Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	298×	body	80	valid
7.0ms	97×	body	80	nan

simplify5.1s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
10.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite96.0ms

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:

23.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
8.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms	(/ (* M D) (* 2.0 d))
43.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.9s

Counts

4 → 12

Calls

4 calls:

567.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
488.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms	(/ (* M D) (* 2.0 d))
829.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.2s

Counts

133 → 133

Iterations

Useful iterations: 2 (376.0ms)

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

prune492.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.5b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.5b	(/ (* M D) (* 2.0 d))

rewrite134.0ms

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

Counts

4 → 104

Calls

4 calls:

39.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
31.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
28.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
29.0ms	(/ (* M D) (* 2.0 d))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
554.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
902.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
36.0ms	(/ (* M D) (* 2.0 d))

simplify1.1s

Counts

116 → 116

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	232	1901
1	550	1737
2	2254	1581
done	5000	1579

prune424.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize27.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 158

Calls

4 calls:

44.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
29.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
13.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(/ (* M D) (* 2.0 d))

series1.8s

Counts

4 → 12

Calls

4 calls:

926.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
852.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
31.0ms	(/ (* M D) (* 2.0 d))
36.0ms	(/ (* M D) (* 2.0 d))

simplify1.3s

Counts

170 → 170

Iterations

Useful iterations: 2 (483.0ms)

Iter	Nodes	Cost
0	289	3978
1	674	2823
2	2609	2495
done	5001	2495

prune622.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
5.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite72.0ms

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:

7.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
28.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
21.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(/ (* M D) (* 2.0 d))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.0s	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l)))))
976.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
32.0ms	(/ (* M D) (* 2.0 d))
45.0ms	(/ (* M D) (* 2.0 d))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	202	2209
1	512	2034
2	2297	1617
done	5000	1614

prune634.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.3b

regimes643.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	39
1	28	39
done	28	39

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	9350×	body	80	valid
335.0ms	3161×	body	80	nan