Details

sample94.0ms

Algorithm

intervals

Results

55.0ms	285×	body	80	valid
12.0ms	106×	body	80	nan

simplify139.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize169.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1182
1	252
0	93

prune612.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize189.0ms

Local error

Found 4 expressions with local error:

8.0b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

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` `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:

14.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify866.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	982
1	236
0	90

prune720.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.1b

localize218.0ms

Local error

Found 4 expressions with local error:

9.6b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`cbrt-div` `add-cbrt-cube` `add-exp-log`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`sum-log` `pow1/3` `sqrt-div`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 54

Calls

4 calls:

9.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
158.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
133.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1535
1	378
0	146

prune762.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.1b

localize232.0ms

Local error

Found 4 expressions with local error:

24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	3090
2	531
1	137
0	52

prune594.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 8.1b

regimes543.0ms

Accuracy

93.9% (0.9b remaining)

Error of 6.6b against oracle of 5.8b and baseline of 20.1b

bsearch234.0ms

Steps

Iters	Range		Point
8	1.0335802065380817e+152	4.346839969020365e+154	1.042426094136288e+152
8	-1.4137780731624028e+101	-4.084920897753177e+97	-1.3906582137854214e+101

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	40

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	8718×	body	80	valid
304.0ms	2875×	body	80	nan