Details

sample1.1s

Algorithm

intervals

Results

860.0ms	1107×	body	80	nan
152.0ms	398×	body	80	valid

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
4	9030
3	1081
2	188
1	55
0	22

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.7b

localize61.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
13.5b	(sqrt (/ d l))
13.5b	(sqrt (/ d l))
13.7b	(sqrt (/ d h))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

16265×	`times-frac`
5466×	`add-sqr-sqrt`
5457×	`*-un-lft-identity` `add-cube-cbrt`
4043×	`sqrt-prod`
3808×	`frac-times`
3375×	`associate-/r/`
2464×	`associate-l/` `associate-r/`
908×	`div-inv`
460×	`add-cbrt-cube` `add-exp-log`
357×	`associate-/l*`
270×	`cbrt-undiv` `div-exp`
130×	`prod-exp` `cbrt-unprod`
13×	`associate-/r*`
7×	`pow1`
6×	`rem-sqrt-square`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 5214

Calls

4 calls:

78.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
2.0ms	(sqrt (/ d l))
4.0ms	(sqrt (/ d l))
4.0ms	(sqrt (/ d h))

series566.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
64.0ms	(sqrt (/ d l))
88.0ms	(sqrt (/ d l))
70.0ms	(sqrt (/ d h))

simplify1.3m

Counts

5226 → 5226

Iterations

Iter	Nodes
1	28544
0	8555

prune1.4m

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.3b

localize55.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
10.2b	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
13.5b	(sqrt (/ d l))
13.5b	(sqrt (/ d l))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

16865×	`times-frac`
5674×	`add-sqr-sqrt`
5668×	`*-un-lft-identity` `add-cube-cbrt`
4329×	`sqrt-prod`
4097×	`frac-times`
3631×	`associate-/r/`
2651×	`associate-l/` `associate-r/`
948×	`div-inv`
645×	`add-cbrt-cube` `add-exp-log`
373×	`associate-/l*`
363×	`cbrt-undiv` `div-exp`
195×	`prod-exp` `cbrt-unprod`
35×	`associate-/r*`
6×	`pow1`
4×	`rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`sqrt-div`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 5645

Calls

4 calls:

56.0ms	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
65.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
2.0ms	(sqrt (/ d l))
2.0ms	(sqrt (/ d l))

series808.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
548.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))
47.0ms	(sqrt (/ d l))
63.0ms	(sqrt (/ d l))

simplify53.3s

Counts

5657 → 5657

Iterations

Iter	Nodes
1	28392
0	8551

prune1.5m

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.8b

localize81.0ms

Local error

Found 4 expressions with local error:

4.8b	(* (- (sqrt (/ d l)) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
5.4b	(* (/ M 2) (/ D d))
5.4b	(* (/ M 2) (/ D d))
13.5b	(sqrt (/ d l))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
54×	`times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
33×	`add-cbrt-cube` `add-exp-log`
29×	`associate-l`
27×	`associate-r`
14×	`pow1`
13×	`sqrt-div` `sqrt-prod`
11×	`prod-exp` `associate-*r/` `cbrt-unprod`
9×	`frac-times` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`frac-sub`
5×	`pow-prod-down` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`rem-sqrt-square` `flip3--` `flip--`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 158

Calls

4 calls:

86.0ms	(* (- (sqrt (/ d l)) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
12.0ms	(* (/ M 2) (/ D d))
12.0ms	(* (/ M 2) (/ D d))
2.0ms	(sqrt (/ d l))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (- (sqrt (/ d l)) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
29.0ms	(* (/ M 2) (/ D d))
34.0ms	(* (/ M 2) (/ D d))
49.0ms	(sqrt (/ d l))

simplify1.1s

Counts

170 → 170

Iterations

Iter	Nodes
2	3504
1	849
0	308

prune3.3s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 6.3b

localize84.0ms

Local error

Found 4 expressions with local error:

4.4b	(sqrt (/ (cbrt d) l))
4.8b	(* (- (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
5.4b	(* (/ M 2) (/ D d))
5.4b	(* (/ M 2) (/ D d))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
64×	`times-frac`
46×	`*-un-lft-identity` `add-cube-cbrt`
33×	`add-cbrt-cube` `add-exp-log`
29×	`associate-l`
27×	`associate-r`
22×	`sqrt-prod`
17×	`associate-*r/`
14×	`pow1`
13×	`sqrt-div`
11×	`prod-exp` `cbrt-unprod`
10×	`cbrt-prod`
9×	`frac-times` `associate-*l/`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`frac-sub`
5×	`pow-prod-down` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `*-commutative`
2×	`flip3--` `flip--`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 168

Calls

4 calls:

2.0ms	(sqrt (/ (cbrt d) l))
85.0ms	(* (- (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
11.0ms	(* (/ M 2) (/ D d))
17.0ms	(* (/ M 2) (/ D d))

series1.9s

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (/ (cbrt d) l))
1.7s	(* (- (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (* (/ (* (/ (sqrt (* (cbrt d) (cbrt d))) (sqrt 2)) (* (/ M 2) (/ D d))) l) (/ (/ (sqrt (/ (cbrt d) l)) (/ (sqrt 2) (* (/ M 2) (/ D d)))) (/ 1 h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))))
28.0ms	(* (/ M 2) (/ D d))
32.0ms	(* (/ M 2) (/ D d))

simplify1.1s

Counts

180 → 180

Iterations

Iter	Nodes
2	3926
1	989
0	365

prune3.3s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 5.5b

regimes2.2s

Accuracy

10.2% (5.1b remaining)

Error of 9.4b against oracle of 4.3b and baseline of 9.9b

bsearch651.0ms

Steps

Iters	Range		Point
6	1.585771030946342e+37	8.304287440210865e+37	8.058937538114404e+37
6	-6.921999886571995e-308	3.1212595157882477e-308	1.676306393372541e-308

simplify28.0ms

Iterations

Iter	Nodes
2	82
1	82
0	65

end0.0ms

sample15.6s

Algorithm

intervals

Results

9.6s	38268×	body	80	nan
4.4s	12725×	body	80	valid