Details

sample67.0ms

Algorithm

intervals

Results

23.0ms	288×	body	80	valid
11.0ms	84×	body	80	nan

simplify673.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	173	18
4	428	18
5	1345	18
done	5000	18

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b	(/ (* M D) (* 2.0 d))
12.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series622.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
171.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.0ms	(/ (* M D) (* 2.0 d))
242.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify622.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	281	2382
1	744	2144
2	2676	1968
done	5000	1968

prune288.0ms

Filtered

80 candidates to 125 candidates (-56.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 9.1b

Counts

126 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.9b	(/ (* M D) (* 2.0 d))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
8.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
9.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(/ (* M D) (* 2.0 d))

series654.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
234.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
244.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(/ (* M D) (* 2.0 d))

simplify813.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (203.0ms)

Iter	Nodes	Cost
0	269	1937
1	700	1750
2	2579	1557
done	5000	1557

prune226.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 8.8b

Counts

117 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
5.2b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
5.3b	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
6.1b	(/ (* 2.0 d) (* M D))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-exp-log`
67×	`div-exp`
64×	`prod-exp`
32×	`pow-exp`
31×	`add-sqr-sqrt`
24×	`times-frac` `associate-l`
23×	`unpow-prod-down` `add-cbrt-cube`
21×	`*-un-lft-identity`
18×	`add-cube-cbrt`
10×	`rec-exp` `1-exp`
6×	`cbrt-undiv` `cbrt-unprod` `div-inv`
5×	`pow1` `sqrt-prod` `unswap-sqr`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
16.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
13.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
7.0ms	(/ (* 2.0 d) (* M D))

series614.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
233.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
240.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
7.0ms	(/ (* 2.0 d) (* M D))

simplify679.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (252.0ms)

Iter	Nodes	Cost
0	365	2779
1	936	2493
2	3057	2070
done	5000	2070

prune271.0ms

Filtered

87 candidates to 147 candidates (-69.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Merged error: 8.8b

Counts

155 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.9b	(/ (* M D) (* 2.0 d))
5.9b	(/ (* M D) (* 2.0 d))
12.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 110

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
7.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series421.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(/ (* M D) (* 2.0 d))
240.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify637.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	257	2497
1	709	2084
2	2613	1846
done	5000	1846

prune239.0ms

Filtered

78 candidates to 122 candidates (-56.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	122	8	130

Merged error: 8.7b

Counts

130 → 8

regimes2.0s

Accuracy

58% (1.4b remaining)

Error of 9.4b against oracle of 8.1b and baseline of 11.4b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	103
1	51	103
done	51	103

end0.0ms

sample1.9s

Algorithm

intervals

Results

752.0ms	9345×	body	80	valid
255.0ms	3190×	body	80	nan

Details

sample67.0ms

simplify673.0ms

prune11.0ms

localize14.0ms

rewrite32.0ms

series622.0ms

simplify622.0ms

prune288.0ms

localize14.0ms

rewrite32.0ms

series654.0ms

simplify813.0ms

prune226.0ms

localize16.0ms

rewrite48.0ms

series614.0ms

simplify679.0ms

prune271.0ms

localize17.0ms

rewrite35.0ms

series421.0ms

simplify637.0ms

prune239.0ms

regimes2.0s

bsearch1.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling