Details

sample76.0ms

Algorithm

intervals

Results

16.0ms	311×	body	80	nan
15.0ms	285×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize43.0ms

Local error

Found 3 expressions with local error:

2.2b	(* c0 (sqrt (/ A (* V l))))
4.3b	(/ A (* V l))
13.5b	(sqrt (/ A (* V l)))

rewrite63.0ms

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:

36.0ms	(* c0 (sqrt (/ A (* V l))))
12.0ms	(/ A (* V l))
12.0ms	(sqrt (/ A (* V l)))

series533.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* c0 (sqrt (/ A (* V l))))
412.0ms	(/ A (* V l))
54.0ms	(sqrt (/ A (* V l)))

simplify2.5s

Counts

81 → 81

Iterations

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

prune569.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* l V) A))
2.2b	(* c0 (sqrt (/ 1 (/ (* l V) A))))
4.2b	(/ (* l V) A)
13.5b	(sqrt (/ 1 (/ (* l V) A)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
65×	`add-sqr-sqrt`
55×	`sqrt-prod`
54×	`*-un-lft-identity`
52×	`add-cube-cbrt`
32×	`add-exp-log`
29×	`associate-r`
20×	`add-cbrt-cube`
14×	`div-exp` `div-inv`
10×	`associate-/r*`
9×	`pow1`
7×	`cbrt-undiv`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `1-exp` `associate-l` `associate-/r/` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-div` `pow-flip` `inv-pow`
1×	`pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 174

Calls

4 calls:

10.0ms	(/ 1 (/ (* l V) A))
47.0ms	(* c0 (sqrt (/ 1 (/ (* l V) A))))
9.0ms	(/ (* l V) A)
14.0ms	(sqrt (/ 1 (/ (* l V) A)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (/ (* l V) A))
61.0ms	(* c0 (sqrt (/ 1 (/ (* l V) A))))
40.0ms	(/ (* l V) A)
76.0ms	(sqrt (/ 1 (/ (* l V) A)))

simplify818.0ms

Counts

186 → 186

Iterations

Iter	Nodes
done	5002
2	2090
1	502
0	233

prune997.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 3 expressions with local error:

2.3b	(/ c0 (sqrt (/ (* l V) A)))
4.2b	(/ (* l V) A)
13.0b	(sqrt (/ (* l V) A))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
35×	`sqrt-prod`
31×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
7×	`div-inv`
4×	`pow1` `associate-/l*`
3×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-exp` `associate-/r/` `cbrt-unprod`

Counts

3 → 101

Calls

3 calls:

9.0ms	(/ c0 (sqrt (/ (* l V) A)))
13.0ms	(/ (* l V) A)
6.0ms	(sqrt (/ (* l V) A))

series239.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ c0 (sqrt (/ (* l V) A)))
41.0ms	(/ (* l V) A)
78.0ms	(sqrt (/ (* l V) A))

simplify814.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	1260
1	323
0	168

prune718.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
2.3b	(/ c0 (sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))))
4.4b	(* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))
13.0b	(sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

1.0ms	(cbrt A)
32.0ms	(/ c0 (sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))))
39.0ms	(* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))
19.0ms	(sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt A)
108.0ms	(/ c0 (sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))))
59.0ms	(* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A)))
94.0ms	(sqrt (* (/ l (* (cbrt A) (cbrt A))) (/ V (cbrt A))))

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
2	3315
1	581
0	220

prune845.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

regimes856.0ms

Accuracy

6.2% (10.2b remaining)

Error of 13.7b against oracle of 3.4b and baseline of 14.4b

bsearch354.0ms

Steps

Iters	Range		Point
7	1.596912091549096e+231	4.0087646009344313e+232	4.1486363202651826e+231
8	4.2309919062731585e-260	1.59557376955987e-257	5.161254179931936e-260
7	-1.419241376206283e-142	-6.498174607631055e-144	-1.4049454919010747e-142
8	-7.150951066432917e-125	-9.53326816478898e-129	-9.678217132402726e-129

simplify9.0ms

Iterations

Iter	Nodes
done	51
1	51
0	44

end0.0ms

sample2.5s

Algorithm

intervals

Results

509.0ms	8985×	body	80	nan
466.0ms	8894×	body	80	valid