Details

sample279.0ms

Algorithm

intervals

Results

63.0ms	427×	body	80	nan
55.0ms	60×	body	5120	valid
43.0ms	72×	body	2560	valid
19.0ms	26×	body	10240	exit
18.0ms	205×	body	80	valid
11.0ms	25×	body	1280	valid
6.0ms	14×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	21	52
1	60	52
2	303	50
3	3435	50
done	5000	45

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.8b

localize48.0ms

Local error

Found 4 expressions with local error:

18.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.1b	(+ (/ (* 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`
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:

66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
842.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
121.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
115.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
330.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify471.0ms

Counts

168 → 168

Iterations

Useful iterations: done (464.0ms)

Iter	Nodes	Cost
0	161	4866
1	619	4432
done	5000	3209

prune496.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.4b

localize7.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ 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×	`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:

30.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.0s

Counts

33 → 33

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	69	299
1	188	90
2	873	42
done	5000	42

prune110.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.2b

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

prune28.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.2b

localize46.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
18.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
51.9b	(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite718.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log` `add-cbrt-cube`
78×	`prod-exp` `cbrt-unprod`
30×	`cbrt-undiv` `div-exp`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `times-frac` `sqrt-div` `clear-num` `associate-/r` `div-inv` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `fma-udef` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

573.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
68.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
1.0ms	(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series831.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
120.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
327.0ms	(fma (* c0 (* d d)) (/ 1 (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify458.0ms

Counts

130 → 130

Iterations

Useful iterations: done (453.0ms)

Iter	Nodes	Cost
0	165	3778
1	560	3576
done	5000	2638

prune441.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 31.5b

regimes495.0ms

Accuracy

0% (3.2b remaining)

Error of 34.5b against oracle of 31.3b and baseline of 34.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	2	2
1	4	1
done	4	1

end0.0ms

sample11.9s

Algorithm

intervals

Results

3.1s	2192×	body	5120	valid
2.3s	13305×	body	80	nan
1.4s	1763×	body	2560	valid
1.3s	6911×	body	80	valid
637.0ms	588×	body	10240	exit
573.0ms	918×	body	1280	valid
496.0ms	249×	body	320	valid
219.0ms	458×	body	640	valid
24.0ms	114×	body	160	valid