Details

sample65.0ms

Algorithm

intervals

Results

24.0ms	288×	body	80	valid
7.0ms	84×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1244	18
6	4808	18
done	5000	18

prune6.0ms

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

localize21.0ms

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:

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))

series606.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
167.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
238.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify836.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (298.0ms)

Iter	Nodes	Cost
0	281	2382
1	739	2142
2	2509	1968
done	5000	1968

prune287.0ms

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

localize18.0ms

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))

series629.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
223.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
235.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

simplify790.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (239.0ms)

Iter	Nodes	Cost
0	269	1937
1	694	1750
2	2483	1557
done	5000	1557

prune235.0ms

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

localize18.0ms

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))

series601.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
226.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
235.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
7.0ms	(/ (* 2.0 d) (* M D))

simplify869.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (292.0ms)

Iter	Nodes	Cost
0	365	2779
1	922	2485
2	2863	2080
done	5000	2080

prune269.0ms

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

localize18.0ms

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))

rewrite34.0ms

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))
12.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series407.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(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))
6.0ms	(/ (* M D) (* 2.0 d))
233.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify857.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (294.0ms)

Iter	Nodes	Cost
0	257	2497
1	706	2084
2	2478	1846
done	5000	1846

prune242.0ms

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

regimes2.3s

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

sample2.0s

Algorithm

intervals

Results

791.0ms	9345×	body	80	valid
274.0ms	3190×	body	80	nan

Details

sample65.0ms

simplify3.8s

prune6.0ms

localize21.0ms

rewrite32.0ms

series606.0ms

simplify836.0ms

prune287.0ms

localize18.0ms

rewrite31.0ms

series629.0ms

simplify790.0ms

prune235.0ms

localize18.0ms

rewrite45.0ms

series601.0ms

simplify869.0ms

prune269.0ms

localize18.0ms

rewrite34.0ms

series407.0ms

simplify857.0ms

prune242.0ms

regimes2.3s

bsearch1.0ms

simplify4.0ms

end0.0ms

sample2.0s

Profiling