Details

sample71.0ms

Algorithm

intervals

Results

13.0ms	36×	body	2560	valid
12.0ms	179×	body	80	valid
10.0ms	28×	body	1280	valid
5.0ms	79×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify125.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

134.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
75.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
108.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
63.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	154	1592
1	386	1488
2	1234	1332
3	4639	1324
done	5002	1324

prune347.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 118

Calls

4 calls:

73.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
82.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
117.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
63.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	220	3137
1	497	2801
2	1463	2561
done	5000	2481

prune282.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
6.7b	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

22.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a))
57.0ms	(- (* b b) (* (* 4.0 a) c))
157.0ms	(- (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* 2.0 a)) (/ b (* 2.0 a)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

86 → 86

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	163	1718
1	408	1572
2	1261	1436
done	5000	1432

prune327.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

103.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
61.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
129.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
64.0ms	(- (* b b) (* (* 4.0 a) c))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	154	1592
1	386	1488
2	1234	1332
3	4639	1324
done	5002	1324

prune198.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.5b

regimes583.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.3b

bsearch91.0ms

Steps

Iters	Range		Point
5	1.8656011488683937e-53	5.89324344694736e-53	1.8920981354719558e-53
8	-3.0008378519073826e+120	-1.7813274366303991e+117	-1.0062396840173395e+118

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	38
1	31	38
done	31	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

892.0ms	5914×	body	80	valid
439.0ms	1022×	body	2560	valid
419.0ms	872×	body	1280	valid
256.0ms	2922×	body	80	nan
154.0ms	467×	body	640	valid
75.0ms	236×	body	320	valid
57.0ms	125×	body	5120	valid
13.0ms	109×	body	160	valid