Details

sample448.0ms

Algorithm

intervals

Results

78.0ms	231×	body	80	valid
76.0ms	24×	body	10240	exit
74.0ms	77×	body	5120	valid
57.0ms	454×	body	80	nan
51.0ms	62×	body	2560	valid
17.0ms	26×	body	1280	valid
6.0ms	6×	body	320	valid
5.0ms	9×	body	640	valid
1.0ms	3×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: done (2.3s)

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.7b

localize58.0ms

Local error

Found 4 expressions with local error:

18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.5b	(+ (/ (* 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:

87.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
80.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
54.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
979.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.2s

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
135.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
506.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
408.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify552.0ms

Counts

168 → 168

Iterations

Useful iterations: done (547.0ms)

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

prune625.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.2b

localize7.0ms

Local error

Found 1 expressions with local error:

5.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite44.0ms

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:

42.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.2s

Counts

33 → 33

Iterations

Useful iterations: 2 (130.0ms)

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

prune137.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 28.9b

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

prune38.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 28.9b

localize73.0ms

Local error

Found 4 expressions with local error:

15.9b	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))

rewrite744.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`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`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `difference-of-squares`

Counts

4 → 153

Calls

4 calls:

527.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
72.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
72.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
59.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))

series731.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
141.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))

simplify463.0ms

Counts

165 → 165

Iterations

Useful iterations: done (458.0ms)

Iter	Nodes	Cost
0	154	4326
1	538	4070
done	5001	2916

prune694.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 27.9b

regimes703.0ms

Accuracy

0% (3.1b remaining)

Error of 33.3b against oracle of 30.2b and baseline of 33.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	3	3
1	5	1
done	5	1

end0.0ms

sample14.5s

Algorithm

intervals

Results

4.0s	2319×	body	5120	valid
2.9s	1716×	body	2560	valid
2.3s	12671×	body	80	nan
1.2s	6805×	body	80	valid
783.0ms	571×	body	10240	exit
782.0ms	906×	body	1280	valid
222.0ms	462×	body	640	valid
80.0ms	228×	body	320	valid
69.0ms	114×	body	160	valid