Details

sample348.0ms

Algorithm

intervals

Results

66.0ms	379×	body	80	nan
62.0ms	70×	body	5120	valid
60.0ms	41×	body	1280	valid
38.0ms	51×	body	2560	valid
26.0ms	201×	body	80	valid
17.0ms	18×	body	10240	exit
4.0ms	9×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5207
3	2972
2	280
1	59
0	21

prune63.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.7b

localize175.0ms

Local error

Found 4 expressions with local error:

15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
26.3b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-cbrt-cube` `add-exp-log`
81×	`prod-exp` `cbrt-unprod`
72×	`cbrt-undiv` `div-exp`
11×	`associate-*r/`
9×	`associate-/l/`
8×	`sqrt-div` `frac-add`
7×	`frac-times`
6×	`*-un-lft-identity` `add-log-exp`
5×	`associate-*l/`
4×	`add-sqr-sqrt` `pow1` `flip3-+` `add-cube-cbrt` `flip-+` `insert-posit16`
3×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `flip3--` `div-inv` `flip--` `associate-/l`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

56.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
56.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
63.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
117.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.5s

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
171.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
225.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
1.9s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify6.6s

Counts

168 → 168

Iterations

Iter	Nodes
done	5008
2	3525
1	661
0	215

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 49.1b

localize415.0ms

Local error

Found 4 expressions with local error:

15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
26.3b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
26.3b	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
16×	`sqrt-div` `frac-add`
10×	`frac-times` `associate-*r/`
8×	`*-un-lft-identity` `flip3-+` `flip-+` `add-log-exp`
6×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
4×	`add-sqr-sqrt` `pow1` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `times-frac` `div-inv` `distribute-lft-out` `associate-/l`

Counts

4 → 132

Calls

4 calls:

71.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
55.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
134.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
97.0ms	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series4.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
179.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
1.8s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
1.9s	(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify6.2s

Counts

144 → 144

Iterations

Iter	Nodes
done	5008
2	3525
1	661
0	215

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 49.1b

localize167.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
29.6b	(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
10×	`frac-times` `associate-*r/`
8×	`frac-add`
7×	`pow1` `flip3-+` `flip-+`
6×	`-un-lft-identity` `flip3--` `associate-l/` `flip--` `add-log-exp` `associate-/l/`
4×	`add-sqr-sqrt` `add-cube-cbrt` `insert-posit16`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `times-frac` `div-inv` `associate-/l`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

4 → 131

Calls

4 calls:

120.0ms	(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
67.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
95.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
149.0ms	(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
203.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
198.0ms	(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
1.8s	(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify6.5s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	3727
1	704
0	227

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 45.4b

localize255.0ms

Local error

Found 4 expressions with local error:

9.0b	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
9.0b	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
14.3b	(sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M)))
26.3b	(+ (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

2374×	`times-frac`
891×	`*-un-lft-identity`
890×	`add-sqr-sqrt`
889×	`add-cube-cbrt`
218×	`associate-/l*`
178×	`div-inv`
112×	`associate-/r/`
104×	`associate-*r/`
88×	`add-cbrt-cube` `add-exp-log`
58×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `sqrt-prod` `insert-posit16`
2×	`clear-num` `frac-2neg` `flip3--` `frac-add` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

4 → 970

Calls

4 calls:

72.0ms	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
83.0ms	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
402.0ms	(sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M)))
1.1s	(+ (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M))))

series1.7s

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
153.0ms	(/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)
619.0ms	(sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M)))
771.0ms	(+ (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (sqrt (- (* (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w) (/ (/ (/ d D) (/ h (* c0 (/ d D)))) w)) (* M M))))

simplify5.2s

Counts

982 → 982

Iterations

Iter	Nodes
done	5001
1	2814
0	1141

prune22.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 24.8b

regimes6.4s

Accuracy

-3% (9.9b remaining)

Error of 34.0b against oracle of 24.2b and baseline of 33.7b

bsearch13.0ms

simplify32.0ms

Iterations

Iter	Nodes
done	45
1	45
0	36

end0.0ms

sample14.9s

Algorithm

intervals

Results

3.7s	2263×	body	5120	valid
2.5s	13010×	body	80	nan
2.5s	1817×	body	2560	valid
1.6s	6718×	body	80	valid
1.1s	877×	body	1280	valid
852.0ms	616×	body	10240	exit
276.0ms	443×	body	640	valid
164.0ms	229×	body	320	valid
106.0ms	118×	body	160	valid