Details

sample395.0ms

Algorithm

intervals

Results

136.0ms	422×	body	80	nan
61.0ms	68×	body	5120	valid
42.0ms	54×	body	2560	valid
29.0ms	232×	body	80	valid
22.0ms	38×	body	1280	valid
10.0ms	11×	body	10240	exit
5.0ms	11×	body	640	valid
3.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: done (2.2s)

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.9b

localize33.0ms

Local error

Found 4 expressions with local error:

20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.8b	(+ (/ (* 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:

66.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
88.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
45.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
987.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series847.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
137.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
158.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
405.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify610.0ms

Counts

168 → 168

Iterations

Useful iterations: done (600.0ms)

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

prune744.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.6b

localize6.0ms

Local error

Found 1 expressions with local error:

5.2b	(* (/ c0 (* 2.0 w)) 0)

rewrite30.0ms

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)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.3s

Counts

33 → 33

Iterations

Useful iterations: 2 (153.0ms)

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

prune163.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 30.7b

localize4.0ms

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

prune48.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 30.7b

localize59.0ms

Local error

Found 4 expressions with local error:

20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
21.2b	(/ (* (* w h) (* D D)) (* d d))
33.2b	(+ (/ c0 (/ (* (* w h) (* D D)) (* 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

183×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
40×	`cbrt-undiv` `div-exp`
21×	`times-frac`
20×	`fma-def`
15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`div-inv`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `associate-/r/` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 161

Calls

4 calls:

88.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
85.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
53.0ms	(/ (* (* w h) (* D D)) (* d d))
917.0ms	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series1.4s

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
143.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
96.0ms	(/ (* (* w h) (* D D)) (* d d))
1.1s	(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify474.0ms

Counts

173 → 173

Iterations

Useful iterations: done (467.0ms)

Iter	Nodes	Cost
0	201	4466
1	766	4208
done	5000	3135

prune737.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 29.7b

regimes874.0ms

Accuracy

0% (3.6b remaining)

Error of 33.9b against oracle of 30.3b and baseline of 33.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	7	5
done	7	5

end0.0ms

sample14.3s

Algorithm

intervals

Results

2.7s	2339×	body	5120	valid
2.5s	13266×	body	80	nan
2.2s	1674×	body	2560	valid
1.5s	570×	body	10240	exit
1.3s	6996×	body	80	valid
1.1s	903×	body	1280	valid
677.0ms	468×	body	640	valid
119.0ms	239×	body	320	valid
24.0ms	111×	body	160	valid