Details

sample45.0ms

Algorithm

intervals

Results

15.0ms	303×	body	80	valid
5.0ms	99×	body	80	nan

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9
done	5001	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(/ (* M D) (* 2.0 d))
6.1b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite69.0ms

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:

17.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

447.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
29.0ms	(/ (* M D) (* 2.0 d))
397.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
698.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5002	994
done	5002	994

prune356.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.9b

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
4.7b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.1b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

12.0ms	(/ (* M D) (* 2.0 d))
25.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
38.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

series1.9s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2.0 d))
752.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
720.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
404.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

simplify83.0ms

Counts

140 → 140

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	752	1137
1	3467	1014
2	5001	1001
done	5001	1001

prune349.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.9b

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (/ M 2.0) (/ D d))
4.7b	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
5.1b	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
6.1b	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
44×	`add-sqr-sqrt`
40×	`div-exp`
31×	`times-frac`
30×	`add-cbrt-cube`
29×	`associate-r`
28×	`add-cube-cbrt` `*-un-lft-identity`
25×	`pow-exp`
19×	`associate-l`
11×	`cbrt-unprod`
9×	`pow1`
8×	`rec-exp` `1-exp`
6×	`cbrt-undiv` `unswap-sqr`
5×	`pow-to-exp`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative` `div-inv`
2×	`sqrt-div` `associate-*r/` `pow-prod-down` `sqr-pow`
1×	`frac-times` `unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-*l/` `un-div-inv` `flip--`

Counts

4 → 152

Calls

4 calls:

21.0ms	(* (/ M 2.0) (/ D d))
16.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
30.0ms	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
5.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

series1.9s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ M 2.0) (/ D d))
776.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
734.0ms	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
409.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

simplify93.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	892	1255
1	3905	1133
2	5001	1120
done	5001	1120

prune449.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.9b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
3.8b	(/ (* M D) (* 2.0 d))
6.1b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
8.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite67.0ms

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:

12.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
34.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(/ (* M D) (* 2.0 d))
422.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
745.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify67.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	576	1133
1	2582	1013
2	5001	1012
done	5001	1012

prune380.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.9b

regimes430.0ms

Accuracy

70.3% (0.9b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 10.9b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	47	30
done	47	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

483.0ms	9406×	body	80	valid
185.0ms	3155×	body	80	nan