Details

sample72.0ms

Algorithm

intervals

Results

40.0ms	277×	body	80	valid
7.0ms	104×	body	80	nan

simplify167.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	179
6	179
5	175
4	163
3	136
2	78
1	38
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.8b

localize143.0ms

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)))

rewrite42.0ms

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:

13.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	4973
2	753
1	165
0	62

prune600.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.6b

localize167.0ms

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)))

rewrite57.0ms

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:

17.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (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)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1031
1	242
0	86

prune747.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.6b

localize208.0ms

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)))

rewrite26.0ms

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:

10.0ms	(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)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
154.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3628
2	700
1	211
0	90

prune702.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.6b

localize240.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
163.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	3255
2	581
1	161
0	65

prune752.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.6b

regimes288.0ms

Accuracy

93.3% (0.8b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 20.0b

bsearch213.0ms

Steps

Iters	Range		Point
8	1.0335802065380817e+152	4.346839969020365e+154	1.042426094136288e+152
9	-1.8060553248805222e+109	-1.4137780731624028e+101	-9.912992538019245e+108

simplify11.0ms

Iterations

Iter	Nodes
done	50
1	50
0	41

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	8769×	body	80	valid
250.0ms	2889×	body	80	nan