Details

sample64.0ms

Algorithm

intervals

Results

12.0ms	202×	body	80	valid
11.0ms	31×	body	2560	valid
6.0ms	24×	body	1280	valid
4.0ms	79×	body	80	nan
4.0ms	18×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	131	17
5	137	17
6	140	17
done	140	17

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

16.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify471.0ms

Counts

89 → 89

Iterations

Useful iterations: done (468.0ms)

Iter	Nodes	Cost
0	155	1752
1	405	1663
2	1365	1487
done	5000	1467

prune181.0ms

Filtered

66 candidates to 89 candidates (-34.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 6.2b

Counts

90 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

17.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify646.0ms

Counts

97 → 97

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	181	2005
1	475	1825
2	1794	1585
done	5000	1574

prune161.0ms

Filtered

68 candidates to 97 candidates (-42.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 6.2b

Counts

105 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.2b	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.6b	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
17.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
52.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
64.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify642.0ms

Counts

153 → 153

Iterations

Useful iterations: done (636.0ms)

Iter	Nodes	Cost
0	248	4590
1	627	4116
2	2700	3795
done	5000	3784

prune306.0ms

Filtered

113 candidates to 153 candidates (-35.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	151	9	160

Merged error: 6.1b

Counts

160 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
5.7b	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`times-frac`
9×	`add-exp-log` `add-cube-cbrt` `sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--`
3×	`div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

8.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify427.0ms

Counts

88 → 88

Iterations

Useful iterations: done (424.0ms)

Iter	Nodes	Cost
0	164	1804
1	418	1673
2	1392	1526
done	5000	1521

prune137.0ms

Filtered

67 candidates to 88 candidates (-31.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	88	9	97

Merged error: 6.1b

Counts

97 → 9

regimes316.0ms

Accuracy

87.1% (3.5b remaining)

Error of 9.3b against oracle of 5.8b and baseline of 32.7b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.1487243557305423e+102	3.920821933018458e+112	8.235765262469676e+111
7	-5.1440606176194e-107	-1.3691623995958124e-108	-1.6677459094321907e-108
9	-5050.104235080154	-0.0001616040529746431	-660.2639796459094

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	34	67
1	42	65
2	44	65
done	44	65

end0.0ms

sample1.8s

Algorithm

intervals

Results

356.0ms	5949×	body	80	valid
348.0ms	1061×	body	2560	valid
240.0ms	858×	body	1280	valid
171.0ms	2992×	body	80	nan
97.0ms	454×	body	640	valid
46.0ms	116×	body	5120	valid
38.0ms	236×	body	320	valid
15.0ms	111×	body	160	valid

Details

sample64.0ms

simplify73.0ms

prune4.0ms

localize12.0ms

rewrite37.0ms

series66.0ms

simplify471.0ms

prune181.0ms

localize14.0ms

rewrite38.0ms

series69.0ms

simplify646.0ms

prune161.0ms

localize14.0ms

rewrite55.0ms

series152.0ms

simplify642.0ms

prune306.0ms

localize14.0ms

rewrite36.0ms

series89.0ms

simplify427.0ms

prune137.0ms

regimes316.0ms

bsearch114.0ms

simplify5.0ms

end0.0ms

sample1.8s

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