Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	277×	body	80	valid
7.0ms	104×	body	80	nan

simplify157.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
7	168
6	166
5	160
4	151
3	127
2	74
1	38
0	20

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize176.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (* b b) (* (* 4.0 a) c))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
3	2175
2	510
1	157
0	62

prune638.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize192.0ms

Local error

Found 4 expressions with local error:

7.6b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

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`
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 → 58

Calls

4 calls:

9.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2860
2	724
1	229
0	86

prune708.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize219.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

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` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

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

series467.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
137.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
131.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2014
2	578
1	203
0	90

prune931.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

localize200.0ms

Local error

Found 4 expressions with local error:

26.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2014
2	578
1	203
0	90

prune715.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

regimes504.0ms

Accuracy

93.7% (0.9b remaining)

Error of 6.7b against oracle of 5.8b and baseline of 20.0b

bsearch314.0ms

Steps

Iters	Range		Point
8	1.0335802065380817e+152	4.346839969020365e+154	1.042426094136288e+152
8	-1.4137780731624028e+101	-4.084920897753177e+97	-1.1322413381639178e+101

simplify28.0ms

Iterations

Iter	Nodes
done	56
1	56
0	46

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s	8769×	body	80	valid
266.0ms	2889×	body	80	nan