Details

sample120.0ms

Algorithm

intervals

Results

53.0ms	308×	body	80	valid
15.0ms	115×	body	80	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2702
4	460
3	181
2	81
1	36
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize46.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.5b	(/ (* M D) (* 2.0 d))
9.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite104.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l`

Counts

4 → 121

Calls

4 calls:

28.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
10.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
16.0ms	(/ (* M D) (* 2.0 d))
42.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

626.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
540.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms	(/ (* M D) (* 2.0 d))
932.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	3154
1	643
0	244

prune927.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.0b

localize35.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
5.9b	(/ M (* (/ 2.0 D) d))
6.0b	(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
6.5b	(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
21×	`add-sqr-sqrt`
20×	`add-cbrt-cube`
19×	`div-exp`
18×	`prod-exp`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`associate-l`
9×	`unpow-prod-down` `times-frac`
8×	`pow-exp`
6×	`cbrt-undiv`
5×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `clear-num` `frac-2neg` `sqrt-div` `associate-*l/` `associate-/r/` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

19.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
17.0ms	(/ M (* (/ 2.0 D) d))
18.0ms	(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
23.0ms	(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

series2.7s

Counts

4 → 12

Calls

4 calls:

609.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
52.0ms	(/ M (* (/ 2.0 D) d))
982.0ms	(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
1.1s	(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

simplify1.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2835
1	595
0	245

prune862.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize35.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)))
5.9b	(/ M (* (/ 2.0 D) d))
5.9b	(/ (/ M 2.0) (/ d D))
6.0b	(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

427×	`times-frac`
295×	`add-exp-log`
208×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
205×	`add-cube-cbrt`
141×	`div-exp`
108×	`prod-exp`
62×	`pow-exp`
34×	`add-cbrt-cube`
31×	`div-inv`
17×	`associate-/r` `associate-/l`
15×	`cbrt-undiv`
14×	`pow-to-exp`
5×	`pow1` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 333

Calls

4 calls:

29.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)))
13.0ms	(/ M (* (/ 2.0 D) d))
14.0ms	(/ (/ M 2.0) (/ d D))
191.0ms	(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

series1.7s

Counts

4 → 12

Calls

4 calls:

551.0ms	(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)))
37.0ms	(/ M (* (/ 2.0 D) d))
51.0ms	(/ (/ M 2.0) (/ d D))
1.0s	(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

simplify1.0s

Counts

345 → 345

Iterations

Iter	Nodes
done	5001
1	2226
0	687

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize36.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)
3.8b	(sqrt (- 1.0 (/ 1 (/ (/ l (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2))) (* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)))))
5.9b	(/ M (* 2.0 (/ d D)))
5.9b	(/ M (* 2.0 (/ d D)))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
26×	`add-sqr-sqrt`
24×	`add-cbrt-cube`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`div-exp` `associate-l` `prod-exp`
11×	`times-frac`
9×	`unpow-prod-down`
8×	`cbrt-undiv` `sqrt-prod`
6×	`associate-/l*`
5×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r` `associate-*r/` `associate-/r/` `difference-of-squares` `unswap-sqr`
2×	`clear-num` `associate-/r*` `frac-2neg` `sqrt-div` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `*-commutative` `flip--`

Counts

4 → 109

Calls

4 calls:

22.0ms	(* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)
266.0ms	(sqrt (- 1.0 (/ 1 (/ (/ l (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2))) (* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)))))
16.0ms	(/ M (* 2.0 (/ d D)))
9.0ms	(/ M (* 2.0 (/ d D)))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)
634.0ms	(sqrt (- 1.0 (/ 1 (/ (/ l (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2))) (* (pow (/ M (* 2.0 (/ d D))) (/ 2.0 2)) h)))))
37.0ms	(/ M (* 2.0 (/ d D)))
44.0ms	(/ M (* 2.0 (/ d D)))

simplify1.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	2588
1	566
0	231

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.1b

regimes793.0ms

Accuracy

0% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 8.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	9324×	body	80	valid
338.0ms	3058×	body	80	nan