Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	292×	body	80	valid
6.0ms	89×	body	80	nan

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	176	18
4	422	18
5	1174	18
6	4570	18
done	5000	18

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b	(/ (* M D) (* 2.0 d))
11.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite116.0ms

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×	`sqrt-div` `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 → 113

Calls

4 calls:

28.0ms	(* 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))))
26.0ms	(/ (* M D) (* 2.0 d))
48.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.0s

Counts

4 → 12

Calls

4 calls:

517.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
501.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms	(/ (* M D) (* 2.0 d))
926.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.2s

Counts

125 → 125

Iterations

Useful iterations: 2 (366.0ms)

Iter	Nodes	Cost
0	236	2311
1	577	2083
2	2262	1927
done	5000	1927

prune529.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize19.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))
8.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `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 → 110

Calls

4 calls:

8.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
19.0ms	(/ (* M D) (* 2.0 d))
20.0ms	(/ (* M D) (* 2.0 d))
56.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.4s

Counts

4 → 12

Calls

4 calls:

491.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
42.0ms	(/ (* M D) (* 2.0 d))
36.0ms	(/ (* M D) (* 2.0 d))
874.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify1.1s

Counts

122 → 122

Iterations

Useful iterations: 2 (311.0ms)

Iter	Nodes	Cost
0	211	2420
1	538	2019
2	2259	1799
done	5000	1799

prune628.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize27.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.0b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-exp-log`
84×	`prod-exp`
40×	`div-exp` `add-cbrt-cube`
20×	`pow-exp`
14×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac`
10×	`cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`pow1`
4×	`pow-to-exp` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `pow-prod-down` `un-div-inv` `-commutative` `flip--`

Counts

4 → 118

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
48.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
15.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

series1.5s

Counts

4 → 12

Calls

4 calls:

453.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
980.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
36.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(/ (* M D) (* 2.0 d))

simplify1.2s

Counts

130 → 130

Iterations

Useful iterations: 2 (323.0ms)

Iter	Nodes	Cost
0	225	2712
1	566	2263
2	2233	1799
done	5000	1799

prune543.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize25.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.0b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
5.6b	(/ (* 2.0 d) (* M D))
5.7b	(/ (* M D) (* 2.0 d))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-exp-log`
84×	`prod-exp`
40×	`div-exp` `add-cbrt-cube`
20×	`pow-exp`
14×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac`
10×	`cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`pow1`
4×	`pow-to-exp` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `pow-prod-down` `un-div-inv` `-commutative` `flip--`

Counts

4 → 118

Calls

4 calls:

11.0ms	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
71.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
26.0ms	(/ (* 2.0 d) (* M D))
15.0ms	(/ (* M D) (* 2.0 d))

series1.6s

Counts

4 → 12

Calls

4 calls:

510.0ms	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
1.0s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
32.0ms	(/ (* 2.0 d) (* M D))
49.0ms	(/ (* M D) (* 2.0 d))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: 2 (565.0ms)

Iter	Nodes	Cost
0	248	2758
1	637	2313
2	2838	2005
done	5000	2005

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

regimes1.4s

Accuracy

0% (1.1b remaining)

Error of 8.8b against oracle of 7.7b and baseline of 8.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	35	38
done	35	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	9296×	body	80	valid
464.0ms	3069×	body	80	nan