Details

sample60.0ms

Algorithm

intervals

Results

31.0ms	285×	body	80	valid
7.0ms	89×	body	80	nan

simplify153.0ms

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: 19.7b

localize175.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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

series341.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

66 → 66

Iterations

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

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize200.0ms

Local error

Found 4 expressions with local error:

9.5b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

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

series496.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1031
1	242
0	86

prune831.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize174.0ms

Local error

Found 4 expressions with local error:

10.9b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

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:

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

series418.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	982
1	236
0	90

prune658.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.4b

localize229.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

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)))
7.0ms	(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)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

72 → 72

Iterations

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

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.4b

regimes365.0ms

Accuracy

91.8% (1.0b remaining)

Error of 9.1b against oracle of 8.1b and baseline of 20.4b

bsearch143.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	3.9321910650396994e+107
4	-2.6709732094199134e+112	-1.6569790030408257e+112	-1.99047315062329e+112

simplify14.0ms

Iterations

Iter	Nodes
done	56
1	56
0	45

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	8696×	body	80	valid
660.0ms	2883×	body	80	nan