Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	315×	body	80	nan
10.0ms	284×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	12
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize23.0ms

Local error

Found 3 expressions with local error:

1.7b	(* c0 (sqrt (/ A (* V l))))
5.3b	(/ A (* V l))
12.8b	(sqrt (/ A (* V l)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `associate-r` `add-exp-log`
9×	`times-frac`
6×	`pow1`
3×	`associate-l` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `*-commutative`

Counts

3 → 66

Calls

3 calls:

18.0ms	(* c0 (sqrt (/ A (* V l))))
6.0ms	(/ A (* V l))
5.0ms	(sqrt (/ A (* V l)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* c0 (sqrt (/ A (* V l))))
32.0ms	(/ A (* V l))
46.0ms	(sqrt (/ A (* V l)))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	3823
2	807
1	221
0	105

prune445.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

localize38.0ms

Local error

Found 4 expressions with local error:

1.7b	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))))
2.4b	(* l (/ V (cbrt A)))
3.0b	(/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))
12.8b	(sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`add-exp-log`
31×	`associate-r`
23×	`times-frac` `add-cbrt-cube`
22×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sqrt-prod`
10×	`cbrt-prod` `prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-l`
5×	`associate-*r/` `unswap-sqr`
4×	`div-inv` `add-log-exp`
3×	`associate-/r/`
2×	`sqrt-div` `pow-prod-down` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l`

Counts

4 → 111

Calls

4 calls:

38.0ms	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))))
31.0ms	(* l (/ V (cbrt A)))
29.0ms	(/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))
21.0ms	(sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A)))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))))
132.0ms	(* l (/ V (cbrt A)))
51.0ms	(/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A))))
68.0ms	(sqrt (/ (* (cbrt A) (cbrt A)) (* l (/ V (cbrt A)))))

simplify875.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2232
1	499
0	187

prune727.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
1.7b	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ 1 l) V) (cbrt A)))))
2.9b	(* (/ (/ 1 l) V) (cbrt A))
10.8b	(sqrt (* (/ (/ 1 l) V) (cbrt A)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
67×	`add-sqr-sqrt`
46×	`associate-l`
45×	`*-un-lft-identity`
43×	`add-cube-cbrt`
24×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`pow1`
10×	`cbrt-prod`
8×	`prod-exp` `unswap-sqr`
7×	`associate-r`
6×	`div-exp` `cbrt-unprod`
5×	`pow-prod-down`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-*l/`
2×	`sqrt-pow1` `sqrt-div` `associate-r/` `-commutative`
1×	`rec-exp` `pow1/2` `pow1/3` `1-exp` `sqrt-prod`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt A)
148.0ms	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ 1 l) V) (cbrt A)))))
45.0ms	(* (/ (/ 1 l) V) (cbrt A))
20.0ms	(sqrt (* (/ (/ 1 l) V) (cbrt A)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt A)
179.0ms	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ 1 l) V) (cbrt A)))))
85.0ms	(* (/ (/ 1 l) V) (cbrt A))
114.0ms	(sqrt (* (/ (/ 1 l) V) (cbrt A)))

simplify1.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	2513
1	607
0	234

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt l)
0.6b	(cbrt l)
1.7b	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))))
10.8b	(sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `sqrt-div`
4×	`pow-prod-down` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-times` `sqrt-pow1` `pow1/3` `associate-*l/`
1×	`pow1/2` `associate-r` `*-commutative` `sqrt-prod`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt l)
1.0ms	(cbrt l)
632.0ms	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))))
70.0ms	(sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt l)
276.0ms	(cbrt l)
327.0ms	(* c0 (* (fabs (cbrt A)) (sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))))
322.0ms	(sqrt (* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt l) (cbrt l))) (* (cbrt V) (cbrt V))) (/ (cbrt A) (* (cbrt V) (cbrt l)))))

simplify868.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1144
1	284
0	120

prune583.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 2.5b

regimes1.3s

Accuracy

42.2% (5.4b remaining)

Error of 8.0b against oracle of 2.7b and baseline of 12.0b

bsearch125.0ms

Steps

Iters	Range		Point
10	-5.1438265166111916e-300	5.860604158197322e-304	2.6516976256475e-311

simplify8.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

914.0ms	8996×	body	80	nan
495.0ms	8975×	body	80	valid