Details

sample59.0ms

Algorithm

intervals

Results

11.0ms	176×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	29×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune19.0ms

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: 35.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
9.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify754.0ms

Counts

96 → 96

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	147	1616
1	344	1527
2	1013	1429
3	2788	1417
done	5001	1416

prune181.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 5.7b

Counts

97 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify714.0ms

Counts

174 → 174

Iterations

Useful iterations: done (708.0ms)

Iter	Nodes	Cost
0	257	3976
1	575	3579
2	1948	3305
done	5000	3193

prune138.0ms

Filtered

85 candidates to 174 candidates (-104.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	176	10	186

Merged error: 5.6b

Counts

186 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
14.9b	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))
21.5b	(sqrt (- (* b_2 b_2) (* 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:

5.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify599.0ms

Counts

67 → 67

Iterations

Useful iterations: done (597.0ms)

Iter	Nodes	Cost
0	89	1110
1	209	840
2	622	756
3	1724	750
done	5000	746

prune105.0ms

Filtered

53 candidates to 67 candidates (-26.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	67	10	77

Merged error: 5.6b

Counts

77 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.5b	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
16.0ms	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(/ (/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
45.0ms	(/ (- (* b_2 (- b_2 b_2)) (* a c)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify598.0ms

Counts

166 → 166

Iterations

Useful iterations: done (592.0ms)

Iter	Nodes	Cost
0	273	5200
1	711	4589
2	2600	4001
done	5000	3993

prune185.0ms

Filtered

127 candidates to 166 candidates (-30.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	166	10	176

Merged error: 5.6b

Counts

176 → 10

regimes366.0ms

Accuracy

82.5% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 32.4b

bsearch52.0ms

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	26	38
1	32	38
done	32	38

end0.0ms

sample1.6s

Algorithm

intervals

Results

289.0ms	1069×	body	2560	valid
280.0ms	5829×	body	80	valid
205.0ms	907×	body	1280	valid
137.0ms	2967×	body	80	nan
84.0ms	486×	body	640	valid
50.0ms	130×	body	5120	valid
26.0ms	200×	body	320	valid
9.0ms	101×	body	160	valid

Details

sample59.0ms

simplify25.0ms

prune19.0ms

localize11.0ms

rewrite33.0ms

series78.0ms

simplify754.0ms

prune181.0ms

localize11.0ms

rewrite41.0ms

series73.0ms

simplify714.0ms

prune138.0ms

localize11.0ms

rewrite31.0ms

series52.0ms

simplify599.0ms

prune105.0ms

localize13.0ms

rewrite49.0ms

series100.0ms

simplify598.0ms

prune185.0ms

regimes366.0ms

bsearch52.0ms

simplify3.0ms

end0.0ms

sample1.6s

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