Details

sample121.0ms

Algorithm

intervals

Results

12.0ms	34×	body	2560	valid
9.0ms	182×	body	80	valid
7.0ms	32×	body	1280	valid
4.0ms	98×	body	80	nan
4.0ms	22×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify34.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

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:

77.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
63.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts: 103 → 103

prune439.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
5.2b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
145.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
98.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b_2 b_2) (* a c))
205.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
295.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts: 196 → 196

prune766.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.0b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
5.2b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
128.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series700.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b_2 b_2) (* a c))
279.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
240.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify983.0ms

Counts: 449 → 449

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
1.4b	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
21.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

2502×	`times-frac`
1525×	`add-sqr-sqrt`
1270×	`*-un-lft-identity`
1016×	`add-cube-cbrt`
876×	`cbrt-prod`
254×	`difference-of-squares`
137×	`associate-/l*`
130×	`sqrt-prod`
127×	`distribute-lft-out--`
50×	`div-inv`
13×	`add-exp-log`
8×	`add-cbrt-cube` `add-log-exp`
7×	`associate-/r/`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 1024

Calls

4 calls:

76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
140.0ms	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms	(- (* b_2 b_2) (* a c))
255.0ms	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts: 1036 → 1036

prune4.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes816.0ms

Accuracy

92.4% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 29.8b

bsearch306.0ms

Steps

Iters	Range		Point
10	2.1111705398262576e+94	5.238272520421586e+105	3.561111989718156e+98
8	-4.587893386086347e-266	-6.458564774426403e-269	-1.4152177749292482e-267
9	-6.985580462528291e+47	-4.019387695050576e+39	-3.75511861235999e+47

simplify440.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

903.0ms	5768×	body	80	valid
546.0ms	1092×	body	2560	valid
329.0ms	875×	body	1280	valid
243.0ms	2866×	body	80	nan
169.0ms	482×	body	640	valid
56.0ms	119×	body	5120	valid
43.0ms	240×	body	320	valid
12.0ms	106×	body	160	valid