Details

sample71.0ms

Algorithm

intervals

Results

24.0ms	288×	body	80	valid
9.0ms	97×	body	80	nan

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
6	4397
5	1444
4	373
3	161
2	79
1	36
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* 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))))
6.5b	(/ (* M D) (* 2.0 d))
12.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite119.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l`

Counts

4 → 113

Calls

4 calls:

29.0ms	(* 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))))
20.0ms	(/ (* M D) (* 2.0 d))
58.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

622.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
639.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
49.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.9s

Counts

125 → 125

Iterations

Iter	Nodes
done	5036
2	2268
1	597
0	236

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize93.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))
3.1b	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
4.0b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
6.5b	(/ (* M D) (* d 2.0))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

450×	`add-exp-log`
236×	`prod-exp`
140×	`div-exp`
95×	`add-sqr-sqrt`
86×	`times-frac`
84×	`cbrt-prod`
80×	`associate-r`
57×	`*-un-lft-identity` `add-cube-cbrt`
50×	`add-cbrt-cube` `pow-exp`
40×	`cbrt-unprod`
22×	`cbrt-undiv`
15×	`unswap-sqr`
10×	`pow-to-exp` `pow1` `unpow-prod-down` `associate-l`
8×	`associate-*r/`
6×	`sqr-pow`
5×	`frac-times` `associate-*l/`
4×	`div-inv` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`sqrt-div` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `associate-/l`

Counts

4 → 259

Calls

4 calls:

280.0ms	(* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))
67.0ms	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
4.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
10.0ms	(/ (* M D) (* d 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

823.0ms	(* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))
710.0ms	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
548.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
47.0ms	(/ (* M D) (* d 2.0))

simplify2.1s

Counts

271 → 271

Iterations

Iter	Nodes
done	5000
1	1424
0	474

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize93.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
4.3b	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
6.5b	(/ (* M D) (* d 2.0))
6.5b	(/ (* M D) (* d 2.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
70×	`add-sqr-sqrt`
51×	`times-frac`
48×	`cbrt-prod`
40×	`associate-r`
32×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube`
30×	`prod-exp`
23×	`div-exp`
15×	`unswap-sqr`
10×	`unpow-prod-down` `pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
6×	`sqr-pow`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 146

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
41.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
10.0ms	(/ (* M D) (* d 2.0))
10.0ms	(/ (* M D) (* d 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

522.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
702.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
43.0ms	(/ (* M D) (* d 2.0))
31.0ms	(/ (* M D) (* d 2.0))

simplify2.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5142
2	2869
1	794
0	303

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize159.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))))
4.0b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
6.5b	(/ (* M D) (* d 2.0))
6.5b	(/ (* M D) (* d 2.0))

rewrite114.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
7×	`unpow-prod-down` `times-frac`
6×	`unswap-sqr`
5×	`pow-to-exp` `pow1` `associate-r`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 126

Calls

4 calls:

77.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))))
7.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
11.0ms	(/ (* M D) (* d 2.0))
10.0ms	(/ (* M D) (* d 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

740.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))))
602.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
40.0ms	(/ (* M D) (* d 2.0))
33.0ms	(/ (* M D) (* d 2.0))

simplify1.8s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	2769
1	673
0	254

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

regimes3.5s

Accuracy

33.1% (1.9b remaining)

Error of 8.9b against oracle of 7.0b and baseline of 9.8b

bsearch2.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	54
1	54
0	43

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	9297×	body	80	valid
799.0ms	3005×	body	80	nan