Details

sample116.0ms

Algorithm

intervals

Results

22.0ms	36×	body	2560	valid
20.0ms	190×	body	80	valid
19.0ms	92×	body	80	nan
14.0ms	28×	body	1280	valid
6.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify113.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite169.0ms

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:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	152	1565
1	400	1461
2	1315	1245
3	4886	1231
done	5000	1231

prune332.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.4b	(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.2b	(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
150.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
121.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series781.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
223.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
285.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
129.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

166 → 166

Iterations

Useful iterations: 2 (592.0ms)

Iter	Nodes	Cost
0	253	5113
1	622	4538
2	2435	4210
done	5000	4210

prune621.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 118

Calls

4 calls:

91.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
13.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series536.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
77.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

130 → 130

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	218	3137
1	494	2801
2	1432	2561
done	5000	2481

prune377.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-l`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-r`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`sub-neg` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 121

Calls

4 calls:

17.0ms	(- (* b b) (* 4.0 (* a c)))
182.0ms	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* b b) (* 4.0 (* a c)))
213.0ms	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
133.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
136.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

133 → 133

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	244	2733
1	618	2575
2	1802	2263
done	5000	2227

prune442.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.5b

regimes255.0ms

Accuracy

83.5% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.2b

bsearch236.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.5501620157466267e+150

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	5882×	body	80	valid
556.0ms	1076×	body	2560	valid
450.0ms	848×	body	1280	valid
280.0ms	2915×	body	80	nan
129.0ms	468×	body	640	valid
92.0ms	107×	body	5120	valid
42.0ms	212×	body	320	valid
17.0ms	122×	body	160	valid