Details

sample93.0ms

Algorithm

intervals

Results

35.0ms	306×	body	80	valid
13.0ms	102×	body	80	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	177	18
4	441	18
5	2573	18
done	5001	18

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize35.0ms

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))))
5.7b	(/ (* M D) (* 2.0 d))
9.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite128.0ms

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:

19.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms	(/ (* M D) (* 2.0 d))
72.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

717.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
648.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.5s

Counts

125 → 125

Iterations

Useful iterations: 2 (466.0ms)

Iter	Nodes	Cost
0	236	2311
1	620	2115
2	3082	1929
done	5001	1929

prune550.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize28.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.7b	(/ (* M D) (* 2.0 d))
5.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite136.0ms

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:

43.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
8.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
23.0ms	(/ (* M D) (* 2.0 d))
55.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.3s

Counts

4 → 12

Calls

4 calls:

860.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
499.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
42.0ms	(/ (* M D) (* 2.0 d))
902.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.1s

Counts

140 → 140

Iterations

Useful iterations: 2 (651.0ms)

Iter	Nodes	Cost
0	269	2521
1	769	2218
2	4528	1891
done	5001	1891

prune531.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.6b

localize27.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
4.5b	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
5.0b	(* (/ M 2.0) (/ D d))
5.8b	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

rewrite128.0ms

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:

49.0ms	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
7.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
32.0ms	(* (/ M 2.0) (/ D d))
28.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

series2.4s

Counts

4 → 12

Calls

4 calls:

903.0ms	(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
483.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
30.0ms	(* (/ M 2.0) (/ D d))
985.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

simplify2.8s

Counts

164 → 164

Iterations

Useful iterations: 2 (697.0ms)

Iter	Nodes	Cost
0	317	2747
1	923	2464
2	4965	2093
done	5000	2093

prune915.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize21.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
5.0b	(* (/ M 2.0) (/ D d))
5.0b	(* (/ M 2.0) (/ D d))
6.4b	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`add-exp-log`
44×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
31×	`associate-l`
30×	`add-cbrt-cube`
29×	`associate-r`
19×	`prod-exp`
12×	`div-exp`
10×	`unswap-sqr`
9×	`pow1` `cbrt-unprod`
8×	`cbrt-undiv`
5×	`pow-exp`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`frac-times` `sqrt-div` `associate-r/` `pow-prod-down` `associate-l/` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 141

Calls

4 calls:

8.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
34.0ms	(* (/ M 2.0) (/ D d))
35.0ms	(* (/ M 2.0) (/ D d))
27.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)

series1.4s

Counts

4 → 12

Calls

4 calls:

438.0ms	(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) (/ 1 l))))
40.0ms	(* (/ M 2.0) (/ D d))
39.0ms	(* (/ M 2.0) (/ D d))
854.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)

simplify1.5s

Counts

153 → 153

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	220	2418
1	594	2255
2	2737	1811
done	5000	1785

prune716.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

regimes1.5s

Accuracy

35.6% (1.5b remaining)

Error of 8.7b against oracle of 7.2b and baseline of 9.5b

bsearch173.0ms

Steps

Iters	Range		Point
4	6.303743001166409e+140	9.534228538778794e+140	6.374808609886969e+140
7	-33936282923695948.0	-190915152773030.78	-6500259796587717.0

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	41	137
1	57	106
done	57	106

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	9353×	body	80	valid
715.0ms	3171×	body	80	nan