1	1115
0	364

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize41.0ms

Local error

Found 4 expressions with local error:

3.3b	(* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)))
3.8b	(sqrt (- 1.0 (* (* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
5.4b	(/ (/ D d) (/ 2.0 M))
5.4b	(/ (/ D d) (/ 2.0 M))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

1253×	`times-frac`
604×	`add-sqr-sqrt`
582×	`*-un-lft-identity` `add-cube-cbrt`
179×	`unpow-prod-down`
178×	`associate-r`
85×	`div-inv`
49×	`add-exp-log`
30×	`add-cbrt-cube`
26×	`associate-/r` `associate-/l`
24×	`div-exp`
16×	`cbrt-undiv`
7×	`prod-exp` `unswap-sqr`
5×	`pow1` `pow-exp`
4×	`add-log-exp`
3×	`associate-l` `associate-/r/` `sqrt-prod`
2×	`clear-num` `frac-2neg` `sqrt-div` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `*-commutative` `cbrt-unprod` `flip--`

Counts

4 → 649

Calls

4 calls:

179.0ms	(* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)))
18.0ms	(sqrt (- 1.0 (* (* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
18.0ms	(/ (/ D d) (/ 2.0 M))
14.0ms	(/ (/ D d) (/ 2.0 M))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.1s	(* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)))
413.0ms	(sqrt (- 1.0 (* (* h (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
30.0ms	(/ (/ D d) (/ 2.0 M))
33.0ms	(/ (/ D d) (/ 2.0 M))

simplify1.2s

Counts

661 → 661

Iterations

Iter	Nodes
done	5000
1	2596
0	889

prune7.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b	(* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2)))
3.8b	(sqrt (- 1.0 (* (* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
5.3b	(* (/ D d) M)
5.4b	(/ (/ D d) (/ 2.0 M))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

466×	`times-frac`
242×	`add-sqr-sqrt`
227×	`*-un-lft-identity`
226×	`add-cube-cbrt`
72×	`add-exp-log`
36×	`associate-r`
34×	`div-inv`
32×	`unpow-prod-down`
29×	`div-exp`
23×	`add-cbrt-cube` `prod-exp`
16×	`associate-l`
13×	`associate-/r` `pow-exp` `associate-/l`
9×	`cbrt-undiv`
7×	`pow1` `unswap-sqr`
5×	`associate-/r/`
4×	`rec-exp` `1-exp` `associate-*l/` `add-log-exp`
3×	`sqrt-prod` `cbrt-unprod`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--` `associate-/l/`

Counts

4 → 327

Calls

4 calls:

49.0ms	(* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2)))
8.0ms	(sqrt (- 1.0 (* (* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
23.0ms	(* (/ D d) M)
29.0ms	(/ (/ D d) (/ 2.0 M))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.1s	(* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2)))
386.0ms	(sqrt (- 1.0 (* (* h (pow (/ 1 (/ 2.0 (* (/ D d) M))) (/ 2.0 2))) (/ (pow (/ (/ D d) (/ 2.0 M)) (/ 2.0 2)) l))))
39.0ms	(* (/ D d) M)
36.0ms	(/ (/ D d) (/ 2.0 M))

simplify1.1s

Counts

339 → 339

Iterations

Iter	Nodes
done	5001
1	2138
0	693

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes812.0ms

Accuracy

0% (1.4b remaining)

Error of 8.5b against oracle of 7.1b and baseline of 8.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	9324×	body	80	valid
830.0ms	3058×	body	80	nan