Details

sample152.0ms

Algorithm

intervals

Results

35.0ms	76×	body	5120	valid
23.0ms	383×	body	80	nan
22.0ms	53×	body	2560	valid
11.0ms	186×	body	80	valid
10.0ms	21×	body	10240	exit
9.0ms	30×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	21	52
1	60	52
2	291	50
3	3205	50
done	5001	50

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 61.1b

localize19.0ms

Local error

Found 4 expressions with local error:

18.5b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.5b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.5b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.7b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite347.0ms

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:

17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
287.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
95.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
97.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
250.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.1s

Counts

168 → 168

Iterations

Useful iterations: 2 (287.0ms)

Iter	Nodes	Cost
0	161	4866
1	572	4432
2	3266	2929
done	5000	2929

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ c0 (* 2.0 w))
7.2b	(* (/ c0 (* 2.0 w)) 0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`associate-r` `associate-/l*`
2×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-2neg` `mul0` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `*-commutative` `unswap-sqr`

Counts

2 → 53

Calls

2 calls:

3.0ms	(/ c0 (* 2.0 w))
10.0ms	(* (/ c0 (* 2.0 w)) 0)

series19.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(/ c0 (* 2.0 w))
1.0ms	(* (/ c0 (* 2.0 w)) 0)

simplify6.1s

Counts

59 → 59

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	85	496
1	202	272
2	1173	206
done	5000	206

prune144.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.9b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune29.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 31.9b

localize24.0ms

Local error

Found 4 expressions with local error:

18.5b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.5b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.9b	(/ (* (* w h) (* D D)) (* c0 (* d d)))
28.4b	(+ (/ (* 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))))

rewrite454.0ms

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:

17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
392.0ms	(+ (/ (* 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))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
97.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
105.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
249.0ms	(+ (/ (* 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))))

simplify1.5s

Counts

168 → 168

Iterations

Useful iterations: 2 (448.0ms)

Iter	Nodes	Cost
0	209	4926
1	762	4621
2	4641	2989
done	5000	2989

prune348.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 31.8b

regimes436.0ms

Accuracy

0% (2.4b remaining)

Error of 33.6b against oracle of 31.1b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3
done	2	3

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	2244×	body	5120	valid
799.0ms	13170×	body	80	nan
679.0ms	1790×	body	2560	valid
419.0ms	6796×	body	80	valid
297.0ms	573×	body	10240	exit
286.0ms	930×	body	1280	valid
104.0ms	434×	body	640	valid
39.0ms	210×	body	320	valid
13.0ms	115×	body	160	valid