Details

sample120.0ms

Algorithm

intervals

Results

65.0ms	289×	body	80	valid
32.0ms	86×	body	80	nan

simplify184.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
7	168
6	166
5	160
4	151
3	125
2	75
1	38
0	20

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize151.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4 a) c))
1.0b	(- (* b b) (* (* 4 a) c))
25.0b	(sqrt (- (* b b) (* (* 4 a) c)))
25.0b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite63.0ms

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:

15.0ms	(- (* b b) (* (* 4 a) c))
15.0ms	(- (* b b) (* (* 4 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* b b) (* (* 4 a) c))
73.0ms	(- (* b b) (* (* 4 a) c))
107.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
135.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts

70 → 70

Iterations

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

prune584.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize188.0ms

Local error

Found 4 expressions with local error:

8.3b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
25.0b	(sqrt (- (* b b) (* (* 4 a) c)))
25.0b	(sqrt (- (* b b) (* (* 4 a) c)))
25.0b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 62

Calls

4 calls:

16.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
96.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
93.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
115.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify996.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	2004
3	2004
2	727
1	232
0	87

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize163.0ms

Local error

Found 4 expressions with local error:

25.0b	(sqrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite27.0ms

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:

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

series486.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
101.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
144.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
122.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts

70 → 70

Iterations

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

prune809.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.5b

localize166.0ms

Local error

Found 4 expressions with local error:

25.0b	(sqrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))
25.8b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite38.0ms

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:

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

series531.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
160.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
127.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
135.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts

70 → 70

Iterations

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

prune824.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.5b

regimes538.0ms

Accuracy

91.2% (1.1b remaining)

Error of 8.1b against oracle of 7.0b and baseline of 19.3b

bsearch369.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	7.947663392061663e+104
8	-4.336983712965787e+155	-6.488343844980391e+152	-1.3441037991607355e+154

simplify23.0ms

Iterations

Iter	Nodes
done	53
1	53
0	44

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.8s	8747×	body	80	valid
667.0ms	2996×	body	80	nan