Details

sample98.0ms

Algorithm

intervals

Results

49.0ms	268×	body	80	valid
12.0ms	105×	body	80	nan

simplify327.0ms

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: 19.2b

localize204.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
39.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* b b) (* (* 4.0 a) c))
139.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	3187
2	740
1	235
0	97

prune866.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.7b

localize236.0ms

Local error

Found 4 expressions with local error:

13.0b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `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:

26.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
135.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
136.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.5s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2375
2	669
1	223
0	90

prune931.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.7b

localize271.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `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:

17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
185.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
193.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
203.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
3	2007
2	578
1	203
0	90

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.7b

localize231.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
4.4b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.9b	(/ (* a c) b)
22.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

17.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
20.0ms	(/ (* a c) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* b b) (* (* 4.0 a) c))
157.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
38.0ms	(/ (* a c) b)
136.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1787
1	452
0	166

prune976.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

regimes708.0ms

Accuracy

91.3% (1.2b remaining)

Error of 7.7b against oracle of 6.5b and baseline of 20.1b

bsearch343.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	8.750034852221899e+142
8	-2.0454571348958448e+161	-1.3020535063399952e+158	-1.3248643256430535e+158

simplify22.0ms

Iterations

Iter	Nodes
done	52
1	52
0	43

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	8710×	body	80	valid
381.0ms	2825×	body	80	nan