Details

sample83.0ms

Algorithm

intervals

Results

31.0ms	281×	body	80	valid
15.0ms	89×	body	80	nan

simplify180.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize176.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms	(- (- b) (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)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1036
1	254
0	100

prune647.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.1b

localize138.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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:

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

series387.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms	(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

prune692.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize194.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

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:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

72 → 72

Iterations

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

prune737.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.1b

localize132.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
7.1b	(/ (* a c) b)
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `sqrt-prod` `distribute-lft-out`
3×	`distribute-rgt-neg-in`
2×	`clear-num` `frac-2neg` `flip3--` `sqrt-div` `diff-log` `prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 81

Calls

4 calls:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
9.0ms	(/ (* a c) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
231.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
26.0ms	(/ (* a c) b)
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	2506
1	466
0	176

prune731.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.5b

regimes403.0ms

Accuracy

88.8% (1.5b remaining)

Error of 8.0b against oracle of 6.5b and baseline of 19.6b

bsearch283.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.628799960716312e+50
5	-4.620363368011112e+123	-1.2441774927265154e+123	-3.926786644154185e+123

simplify13.0ms

Iterations

Iter	Nodes
done	59
1	59
0	48

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	8698×	body	80	valid
325.0ms	2819×	body	80	nan