Details

sample102.0ms

Algorithm

intervals

Results

55.0ms	277×	body	80	valid
12.0ms	107×	body	80	nan

simplify300.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	153
7	153
6	152
5	145
4	133
3	103
2	61
1	35
0	20

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize656.0ms

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))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite117.0ms

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:

26.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
167.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts

72 → 72

Iterations

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

prune880.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.7b

localize230.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

10×	`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` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

28.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	2872
2	724
1	229
0	86

prune923.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.7b

localize258.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:

18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series739.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
180.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
223.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
204.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts

66 → 66

Iterations

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

prune990.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.7b

localize253.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* a c) b)
11.1b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`pow1` `sqrt-prod`
4×	`sqrt-div`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-exp` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `frac-2neg` `flip3-+` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 64

Calls

4 calls:

20.0ms	(/ (* a c) b)
22.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* a c) b)
154.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
137.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
136.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
2	1250
1	336
0	126

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.4b

regimes535.0ms

Accuracy

91.1% (1.2b remaining)

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

bsearch367.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	9.530261110323185e+142
9	-1.8545384403947072e+60	-1.5101311291801297e+53	-1.817538956128738e+60

simplify25.0ms

Iterations

Iter	Nodes
done	61
1	61
0	49

end3.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	8692×	body	80	valid
346.0ms	2818×	body	80	nan