Details

sample65.0ms

Algorithm

intervals

Results

12.0ms	29×	body	1280	valid
11.0ms	176×	body	80	valid
11.0ms	33×	body	2560	valid
4.0ms	78×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	92	16
5	100	16
done	100	16

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
1.0b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

13.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
10.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify508.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (180.0ms)

Iter	Nodes	Cost
0	275	4079
1	658	3908
2	2089	3756
done	5001	3756

prune361.0ms

Filtered

114 candidates to 161 candidates (-41.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	149	12	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	12	162

Merged error: 5.7b

Counts

162 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-r`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-l`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 117

Calls

4 calls:

24.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify565.0ms

Counts

129 → 129

Iterations

Useful iterations: done (561.0ms)

Iter	Nodes	Cost
0	260	2753
1	697	2483
2	2620	2213
done	5000	2205

prune229.0ms

Filtered

95 candidates to 129 candidates (-35.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Merged error: 5.7b

Counts

141 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (/ 1 2.0)) a)
1.0b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ (sqrt (/ 1 2.0)) a)
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify838.0ms

Counts

134 → 134

Iterations

Useful iterations: 3 (309.0ms)

Iter	Nodes	Cost
0	245	1960
1	424	1744
2	1053	1621
3	3110	1615
done	5000	1615

prune262.0ms

Filtered

82 candidates to 134 candidates (-63.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	134	10	144

Merged error: 5.7b

Counts

144 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
14.9b	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify758.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (219.0ms)

Iter	Nodes	Cost
0	92	1324
1	215	964
2	712	904
3	2492	896
done	5000	896

prune141.0ms

Filtered

55 candidates to 67 candidates (-21.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	67	10	77

Merged error: 5.7b

Counts

77 → 10

regimes348.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.6b

bsearch57.0ms

Steps

Iters	Range		Point
7	2.951159271200378e-80	1.7529870675191086e-78	9.827618726336024e-79
8	-8.704679048448932e+71	-1.0976727662850034e+68	-1.013848001599699e+70

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

584.0ms	1070×	body	2560	valid
338.0ms	5830×	body	80	valid
245.0ms	906×	body	1280	valid
174.0ms	2972×	body	80	nan
108.0ms	484×	body	640	valid
54.0ms	130×	body	5120	valid
35.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample65.0ms

simplify41.0ms

prune11.0ms

localize11.0ms

rewrite37.0ms

series76.0ms

simplify508.0ms

prune361.0ms

localize12.0ms

rewrite49.0ms

series70.0ms

simplify565.0ms

prune229.0ms

localize15.0ms

rewrite33.0ms

series46.0ms

simplify838.0ms

prune262.0ms

localize14.0ms

rewrite31.0ms

series60.0ms

simplify758.0ms

prune141.0ms

regimes348.0ms

bsearch57.0ms

simplify3.0ms

end0.0ms

sample2.0s

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