Details

sample65.0ms

Algorithm

intervals

Results

26.0ms	288×	body	80	valid
6.0ms	84×	body	80	nan

simplify676.0ms

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	1402	18
done	5000	18

prune5.0ms

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))

rewrite35.0ms

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:

6.0ms	(* 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))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series609.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
165.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
239.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify657.0ms

Counts

125 → 125

Iterations

Useful iterations: done (652.0ms)

Iter	Nodes	Cost
0	281	2382
1	744	2170
2	2723	1987
done	5000	1971

prune290.0ms

Filtered

82 candidates to 125 candidates (-52.4%)

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))

rewrite31.0ms

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)
8.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(/ (* M D) (* 2.0 d))

series650.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
230.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
246.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

simplify636.0ms

Counts

108 → 108

Iterations

Useful iterations: done (633.0ms)

Iter	Nodes	Cost
0	269	1937
1	700	1781
2	2683	1579
done	5001	1557

prune231.0ms

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))

rewrite45.0ms

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)))
13.0ms	(* (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))

series608.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
228.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
241.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
7.0ms	(/ (* 2.0 d) (* M D))

simplify999.0ms

Counts

147 → 147

Iterations

Useful iterations: done (994.0ms)

Iter	Nodes	Cost
0	365	2779
1	936	2550
2	3256	2136
done	5000	2070

prune273.0ms

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))
9.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series415.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(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))
7.0ms	(/ (* M D) (* 2.0 d))
237.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify665.0ms

Counts

122 → 122

Iterations

Useful iterations: done (661.0ms)

Iter	Nodes	Cost
0	257	2497
1	709	2112
2	2637	1866
done	5000	1846

prune237.0ms

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

regimes2.1s

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

749.0ms	9345×	body	80	valid
252.0ms	3190×	body	80	nan

Details

sample65.0ms

simplify676.0ms

prune5.0ms

localize14.0ms

rewrite35.0ms

series609.0ms

simplify657.0ms

prune290.0ms

localize14.0ms

rewrite31.0ms

series650.0ms

simplify636.0ms

prune231.0ms

localize16.0ms

rewrite45.0ms

series608.0ms

simplify999.0ms

prune273.0ms

localize17.0ms

rewrite35.0ms

series415.0ms

simplify665.0ms

prune237.0ms

regimes2.1s

bsearch1.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling