Details

sample109.0ms

Algorithm

intervals

Results

55.0ms	272×	body	80	valid
11.0ms	90×	body	80	nan

simplify248.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	66	37
3	116	37
4	150	37
5	164	37
6	166	37
done	166	37

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize192.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

94.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
151.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

75 → 75

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	106	1330
1	250	1189
2	1098	1110
done	5001	1100

prune844.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize207.0ms

Local error

Found 4 expressions with local error:

8.9b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

25.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
139.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify993.0ms

Counts

72 → 72

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	90	1506
1	236	1066
2	982	1000
done	5001	992

prune878.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.4b

localize233.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
184.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
200.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts

68 → 68

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	90	1160
1	211	1076
2	700	976
3	3606	966
done	5001	942

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.4b

localize260.0ms

Local error

Found 4 expressions with local error:

23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
205.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
177.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
180.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts

64 → 64

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	65	1180
1	161	1144
2	571	1024
3	3088	1004
done	5001	964

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.4b

regimes501.0ms

Accuracy

92.4% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 20.1b

bsearch340.0ms

Steps

Iters	Range		Point
8	4.049254448328916e+76	2.3057443967677173e+80	2.2766902918844874e+80
8	-1.7982126770691641e+158	-3.251690204975706e+154	-3.316762893443504e+154

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	130
1	47	130
done	47	130

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	8711×	body	80	valid
455.0ms	2982×	body	80	nan