Details

sample62.0ms

Algorithm

intervals

Results

31.0ms	276×	body	80	valid
8.0ms	92×	body	80	nan

simplify242.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (19.0ms)

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize147.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b	(+ (- b) (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)))

rewrite114.0ms

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-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts

75 → 75

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	100	1330
1	246	1186
2	780	1089
3	2740	1070
done	5001	1066

prune493.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.0b

localize127.0ms

Local error

Found 4 expressions with local error:

7.2b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

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

Counts

4 → 54

Calls

4 calls:

12.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
164.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.4s

Counts

66 → 66

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	146	1516
1	367	1425
2	1206	1215
3	4529	1185
done	5001	1155

prune502.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize141.0ms

Local error

Found 4 expressions with local error:

8.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:

20.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
135.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
150.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts

67 → 67

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	149	1566
1	363	1475
2	1172	1275
3	4457	1245
done	5001	1215

prune574.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.0b

localize142.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b	(/ (* a c) b)
4.8b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
23.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(/ (* a c) b)
73.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms	(/ (* a c) b)
85.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

89 → 89

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	177	1422
1	450	1334
2	1705	1172
done	5001	1164

prune545.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes176.0ms

Accuracy

93.3% (0.9b remaining)

Error of 7.2b against oracle of 6.3b and baseline of 20.0b

bsearch361.0ms

Steps

Iters	Range		Point
10	4.61796087672408e+142	1.3206820209921783e+153	4.623731436085777e+144
7	-6.338089291324522e+142	-9.408663701389454e+140	-2.415824536209925e+141

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	138
1	61	138
done	61	138

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	8712×	body	80	valid
461.0ms	2914×	body	80	nan