Details

sample96.0ms

Algorithm

intervals

Results

20.0ms	32×	body	1280	valid
20.0ms	43×	body	2560	valid
12.0ms	164×	body	80	valid
6.0ms	80×	body	80	nan
4.0ms	16×	body	640	valid
4.0ms	8×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 4.0 c) a))
0.4b	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
1.5b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

14.0ms	(- (* b b) (* (* 4.0 c) a))
117.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
52.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 c) a))
138.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
106.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
123.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.9s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
2	2308
1	512
0	198

prune846.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -2.0 (/ c b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 34

Calls

1 calls:

23.0ms

(* -2.0 (/ c b))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(* -2.0 (/ c b))

simplify2.4s

Counts

37 → 37

Iterations

Iter	Nodes
done	5001
3	4654
2	669
1	177
0	70

prune224.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

localize12.0ms

Local error

Found 1 expressions with local error:

0.2b	(* (* -2.0 c) (/ 1 b))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
12×	`prod-exp`
9×	`times-frac`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `rec-exp` `1-exp`
1×	`expm1-log1p-u` `associate-l` `associate-r/` `un-div-inv` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 40

Calls

1 calls:

37.0ms

(* (* -2.0 c) (/ 1 b))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(* (* -2.0 c) (/ 1 b))

simplify2.3s

Counts

43 → 43

Iterations

Iter	Nodes
done	5002
2	1687
1	252
0	86

prune212.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
0.5b	(cbrt (/ 1 b))
0.5b	(cbrt (/ 1 b))
0.5b	(cbrt (/ 1 b))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

22.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
2.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))

series967.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
207.0ms	(cbrt (/ 1 b))
244.0ms	(cbrt (/ 1 b))
238.0ms	(cbrt (/ 1 b))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	1088
1	255
0	143

prune846.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

regimes624.0ms

Accuracy

87.9% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 39.5b

bsearch86.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.7108875578650606e+138

simplify28.0ms

Iterations

Iter	Nodes
done	32
1	32
0	28

end0.0ms

sample3.3s

Algorithm

intervals

Results

770.0ms	1094×	body	2560	valid
579.0ms	5792×	body	80	valid
527.0ms	887×	body	1280	valid
467.0ms	2874×	body	80	nan
151.0ms	467×	body	640	valid
101.0ms	108×	body	5120	valid
52.0ms	243×	body	320	valid
18.0ms	117×	body	160	valid