Details

sample193.0ms

Algorithm

intervals

Results

19.0ms	41×	body	2560	valid
11.0ms	186×	body	80	valid
7.0ms	28×	body	1280	valid
6.0ms	108×	body	80	nan
4.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	23	13
2	42	13
3	46	13
done	46	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

111.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
52.0ms	(- (* b_2 b_2) (* a c))
106.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	156	1821
1	912	1704
done	5000	1619

prune407.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.1b	(/ (/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.3b	(/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
138×	`times-frac`
74×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
34×	`distribute-lft-out`
24×	`associate-/l*`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`associate-/r*` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `neg-log` `flip--`

Counts

4 → 171

Calls

4 calls:

47.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
136.0ms	(/ (/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
105.0ms	(/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
289.0ms	(/ (/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
319.0ms	(/ (+ (* a c) 0) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	278	5104
done	5000	4367

prune701.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

69.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
51.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

189 → 189

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	266	4484
1	1950	3907
done	5000	3774

prune464.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.7b	(/ a (+ (* a c) 0))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ a (+ (* a c) 0))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(/ a (+ (* a c) 0))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.3m

Counts

83 → 83

Iterations

Useful iterations: done (7.3m)

Iter	Nodes	Cost
0	144	1092
1	2368	913
done	5001	829

prune200.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

regimes159.0ms

Accuracy

77.1% (5.5b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 30.0b

bsearch62.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
5	-6.644598008915225e+100	-2.936095699822542e+100	-5.776846430852749e+100

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	41
1	35	41
done	35	41

end0.0ms

sample1.8s

Algorithm

intervals

Results

551.0ms	5894×	body	80	valid
322.0ms	1051×	body	2560	valid
202.0ms	835×	body	1280	valid
180.0ms	2996×	body	80	nan
110.0ms	450×	body	640	valid
37.0ms	135×	body	5120	valid
25.0ms	226×	body	320	valid
9.0ms	119×	body	160	valid