Details

sample90.0ms

Algorithm

intervals

Results

19.0ms	43×	body	2560	valid
13.0ms	164×	body	80	valid
11.0ms	32×	body	1280	valid
6.0ms	80×	body	80	nan
5.0ms	16×	body	640	valid
5.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	129
5	129
4	120
3	87
2	46
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite203.0ms

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:

12.0ms	(- (* b b) (* a (* 4.0 c)))
109.0ms	(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
69.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
9.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* a (* 4.0 c)))
145.0ms	(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
109.0ms	(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
102.0ms	(sqrt (- (* b b) (* a (* 4.0 c))))

simplify2.9s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2334
1	515
0	199

prune749.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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:

25.0ms

(* -2.0 (/ c b))

series36.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(* -2.0 (/ c b))

simplify2.2s

Counts

37 → 37

Iterations

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

prune254.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

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:

27.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify1.8s

Counts

43 → 43

Iterations

Iter	Nodes
done	5002
2	1687
1	252
0	86

prune265.0ms

Pruning

12 alts after pruning (11 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))

rewrite70.0ms

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:

46.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
4.0ms	(cbrt (/ 1 b))
4.0ms	(cbrt (/ 1 b))
4.0ms	(cbrt (/ 1 b))

series1.1s

Counts

4 → 12

Calls

4 calls:

292.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
280.0ms	(cbrt (/ 1 b))
301.0ms	(cbrt (/ 1 b))
263.0ms	(cbrt (/ 1 b))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	1088
1	255
0	143

prune967.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

regimes577.0ms

Accuracy

87.9% (4.1b remaining)

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

bsearch96.0ms

Steps

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

simplify17.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample3.9s

Algorithm

intervals

Results

937.0ms	887×	body	1280	valid
806.0ms	5792×	body	80	valid
609.0ms	1094×	body	2560	valid
472.0ms	243×	body	320	valid
269.0ms	2874×	body	80	nan
153.0ms	467×	body	640	valid
58.0ms	108×	body	5120	valid
18.0ms	117×	body	160	valid