Details

sample382.0ms

Algorithm

intervals

Results

84.0ms	76×	body	5120	valid
58.0ms	466×	body	80	nan
54.0ms	14×	body	10240	exit
43.0ms	56×	body	2560	valid
27.0ms	211×	body	80	valid
16.0ms	24×	body	1280	valid
8.0ms	16×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	21	52
1	60	52
2	295	50
3	3269	50
done	5000	45

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.6b

localize57.0ms

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))))

rewrite961.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `div-inv`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

54.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
45.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
45.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
802.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series894.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
152.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
156.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
423.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.0s

Counts

168 → 168

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	161	4866
1	484	4432
2	3124	2971
done	5002	2933

prune517.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite41.0ms

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×	`expm1-log1p-u` `mul0` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

40.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify3.2s

Counts

33 → 33

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	69	299
1	160	78
2	472	42
3	2122	42
done	5001	42

prune111.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.6b

localize3.0ms

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

prune24.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.6b

localize63.0ms

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))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

183×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
40×	`cbrt-undiv` `div-exp`
21×	`times-frac`
20×	`fma-def`
15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 161

Calls

4 calls:

44.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
54.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
35.0ms	(/ (* (* w h) (* D D)) (* d d))
929.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series943.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
135.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
117.0ms	(/ (* (* w h) (* D D)) (* d d))
565.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.4s

Counts

173 → 173

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	201	4466
1	590	4081
2	3862	2768
done	5000	2755

prune628.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 29.1b

regimes644.0ms

Accuracy

-41.3% (5.0b remaining)

Error of 34.5b against oracle of 29.4b and baseline of 33.0b

bsearch165.0ms

Steps

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

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

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

end0.0ms

sample15.2s

Algorithm

intervals

Results

3.2s	2302×	body	5120	valid
2.8s	6735×	body	80	valid
2.8s	13026×	body	80	nan
1.7s	1753×	body	2560	valid
1.2s	538×	body	10240	exit
802.0ms	911×	body	1280	valid
422.0ms	472×	body	640	valid
87.0ms	223×	body	320	valid
27.0ms	108×	body	160	valid