Details

sample308.0ms

Algorithm

intervals

Results

107.0ms	84×	body	5120	valid
40.0ms	386×	body	80	nan
28.0ms	44×	body	2560	valid
22.0ms	198×	body	80	valid
14.0ms	26×	body	1280	valid
13.0ms	15×	body	10240	exit
5.0ms	12×	body	640	valid
3.0ms	9×	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	60	52
2	295	50
3	3269	50
done	5000	45

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.8b

localize35.0ms

Local error

Found 4 expressions with local error:

15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
29.9b	(+ (/ (* 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)))
52.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
63.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
857.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series762.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
134.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
131.0ms	(/ (* 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))))

simplify2.0s

Counts

168 → 168

Iterations

Useful iterations: done (2.0s)

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

prune592.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.2b

localize11.0ms

Local error

Found 1 expressions with local error:

5.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite29.0ms

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:

28.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify2.6s

Counts

33 → 33

Iterations

Useful iterations: 2 (104.0ms)

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

prune82.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 29.0b

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

prune23.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 29.0b

localize41.0ms

Local error

Found 4 expressions with local error:

15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
15.9b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.2b	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
29.9b	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log` `add-cbrt-cube`
78×	`prod-exp` `cbrt-unprod`
32×	`cbrt-prod`
30×	`cbrt-undiv` `div-exp`
19×	`fma-def`
13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down` `cube-prod`
6×	`times-frac` `div-inv` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cube-div` `cbrt-div`
2×	`cube-mult` `frac-2neg` `sqrt-div` `unpow3` `frac-add` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`+-commutative` `flip3--` `flip3-+` `pow1/3` `sum-log` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

4 → 153

Calls

4 calls:

58.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
63.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
14.0ms	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
1.0s	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
132.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
129.0ms	(cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))
373.0ms	(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify1.9s

Counts

165 → 165

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	204	4564
1	575	3790
2	3645	2726
done	5000	2725

prune586.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 28.3b

regimes417.0ms

Accuracy

0% (3.3b remaining)

Error of 33.7b against oracle of 30.4b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
done	4	3

end0.0ms

sample14.0s

Algorithm

intervals

Results

3.6s	2315×	body	5120	valid
2.6s	12983×	body	80	nan
1.8s	1758×	body	2560	valid
1.6s	6655×	body	80	valid
1.1s	876×	body	1280	valid
671.0ms	575×	body	10240	exit
306.0ms	427×	body	640	valid
111.0ms	229×	body	320	valid
61.0ms	128×	body	160	valid