Details

sample278.0ms

Algorithm

intervals

Results

7.0ms	39×	body	2560	valid
7.0ms	183×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	45	13
4	47	13
done	47	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

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))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

41.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify759.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (176.0ms)

Iter	Nodes	Cost
0	242	5993
1	566	4363
2	1712	3549
done	5001	3549

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

181 → 181

Iterations

Useful iterations: 2 (216.0ms)

Iter	Nodes	Cost
0	261	5917
1	631	4195
2	2125	3313
done	5000	3313

prune353.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

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))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 257

Calls

4 calls:

27.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

269 → 269

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	351	8660
1	796	6655
2	2730	5553
done	5001	5553

prune402.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

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))
1.0b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u`
3×	`fma-def` `associate-/r*` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

4 → 119

Calls

4 calls:

42.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify524.0ms

Counts

131 → 131

Iterations

Useful iterations: done (520.0ms)

Iter	Nodes	Cost
0	197	2260
1	442	2136
2	1441	2031
done	5000	2020

prune322.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.3b

regimes159.0ms

Accuracy

82.4% (5.0b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 33.6b

bsearch55.0ms

Steps

Iters	Range		Point
9	1.790439840991813e+53	4.6520850645607246e+61	1.3316184968738608e+61
2	-4.223797038045246e-104	-3.7861133082378615e-104	-4.1690865718193236e-104

simplify9.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	35
1	38	31
2	47	31
3	54	31
4	56	31
done	56	31

end0.0ms

sample972.0ms

Algorithm

intervals

Results

204.0ms	1071×	body	2560	valid
190.0ms	5863×	body	80	valid
127.0ms	830×	body	1280	valid
91.0ms	2880×	body	80	nan
57.0ms	477×	body	640	valid
26.0ms	110×	body	5120	valid
22.0ms	244×	body	320	valid
7.0ms	116×	body	160	valid