Details

sample83.0ms

Algorithm

intervals

Results

27.0ms	297×	body	80	valid
9.0ms	97×	body	80	nan

simplify6.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize29.0ms

Local error

Found 4 expressions with local error:

1.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b	(/ (* M D) (* 2.0 d))
12.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite90.0ms

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:

25.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

631.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
528.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
52.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.4s

Counts

133 → 133

Iterations

Useful iterations: 2 (466.0ms)

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

prune536.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.8b	(/ (* M D) (* 2.0 d))
7.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

609×	`add-exp-log`
325×	`prod-exp`
184×	`div-exp`
75×	`pow-exp`
54×	`add-cbrt-cube`
45×	`associate-r`
43×	`cbrt-unprod`
42×	`times-frac`
41×	`add-sqr-sqrt`
36×	`cbrt-prod`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`cbrt-undiv`
15×	`pow-to-exp`
10×	`associate-l`
7×	`pow1` `unpow-prod-down`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`sqrt-div` `*-commutative`
1×	`frac-times` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `flip--` `associate-/l*`

Counts

4 → 250

Calls

4 calls:

187.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
16.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
25.0ms	(/ (* M D) (* 2.0 d))
104.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.0s

Counts

4 → 12

Calls

4 calls:

916.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
486.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
31.0ms	(/ (* M D) (* 2.0 d))
590.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify916.0ms

Counts

262 → 262

Iterations

Useful iterations: done (901.0ms)

Iter	Nodes	Cost
0	452	8045
1	1149	7127
done	5001	5253

prune927.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize27.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
4.0b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.8b	(/ (* M D) (* 2.0 d))
4.8b	(/ (* M D) (* 2.0 d))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

47.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
7.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
15.0ms	(/ (* M D) (* 2.0 d))
20.0ms	(/ (* M D) (* 2.0 d))

series1.2s

Counts

4 → 12

Calls

4 calls:

602.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
500.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
46.0ms	(/ (* M D) (* 2.0 d))
48.0ms	(/ (* M D) (* 2.0 d))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	177	2603
1	428	2178
2	1818	1934
done	5000	1910

prune715.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

localize28.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.8b	(/ (* M D) (* 2.0 d))
4.8b	(/ (* M D) (* 2.0 d))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

189×	`add-exp-log`
91×	`prod-exp`
56×	`div-exp`
38×	`add-cbrt-cube`
25×	`pow-exp`
17×	`cbrt-unprod`
16×	`add-sqr-sqrt`
12×	`cbrt-undiv`
9×	`associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down` `times-frac`
6×	`unswap-sqr`
5×	`pow1` `pow-to-exp` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 134

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
22.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
75.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.2s

Counts

4 → 12

Calls

4 calls:

476.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
51.0ms	(/ (* M D) (* 2.0 d))
44.0ms	(/ (* M D) (* 2.0 d))
662.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify1.6s

Counts

146 → 146

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	256	3956
1	671	3336
2	2886	2664
done	5001	2514

prune568.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

regimes1.2s

Accuracy

0% (1.5b remaining)

Error of 8.7b against oracle of 7.1b and baseline of 8.7b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	48
1	29	48
done	29	48

end0.0ms

sample1.7s

Algorithm

intervals

Results

628.0ms	9267×	body	80	valid
214.0ms	3186×	body	80	nan