Details

sample64.0ms

Algorithm

intervals

Results

15.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
8.0ms	29×	body	1280	valid
5.0ms	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

simplify44.0ms

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

prune9.0ms

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

simplify542.0ms

Counts

161 → 161

Iterations

Useful iterations: done (535.0ms)

Iter	Nodes	Cost
0	275	4079
1	658	3918
2	2184	3762
done	5001	3756

prune356.0ms

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))))

rewrite48.0ms

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:

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify585.0ms

Counts

129 → 129

Iterations

Useful iterations: done (581.0ms)

Iter	Nodes	Cost
0	260	2753
1	697	2517
2	2542	2237
done	5000	2213

prune233.0ms

Filtered

96 candidates to 129 candidates (-34.4%)

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

localize16.0ms

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))))

rewrite29.0ms

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:

7.0ms	(/ (sqrt (/ 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))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (sqrt (/ 1 2.0)) a)
10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify869.0ms

Counts

134 → 134

Iterations

Useful iterations: 3 (326.0ms)

Iter	Nodes	Cost
0	245	1960
1	424	1753
2	1139	1642
3	3189	1615
done	5000	1615

prune256.0ms

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

localize17.0ms

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))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (* 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))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify727.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (212.0ms)

Iter	Nodes	Cost
0	92	1324
1	215	1004
2	700	904
3	2449	898
done	5001	898

prune137.0ms

Filtered

54 candidates to 67 candidates (-24.1%)

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

regimes350.0ms

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

sample1.8s

Algorithm

intervals

Results

351.0ms	1070×	body	2560	valid
347.0ms	5830×	body	80	valid
247.0ms	906×	body	1280	valid
171.0ms	2972×	body	80	nan
103.0ms	484×	body	640	valid
50.0ms	130×	body	5120	valid
35.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample64.0ms

simplify44.0ms

prune9.0ms

localize11.0ms

rewrite37.0ms

series76.0ms

simplify542.0ms

prune356.0ms

localize12.0ms

rewrite48.0ms

series75.0ms

simplify585.0ms

prune233.0ms

localize16.0ms

rewrite29.0ms

series50.0ms

simplify869.0ms

prune256.0ms

localize17.0ms

rewrite31.0ms

series62.0ms

simplify727.0ms

prune137.0ms

regimes350.0ms

bsearch57.0ms

simplify3.0ms

end0.0ms

sample1.8s

Profiling