Details

sample176.0ms

Algorithm

intervals

Results

17.0ms	40×	body	2560	valid
16.0ms	178×	body	80	valid
12.0ms	36×	body	1280	valid
6.0ms	88×	body	80	nan
4.0ms	15×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (* b_2 b_2) (* a c))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite243.0ms

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:

112.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
12.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	2129
1	493
0	195

prune784.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
6.8b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
287×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
23×	`fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 411

Calls

4 calls:

27.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
13.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
41.0ms	(- (* b_2 b_2) (* a c))
113.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

423 → 423

Iterations

Iter	Nodes
done	5000
2	3641
1	1143
0	499

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
11.9b	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

2630×	`times-frac`
1567×	`add-sqr-sqrt`
1530×	`*-un-lft-identity`
1517×	`add-cube-cbrt`
1002×	`prod-diff`
421×	`sqrt-prod`
139×	`div-inv`
107×	`associate-/r/`
94×	`sqrt-div`
78×	`fma-neg`
49×	`flip3--` `flip--`
24×	`associate-/r*`
15×	`add-exp-log`
14×	`difference-of-squares`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*` `distribute-lft-out--`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 1265

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
259.0ms	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
90.0ms	(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
157.0ms	(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
116.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

1277 → 1277

Iterations

Iter	Nodes
done	5000
1	2780
0	1240

prune5.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite12.0ms

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:

11.0ms

(* -1/2 (/ c b_2))

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

(* -1/2 (/ c b_2))

simplify1.8s

Counts

37 → 37

Iterations

Iter	Nodes
done	5001
3	2645
2	584
1	178
0	70

prune157.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 5.4b

regimes629.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.0b

bsearch123.0ms

Steps

Iters	Range		Point
7	4.7547400806771625e-82	1.9034131584556183e-80	3.0476772566360775e-81
7	-9.685109581380507e+154	-1.5171851739610474e+153	-2.0256498248166784e+153

simplify7.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample3.3s

Algorithm

intervals

Results

916.0ms	1055×	body	2560	valid
867.0ms	5904×	body	80	valid
331.0ms	2832×	body	80	nan
296.0ms	899×	body	1280	valid
134.0ms	111×	body	5120	valid
106.0ms	447×	body	640	valid
51.0ms	241×	body	320	valid
13.0ms	102×	body	160	valid