Details

sample288.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
8.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize11.0ms

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))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

32.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
2.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

92 → 92

Iterations

Useful iterations: 3 (457.0ms)

Iter	Nodes	Cost
0	151	1534
1	366	1440
2	1165	1266
3	4578	1252
done	5000	1252

prune236.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.8b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
25.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
144.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

218 → 218

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	307	6418
1	745	5559
2	3293	5355
done	5000	5353

prune482.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.8b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
8.8b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
58×	`times-frac`
35×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`associate-l`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`distribute-rgt-neg-in` `prod-exp` `add-log-exp`
7×	`pow1` `associate-/r*`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 151

Calls

4 calls:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
27.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
171.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

163 → 163

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	253	3897
1	723	3342
2	3089	2996
done	5001	2994

prune349.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0b	(/ (* a c) a)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

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` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 66

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (* a c) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify461.0ms

Counts

78 → 78

Iterations

Useful iterations: done (459.0ms)

Iter	Nodes	Cost
0	131	952
1	318	874
2	1211	762
done	5000	756

prune181.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

regimes203.0ms

Accuracy

94% (1.4b remaining)

Error of 6.7b against oracle of 5.3b and baseline of 29.0b

bsearch151.0ms

Steps

Iters	Range	Point
9	1.790439840991813e+53	4.6520850645607246e+61	4.144553567986907e+60
11	-2.5535425374078063e-212	-1.1714445965311569e-247	-1.273959369302109e-247
7	-3.550313394724354e+57	-2.3888623512096697e+55	-3.124283374205192e+57

Iters

Range

Point

1.790439840991813e+53

4.6520850645607246e+61

4.144553567986907e+60

-2.5535425374078063e-212

-1.1714445965311569e-247

-1.273959369302109e-247

-3.550313394724354e+57

-2.3888623512096697e+55

-3.124283374205192e+57

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

Iter	Nodes	Cost
0	33	58
1	41	56
done	41	54

end0.0ms

sample984.0ms

Algorithm

intervals

Results

209.0ms	1075×	body	2560	valid
189.0ms	5844×	body	80	valid
140.0ms	911×	body	1280	valid
90.0ms	2888×	body	80	nan
57.0ms	451×	body	640	valid
24.0ms	102×	body	5120	valid
21.0ms	231×	body	320	valid
7.0ms	119×	body	160	valid