Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
7.0ms	180×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	85×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite138.0ms

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:

78.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
50.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (956.0ms)

Iter	Nodes	Cost
0	152	1592
1	385	1488
2	1204	1332
3	4431	1324
done	5000	1324

prune229.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

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:

54.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
40.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
49.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify826.0ms

Counts

130 → 130

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	218	3137
1	494	2801
2	1432	2561
done	5000	2481

prune230.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

75.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
8.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
45.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	156	1888
1	371	1774
2	1022	1658
3	3145	1650
done	5001	1643

prune232.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.4b	(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
9.1b	(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod` `associate-/l/`
2×	`flip3--` `frac-2neg` `sub0-neg` `sqrt-div` `clear-num` `flip--`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 156

Calls

4 calls:

28.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
71.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
48.0ms	(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)
157.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
195.0ms	(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts

168 → 168

Iterations

Useful iterations: 2 (342.0ms)

Iter	Nodes	Cost
0	271	5373
1	681	4872
2	2226	4624
done	5001	4624

prune469.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.0b

regimes142.0ms

Accuracy

81.9% (4.9b remaining)

Error of 10.9b against oracle of 6.0b and baseline of 33.1b

bsearch91.0ms

Steps

Iters	Range		Point
8	1.7227097696114035e-146	1.4073942755830443e-143	1.3880700472259379e-143
7	-1.6239005782062206e+154	-7.680972122048022e+152	-2.6152573735422387e+153

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

243.0ms	1092×	body	2560	valid
220.0ms	5865×	body	80	valid
156.0ms	916×	body	1280	valid
110.0ms	2944×	body	80	nan
62.0ms	460×	body	640	valid
31.0ms	116×	body	5120	valid
21.0ms	209×	body	320	valid
7.0ms	105×	body	160	valid