Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	315×	body	80	nan
12.0ms	284×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	12
0	8

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize19.0ms

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)))

rewrite62.0ms

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×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `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 → 72

Calls

3 calls:

37.0ms	(* c0 (sqrt (/ A (* V l))))
12.0ms	(/ A (* V l))
11.0ms	(sqrt (/ A (* V l)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(* c0 (sqrt (/ A (* V l))))
35.0ms	(/ A (* V l))
63.0ms	(sqrt (/ A (* V l)))

simplify2.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
3	4743
2	895
1	225
0	111

prune520.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
1.7b	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
4.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
12.8b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-exp-log`
26×	`associate-r`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
14×	`cbrt-prod`
11×	`pow1`
10×	`associate-l`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`sqrt-div` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-prod-down` `associate-*l/`
2×	`sqrt-pow1` `*-commutative` `sqrt-prod` `div-inv`
1×	`pow1/2` `pow1/3`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt A)
87.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
58.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
25.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt A)
86.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
65.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
88.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify1.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	3298
1	558
0	194

prune770.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
0.7b	(* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))
1.7b	(* c0 (sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))))
12.8b	(sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log`
37×	`add-cbrt-cube`
33×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp` `associate-*r/`
17×	`pow1`
15×	`frac-times`
14×	`sqrt-div`
13×	`associate-l`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-*l/`
7×	`pow-prod-down`
6×	`cbrt-prod` `times-frac`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`*-commutative` `sqrt-prod`
1×	`pow1/2` `pow1/3` `div-inv` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

1.0ms	(cbrt A)
106.0ms	(* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))
195.0ms	(* c0 (sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))))
63.0ms	(sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt A)
26.0ms	(* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))
78.0ms	(* c0 (sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l)))))
57.0ms	(sqrt (* (/ (cbrt A) (* (cbrt V) (cbrt V))) (* (/ (cbrt A) (cbrt V)) (/ (cbrt A) l))))

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	2870
1	580
0	206

prune803.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt V)
1.7b	(/ (/ A (cbrt V)) l)
1.7b	(* c0 (/ (sqrt (/ (/ A (cbrt V)) l)) (fabs (cbrt V))))
10.9b	(sqrt (/ (/ A (cbrt V)) l))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

852×	`times-frac`
437×	`add-sqr-sqrt`
406×	`*-un-lft-identity` `add-cube-cbrt`
284×	`sqrt-prod`
223×	`associate-r`
149×	`cbrt-prod`
22×	`div-inv` `associate-/l*`
14×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `rem-sqrt-square` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l*`
2×	`prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 455

Calls

4 calls:

1.0ms	(cbrt V)
15.0ms	(/ (/ A (cbrt V)) l)
149.0ms	(* c0 (/ (sqrt (/ (/ A (cbrt V)) l)) (fabs (cbrt V))))
25.0ms	(sqrt (/ (/ A (cbrt V)) l))

series1.3s

Counts

4 → 12

Calls

4 calls:

306.0ms	(cbrt V)
129.0ms	(/ (/ A (cbrt V)) l)
228.0ms	(* c0 (/ (sqrt (/ (/ A (cbrt V)) l)) (fabs (cbrt V))))
588.0ms	(sqrt (/ (/ A (cbrt V)) l))

simplify2.0s

Counts

467 → 467

Iterations

Iter	Nodes
done	5000
1	2060
0	841

prune3.3s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.0b

regimes1.8s

Accuracy

16.1% (3.6b remaining)

Error of 4.0b against oracle of 0.5b and baseline of 4.7b

bsearch2.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	41
1	41
0	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

488.0ms	8975×	body	80	valid
448.0ms	8996×	body	80	nan