Details

sample401.0ms

Algorithm

intervals

Results

143.0ms	76×	body	5120	valid
57.0ms	466×	body	80	nan
41.0ms	56×	body	2560	valid
28.0ms	211×	body	80	valid
16.0ms	24×	body	1280	valid
15.0ms	14×	body	10240	exit
9.0ms	16×	body	640	valid
4.0ms	10×	body	320	valid
3.0ms	5×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	21	52
1	206	52
done	5000	50

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.5b

localize43.0ms

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))))

rewrite1.2s

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:

85.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
86.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
84.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
950.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
138.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
135.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
432.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify5.1s

Counts

168 → 168

Iterations

Useful iterations: done (5.1s)

Iter	Nodes	Cost
0	161	4866
1	2873	4240
done	5002	3089

prune630.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.3b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite25.0ms

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:

24.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify2.4m

Counts

33 → 33

Iterations

Useful iterations: done (2.4m)

Iter	Nodes	Cost
0	69	299
done	5000	94

prune88.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 29.7b

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

prune26.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.7b

localize33.0ms

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))))

rewrite672.0ms

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:

39.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
40.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
33.0ms	(/ (* (* w h) (* D D)) (* d d))
550.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
96.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
75.0ms	(/ (* (* w h) (* D D)) (* d d))
445.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.3s

Counts

173 → 173

Iterations

Useful iterations: 1 (875.0ms)

Iter	Nodes	Cost
0	201	4466
1	4235	3909
done	5000	3909

prune466.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.2b

regimes407.0ms

Accuracy

-38% (5.3b remaining)

Error of 34.5b against oracle of 29.1b and baseline of 33.0b

bsearch119.0ms

Steps

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

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	35
1	35	33
done	35	33

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.3s	2302×	body	5120	valid
1.4s	1753×	body	2560	valid
1.3s	13026×	body	80	nan
1.0s	6735×	body	80	valid
714.0ms	538×	body	10240	exit
690.0ms	911×	body	1280	valid
186.0ms	472×	body	640	valid
75.0ms	223×	body	320	valid
17.0ms	108×	body	160	valid