Details

sample109.0ms

Algorithm

intervals

Results

31.0ms	563×	pre	80	true
19.0ms	307×	body	80	nan
19.0ms	150×	body	160	valid
7.0ms	106×	body	80	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
30.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
57.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series446.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
56.0ms	(- (* b b) (* (* 4.0 a) c))
164.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
137.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	2476
1	480	2169
2	1444	1861
done	5001	1789

prune387.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.2b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune59.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/r`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 55

Calls

2 calls:

17.0ms	(/ (* a c) b)
33.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series45.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(/ (* a c) b)
23.0ms	(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify903.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (301.0ms)

Iter	Nodes	Cost
0	111	818
1	314	787
2	1621	559
done	5001	559

prune226.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 9.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* a c) b)
0.4b	(* (* -2.0 (/ (* a c) b)) (/ 1 (* 2.0 a)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-exp-log`
69×	`prod-exp`
61×	`add-cbrt-cube`
32×	`div-exp`
29×	`cbrt-unprod`
16×	`cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-r`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-r/` `pow-prod-down` `associate-/r`
2×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-l` `associate-l/` `clear-num` `un-div-inv` `-commutative` `associate-/l*`

Counts

2 → 87

Calls

2 calls:

10.0ms	(/ (* a c) b)
84.0ms	(* (* -2.0 (/ (* a c) b)) (/ 1 (* 2.0 a)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (* a c) b)
33.0ms	(* (* -2.0 (/ (* a c) b)) (/ 1 (* 2.0 a)))

simplify2.4s

Counts

93 → 93

Iterations

Useful iterations: 2 (397.0ms)

Iter	Nodes	Cost
0	162	1507
1	419	1281
2	1712	923
done	5000	923

prune94.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 9.1b

regimes435.0ms

Accuracy

45.5% (7.6b remaining)

Error of 16.7b against oracle of 9.1b and baseline of 23.0b

bsearch34.0ms

Steps

Iters	Range		Point
3	429.638275575464	508.3649641937415	434.5586936141063

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	38
1	31	38
done	31	38

end0.0ms

sample3.5s

Algorithm

intervals

Results

915.0ms	16589×	pre	80	true
765.0ms	4475×	body	160	valid
739.0ms	8589×	body	80	nan
336.0ms	3525×	body	80	valid