Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	285×	body	80	valid
4.0ms	87×	body	80	nan

simplify95.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	38
1	38	38
2	78	37
3	136	37
4	156	37
5	165	37
6	168	37
done	168	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize111.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

69 → 69

Iterations

Useful iterations: 3 (578.0ms)

Iter	Nodes	Cost
0	93	1129
1	237	1009
2	780	915
3	3126	904
done	5001	904

prune249.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize114.0ms

Local error

Found 4 expressions with local error:

12.2b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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:

6.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (525.0ms)

Iter	Nodes	Cost
0	90	1506
1	224	1066
2	737	1000
3	2796	988
done	5001	988

prune306.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize117.0ms

Local error

Found 4 expressions with local error:

6.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

6.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

67 → 67

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	149	1566
1	365	1475
2	1173	1275
3	4844	1245
done	5000	1245

prune343.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize119.0ms

Local error

Found 4 expressions with local error:

21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
92.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: 3 (285.0ms)

Iter	Nodes	Cost
0	65	1180
1	154	1144
2	474	1024
3	1792	1004
done	5001	1004

prune380.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes165.0ms

Accuracy

88.9% (1.3b remaining)

Error of 8.9b against oracle of 7.6b and baseline of 19.6b

bsearch188.0ms

Steps

Iters	Range		Point
8	2.1878188410446244e+107	3.8616146939177386e+111	7.989761210864844e+108
10	-2.1502820188078274e+175	-2.227381996671495e+165	-2.2572095326645574e+165

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	158
1	56	158
done	56	158

end0.0ms

sample848.0ms

Algorithm

intervals

Results

450.0ms	8712×	body	80	valid
138.0ms	2998×	body	80	nan