Details

sample74.0ms

Algorithm

intervals

Results

29.0ms	301×	body	80	valid
11.0ms	106×	body	80	nan

simplify4.5s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize55.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b	(/ (* M D) (* 2.0 d))
10.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite86.0ms

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:

19.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.0ms	(/ (* M D) (* 2.0 d))
47.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts

4 → 12

Calls

4 calls:

585.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
606.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
50.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (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

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.1b

localize67.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
2.9b	(* w0 (sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))))
3.8b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
4.8b	(/ (* M D) (* d 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
67×	`add-exp-log`
50×	`times-frac`
48×	`cbrt-prod`
46×	`associate-r`
35×	`*-un-lft-identity` `add-cube-cbrt`
27×	`prod-exp`
21×	`add-cbrt-cube`
19×	`div-exp`
17×	`unswap-sqr`
12×	`associate-l`
10×	`unpow-prod-down` `pow-exp`
7×	`pow1` `sqrt-prod` `cbrt-unprod`
6×	`sqr-pow`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv`
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 → 149

Calls

4 calls:

43.0ms	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
14.0ms	(* w0 (sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (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)))))
19.0ms	(/ (* M D) (* d 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

780.0ms	(* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l)))
616.0ms	(* w0 (sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))))
525.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* d 2.0)) 2.0) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))))
34.0ms	(/ (* M D) (* d 2.0))

simplify2.1s

Counts

161 → 161

Iterations

Iter	Nodes
done	5027
2	2903
1	843
0	328

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.4b

localize107.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
3.8b	(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)))))
4.8b	(/ (* M D) (* d 2.0))
4.8b	(/ (* M D) (* d 2.0))

rewrite99.0ms

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:

68.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
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)))))
9.0ms	(/ (* M D) (* d 2.0))
9.0ms	(/ (* M D) (* d 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

783.0ms	(* (pow (/ (* M D) (* d 2.0)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
555.0ms	(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)))))
52.0ms	(/ (* M D) (* d 2.0))
41.0ms	(/ (* M D) (* d 2.0))

simplify2.3s

Counts

158 → 158

Iterations

Iter	Nodes
done	5023
2	2867
1	787
0	303

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize82.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
3.8b	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.8b	(/ (* M D) (* 2.0 d))
4.8b	(/ (* M D) (* 2.0 d))

rewrite90.0ms

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:

44.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
8.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
17.0ms	(/ (* M D) (* 2.0 d))
9.0ms	(/ (* M D) (* 2.0 d))

series1.3s

Counts

4 → 12

Calls

4 calls:

760.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
499.0ms	(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
39.0ms	(/ (* M D) (* 2.0 d))
38.0ms	(/ (* M D) (* 2.0 d))

simplify1.9s

Counts

158 → 158

Iterations

Iter	Nodes
done	5024
2	2735
1	783
0	302

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

regimes2.0s

Accuracy

0% (1.0b remaining)

Error of 8.4b against oracle of 7.5b and baseline of 8.4b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	40
1	40
0	29

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	9267×	body	80	valid
394.0ms	3027×	body	80	nan