Details

sample77.0ms

Algorithm

intervals

Results

16.0ms	29×	body	1280	valid
14.0ms	42×	body	2560	valid
11.0ms	181×	body	80	valid
5.0ms	97×	body	80	nan
3.0ms	14×	body	640	valid
3.0ms	7×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite189.0ms

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:

14.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b_2 b_2) (* a c))
157.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
120.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Counts: 103 → 103

prune412.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.9b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.1b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
147.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
87.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series731.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
227.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
293.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Counts: 139 → 139

prune474.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
0.2b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
148×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
79×	`add-cube-cbrt`
34×	`difference-of-squares`
25×	`associate-/r*`
20×	`sqrt-prod`
17×	`add-exp-log` `distribute-lft-out--`
11×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv`
3×	`flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/` `inv-pow`

Counts

4 → 184

Calls

4 calls:

110.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
65.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
147.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
116.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Counts: 196 → 196

prune761.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.1b	(* (/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (sqrt 1) c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
72×	`times-frac`
56×	`sqrt-prod`
45×	`add-cube-cbrt`
42×	`associate-l`
28×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--`
10×	`pow1`
6×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`sqrt-div` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 154

Calls

4 calls:

69.0ms	(/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
211.0ms	(* (/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (sqrt 1) c))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
114.0ms	(* (/ (sqrt 1) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (sqrt 1) c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Counts: 166 → 166

prune599.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes331.0ms

Accuracy

92.9% (1.7b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 29.2b

bsearch255.0ms

Steps

Iters	Range		Point
8	6.830756908302209e+71	2.772849885831336e+75	2.730494439370032e+75
10	9.277388299403992e-306	2.623522883809734e-288	2.7792211843383316e-301
8	-8.542220381879772e+40	-1.4668325467350965e+37	-8.435186307994013e+40

simplify562.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

849.0ms	924×	body	1280	valid
679.0ms	5903×	body	80	valid
622.0ms	1071×	body	2560	valid
453.0ms	109×	body	5120	valid
220.0ms	2893×	body	80	nan
121.0ms	449×	body	640	valid
39.0ms	203×	body	320	valid
14.0ms	109×	body	160	valid