Details

sample105.0ms

Algorithm

intervals

Results

64.0ms	287×	body	80	valid
16.0ms	85×	body	80	nan

simplify156.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	152
7	152
6	151
5	144
4	132
3	101
2	62
1	35
0	20

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize157.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4 a) c))
1.0b	(- (* b b) (* (* 4 a) c))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4 a) c))
8.0ms	(- (* b b) (* (* 4 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b b) (* (* 4 a) c))
71.0ms	(- (* b b) (* (* 4 a) c))
88.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	2000
3	2000
2	517
1	158
0	63

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize163.0ms

Local error

Found 4 expressions with local error:

7.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `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 → 64

Calls

4 calls:

9.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
131.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
126.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify969.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2002
3	2002
2	669
1	226
0	91

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize145.0ms

Local error

Found 4 expressions with local error:

24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
123.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
127.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	2003
4	2003
3	1931
2	578
1	202
0	89

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.5b

localize147.0ms

Local error

Found 4 expressions with local error:

24.5b	(sqrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))
25.3b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
138.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
136.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	2003
4	2003
3	1931
2	578
1	202
0	89

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

regimes347.0ms

Accuracy

91.4% (1.0b remaining)

Error of 8.0b against oracle of 7.0b and baseline of 19.2b

bsearch360.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	2.2036515185994908e+104
8	-4.336983712965787e+155	-6.488343844980391e+152	-1.3441037991607355e+154

simplify13.0ms

Iterations

Iter	Nodes
done	57
1	57
0	46

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	8774×	body	80	valid
590.0ms	3004×	body	80	nan