Details

sample112.0ms

Algorithm

intervals

Results

36.0ms	36×	body	1280	valid
17.0ms	40×	body	2560	valid
14.0ms	178×	body	80	valid
6.0ms	88×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize41.0ms

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)))

rewrite189.0ms

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:

78.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
17.0ms	(- (* b b) (* (* c a) 4.0))
67.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
15.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
74.0ms	(- (* b b) (* (* c a) 4.0))
149.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
99.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts

161 → 161

Iterations

Iter	Nodes
done	5002
2	3070
1	692
0	280

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize59.0ms

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)))

rewrite293.0ms

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:

36.0ms	(/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a)
6.0ms	(- (* b b) (* (* c a) 4.0))
218.0ms	(- (/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a) (/ (/ b 2.0) a))
14.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a)
69.0ms	(- (* b b) (* (* c a) 4.0))
156.0ms	(- (/ (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0) a) (/ (/ b 2.0) a))
93.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.0s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	3442
1	836
0	341

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize51.0ms

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)))

rewrite129.0ms

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:

61.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
37.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
15.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
14.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
108.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
108.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))
104.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.6s

Counts

72 → 72

Iterations

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

prune555.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize26.0ms

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)))

rewrite638.0ms

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))
34.0ms	(/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0)))
535.0ms	(- (/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0))) (/ (/ b 2.0) a))
11.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* b b) (* (* c a) 4.0))
152.0ms	(/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0)))
156.0ms	(- (/ 1 (/ a (/ (sqrt (- (* b b) (* (* c a) 4.0))) 2.0))) (/ (/ b 2.0) a))
113.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.1s

Counts

394 → 394

Iterations

Iter	Nodes
done	5001
1	1869
0	654

prune2.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes392.0ms

Accuracy

83.3% (4.8b remaining)

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

bsearch197.0ms

Steps

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

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	1052×	body	2560	valid
488.0ms	5902×	body	80	valid
391.0ms	898×	body	1280	valid
321.0ms	2839×	body	80	nan
161.0ms	451×	body	640	valid
60.0ms	111×	body	5120	valid
48.0ms	239×	body	320	valid
14.0ms	105×	body	160	valid