Details

sample359.0ms

Algorithm

intervals

Results

85.0ms	69×	body	5120	valid
55.0ms	430×	body	80	nan
54.0ms	31×	body	1280	valid
35.0ms	50×	body	2560	valid
27.0ms	227×	body	80	valid
12.0ms	15×	body	10240	exit
4.0ms	10×	body	320	valid
4.0ms	7×	body	640	valid
2.0ms	9×	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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 56.9b

localize27.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.6b	(+ (/ (* 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:

57.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
65.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
63.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
890.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
130.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
141.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
367.0ms	(+ (/ (* 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

prune687.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.7b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite34.0ms

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:

33.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify3.1s

Counts

33 → 33

Iterations

Useful iterations: 2 (89.0ms)

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

prune86.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.1b

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

prune33.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.1b

localize30.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b	(/ (* (* w h) (* D D)) (* c0 (* d d)))
26.6b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.4s

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:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
62.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
74.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
1.2s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
106.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
116.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
344.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.4s

Counts

168 → 168

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	209	4926
1	619	4621
2	4385	3021
done	5000	3003

prune464.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 29.9b

regimes545.0ms

Accuracy

0% (2.9b remaining)

Error of 33.6b against oracle of 30.7b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
done	3	3

end0.0ms

sample13.8s

Algorithm

intervals

Results

3.0s	2264×	body	5120	valid
2.8s	13225×	body	80	nan
2.5s	1710×	body	2560	valid
1.5s	6804×	body	80	valid
757.0ms	613×	body	10240	exit
749.0ms	943×	body	1280	valid
279.0ms	445×	body	640	valid
103.0ms	228×	body	320	valid
23.0ms	107×	body	160	valid