Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	274×	body	80	valid
5.0ms	104×	body	80	nan

simplify130.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	20	38
1	38	38
2	78	37
3	135	37
4	155	37
5	165	37
6	169	37
done	169	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-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--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
223.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

69 → 69

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	91	1129
1	207	1001
2	651	935
3	2361	930
done	5000	924

prune261.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize86.0ms

Local error

Found 4 expressions with local error:

14.2b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

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:

13.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	90	1506
1	225	1066
2	726	1000
3	2540	988
done	5000	984

prune313.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize90.0ms

Local error

Found 4 expressions with local error:

23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	52	1140
1	130	1008
2	408	928
3	1510	928
done	5000	924

prune343.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize95.0ms

Local error

Found 4 expressions with local error:

23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

9.0ms	(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)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	52	1140
1	130	1008
2	408	928
3	1510	928
done	5000	924

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

regimes164.0ms

Accuracy

80.9% (2.4b remaining)

Error of 9.8b against oracle of 7.4b and baseline of 19.9b

bsearch119.0ms

Steps

Iters	Range		Point
6	2.0335150395734557e+19	1.0746392320557105e+20	1.0610691325078738e+20
5	-130518226990374.3	-34802195229717.125	-128454993639955.03

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	192
1	56	192
done	56	192

end0.0ms

sample908.0ms

Algorithm

intervals

Results

443.0ms	8685×	body	80	valid
124.0ms	2832×	body	80	nan