Details

sample63.0ms

Algorithm

intervals

Results

13.0ms	40×	body	2560	valid
10.0ms	178×	body	80	valid
9.0ms	36×	body	1280	valid
4.0ms	88×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.2b	(- (* b b) (* (* c a) 4.0))
0.7b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.4b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

84.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
12.0ms	(- (* b b) (* (* c a) 4.0))
71.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
16.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
71.0ms	(- (* b b) (* (* c a) 4.0))
164.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
101.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.1s

Counts

161 → 161

Iterations

Iter	Nodes
done	5002
2	3070
1	692
0	280

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a)
0.2b	(- (* b b) (* (* c a) 4.0))
6.8b	(- (/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a) (/ (/ b 2.0) a))
24.4b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
148×	`add-sqr-sqrt`
122×	`*-un-lft-identity`
96×	`add-cube-cbrt`
42×	`sqrt-prod`
22×	`associate-/l*`
13×	`div-inv` `distribute-lft-out--`
12×	`difference-of-squares`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`distribute-rgt-out--`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `sub-div` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

27.0ms	(/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a)
12.0ms	(- (* b b) (* (* c a) 4.0))
257.0ms	(- (/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a) (/ (/ b 2.0) a))
14.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a)
91.0ms	(- (* b b) (* (* c a) 4.0))
185.0ms	(- (/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a) (/ (/ b 2.0) a))
106.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.1s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	3442
1	836
0	341

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
0.7b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.4b	(sqrt (- (* b b) (* (* c a) 4.0)))
24.4b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

49.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
50.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
17.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
8.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
152.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
101.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
116.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	4798
2	826
1	198
0	81

prune622.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* c a) 4.0))
0.2b	(/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0)))
11.9b	(- (/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0))) (/ (/ b 2.0) a))
24.4b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite641.0ms

Algorithm

rewrite-expression-head

Rules

776×	`times-frac`
449×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
325×	`add-cube-cbrt`
117×	`sqrt-prod`
71×	`associate-/r*`
27×	`difference-of-squares`
25×	`add-exp-log`
18×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/r/`
3×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 382

Calls

4 calls:

7.0ms	(- (* b b) (* (* c a) 4.0))
27.0ms	(/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0)))
564.0ms	(- (/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0))) (/ (/ b 2.0) a))
14.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* c a) 4.0))
143.0ms	(/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0)))
170.0ms	(- (/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0))) (/ (/ b 2.0) a))
85.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts

394 → 394

Iterations

Iter	Nodes
done	5001
1	1869
0	654

prune2.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes405.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 34.1b

bsearch154.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample3.3s

Algorithm

intervals

Results

994.0ms	5902×	body	80	valid
550.0ms	1052×	body	2560	valid
535.0ms	2839×	body	80	nan
397.0ms	898×	body	1280	valid
113.0ms	451×	body	640	valid
81.0ms	111×	body	5120	valid
44.0ms	239×	body	320	valid
13.0ms	105×	body	160	valid