Details

sample340.0ms

Algorithm

intervals

Results

84.0ms	466×	body	80	nan
80.0ms	76×	body	5120	valid
41.0ms	56×	body	2560	valid
25.0ms	211×	body	80	valid
13.0ms	24×	body	1280	valid
11.0ms	14×	body	10240	exit
7.0ms	16×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	21	52
1	59	52
2	289	52
3	3227	52
done	5000	46

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize35.0ms

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:

69.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
49.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
76.0ms	(/ (* 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))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
161.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
145.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
359.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.4s

Counts

155 → 155

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	157	4688
1	468	4293
2	3049	2845
done	5001	2809

prune398.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.8b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite31.0ms

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:

30.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify3.1s

Counts

31 → 31

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	67	283
1	158	74
2	472	38
3	2113	38
done	5000	38

prune105.0ms

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

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune47.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.2b

localize38.0ms

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)))
15.8b	(/ (* (* w h) (* D D)) (* d d))
33.5b	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

183×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
40×	`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 → 133

Calls

4 calls:

46.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
45.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
37.0ms	(/ (* (* w h) (* D D)) (* d d))
859.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.2s

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
141.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
144.0ms	(/ (* (* w h) (* D D)) (* d d))
706.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify3.0s

Counts

145 → 145

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	195	4292
1	574	3946
2	3802	2646
done	5001	2610

prune405.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 29.7b

regimes582.0ms

Accuracy

-47.3% (4.6b remaining)

Error of 34.5b against oracle of 29.9b and baseline of 33.0b

bsearch227.0ms

Steps

Iters	Range		Point
2	1.8495071466723752e+52	2.0865081753980722e+52	1.8791322752630873e+52
5	5.109638427522923e-42	1.0372222338647842e-41	1.0280149463749771e-41

simplify11.0ms

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	25	33
1	34	31
done	34	31

end0.0ms

sample14.3s

Algorithm

intervals

Results

3.3s	2302×	body	5120	valid
3.1s	13026×	body	80	nan
2.3s	1753×	body	2560	valid
1.4s	6735×	body	80	valid
1.1s	911×	body	1280	valid
585.0ms	538×	body	10240	exit
302.0ms	472×	body	640	valid
78.0ms	223×	body	320	valid
25.0ms	108×	body	160	valid