Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	38×	body	2560	valid
10.0ms	178×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

74.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
119.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(- (* b b) (* 4.0 (* a c)))
117.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	152	1565
1	400	1461
2	1331	1245
3	4906	1231
done	5001	1231

prune400.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

186.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
31.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
113.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
84.0ms	(- (* b b) (* 4.0 (* a c)))
119.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	179	1881
1	464	1671
2	1636	1400
done	5001	1376

prune327.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (* b b) (* 4.0 (* a c)))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

18.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (* b b) (* 4.0 (* a c)))
85.0ms	(- (* b b) (* 4.0 (* a c)))
96.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
98.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.9s

Counts

66 → 66

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	60	1010
1	145	930
2	461	834
3	1763	834
done	5000	832

prune428.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.6b	(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
20.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

11.0ms	(- (* b b) (* 4.0 (* a c)))
44.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
55.0ms	(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts

80 → 80

Iterations

Useful iterations: 2 (281.0ms)

Iter	Nodes	Cost
0	151	1323
1	369	1150
2	1710	1044
done	5000	1044

prune344.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

regimes299.0ms

Accuracy

95.9% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 34.4b

bsearch213.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.6082844052603056e+78
11	-1.0472779812871276e-269	-2.473343252086336e-295	-3.3534114850920523e-283
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.6082844052603056e+78

-1.0472779812871276e-269

-2.473343252086336e-295

-3.3534114850920523e-283

-6.990724105819741e+111

-2.6156774686163576e+108

-1.569310777886352e+111

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	62
1	45	62
done	45	62

end0.0ms

sample3.1s

Algorithm

intervals

Results

968.0ms	5806×	body	80	valid
453.0ms	1087×	body	2560	valid
416.0ms	930×	body	1280	valid
325.0ms	2994×	body	80	nan
151.0ms	446×	body	640	valid
138.0ms	117×	body	5120	valid
59.0ms	116×	body	160	valid
43.0ms	210×	body	320	valid