Details

sample82.0ms

Algorithm

intervals

Results

16.0ms	37×	body	2560	valid
14.0ms	184×	body	80	valid
11.0ms	31×	body	1280	valid
6.0ms	90×	body	80	nan
4.0ms	12×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify38.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite142.0ms

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:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts: 103 → 103

prune404.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
130.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
123.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
216.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
251.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts: 199 → 199

prune704.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0b	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
4.6b	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

3063×	`times-frac`
1689×	`add-sqr-sqrt`
1446×	`*-un-lft-identity`
1204×	`add-cube-cbrt`
242×	`difference-of-squares`
237×	`associate-/l*`
124×	`sqrt-prod`
121×	`distribute-lft-out--`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1025

Calls

4 calls:

53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
111.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
185.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms	(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
146.0ms	(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
114.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts: 1037 → 1037

prune4.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
133.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
92.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
220.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
286.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts: 199 → 199

prune647.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.0b

regimes461.0ms

Accuracy

88.8% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 32.9b

bsearch194.0ms

Steps

Iters	Range	Point
8	1.8560558009645164e+92	4.334214702125778e+95	2.4800297213667742e+95
8	-8.047260055985571e-250	-1.260146689984508e-254	-2.569418374988236e-254
8	-3.014080757910363e-12	-3.956563252082953e-16	-2.9683391048089956e-12

Iters

Range

Point

1.8560558009645164e+92

4.334214702125778e+95

2.4800297213667742e+95

-8.047260055985571e-250

-1.260146689984508e-254

-2.569418374988236e-254

-3.014080757910363e-12

-3.956563252082953e-16

-2.9683391048089956e-12

simplify907.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

784.0ms	845×	body	1280	valid
547.0ms	1107×	body	2560	valid
507.0ms	5894×	body	80	valid
250.0ms	2962×	body	80	nan
144.0ms	467×	body	640	valid
49.0ms	106×	body	5120	valid
41.0ms	227×	body	320	valid
12.0ms	100×	body	160	valid