Details

sample373.0ms

Algorithm

intervals

Results

92.0ms	466×	body	80	nan
71.0ms	76×	body	5120	valid
44.0ms	211×	body	80	valid
43.0ms	56×	body	2560	valid
14.0ms	24×	body	1280	valid
13.0ms	14×	body	10240	exit
7.0ms	16×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	52
1	205	52
done	5000	52

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.5b

localize54.0ms

Local error

Found 4 expressions with local error:

15.3b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.3b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.3b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
28.3b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

51.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
62.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
913.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
149.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
414.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify5.7s

Counts

155 → 155

Iterations

Useful iterations: done (5.7s)

Iter	Nodes	Cost
0	157	4688
1	2826	4101
done	5000	2981

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.8b

localize14.0ms

Local error

Found 1 expressions with local error:

4.9b	(* (/ c0 (* 2.0 w)) 0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`mul0` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 28

Calls

1 calls:

45.0ms

(* (/ c0 (* 2.0 w)) 0)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify2.5m

Counts

31 → 31

Iterations

Useful iterations: done (2.5m)

Iter	Nodes	Cost
0	67	283
done	5001	90

prune90.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.2b

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune25.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.2b

localize32.0ms

Local error

Found 4 expressions with local error:

15.3b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.3b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.3b	(/ (* (* w h) (* D D)) (* c0 (* d d)))
30.0b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d))))) (* M M))))

rewrite963.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

42.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
42.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
827.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d))))) (* M M))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
107.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
112.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
268.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d))))) (* M M))))

simplify2.1s

Counts

155 → 155

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	203	4744
1	4637	4269
done	5000	4035

prune409.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.2b

regimes444.0ms

Accuracy

0% (2.3b remaining)

Error of 33.0b against oracle of 30.7b and baseline of 33.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	3	3
1	4	1
done	4	1

end0.0ms

sample9.2s

Algorithm

intervals

Results

1.8s	2302×	body	5120	valid
1.7s	13026×	body	80	nan
1.3s	6735×	body	80	valid
1.2s	1753×	body	2560	valid
758.0ms	911×	body	1280	valid
484.0ms	472×	body	640	valid
433.0ms	538×	body	10240	exit
51.0ms	223×	body	320	valid
18.0ms	108×	body	160	valid