Details

sample106.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
8.0ms	32×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	87×	body	80	nan
3.0ms	20×	body	640	valid
3.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

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:

77.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify38.0ms

Counts: 92 → 92

prune255.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.3b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

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:

24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
84.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
61.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
155.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
187.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Counts: 218 → 218

prune549.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.8b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp` `sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
8×	`add-log-exp`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 180

Calls

4 calls:

46.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
78.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
177.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify92.0ms

Counts: 192 → 192

prune470.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
0.8b	(- (* b_2 b_2) (* a c))
1.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
32×	`add-exp-log`
26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
17×	`div-exp`
13×	`add-cbrt-cube`
10×	`add-log-exp`
7×	`1-exp` `associate-/r*`
6×	`pow1` `prod-exp`
5×	`cbrt-undiv` `div-inv`
4×	`rec-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `cbrt-unprod` `inv-pow`

Counts

4 → 104

Calls

4 calls:

51.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
8.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1 (/ (* 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) c))
37.0ms	(- (* b_2 b_2) (* a c))
82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Counts: 116 → 116

prune225.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes282.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.2b against oracle of 5.3b and baseline of 30.0b

bsearch135.0ms

Steps

Iters	Range	Point
4	9.012561940608131e+125	1.467599966670541e+126	1.0763848226380752e+126
7	-4.532619757041417e-294	-8.312848984102269e-296	-1.3101258183672603e-294
9	-7.230061550164269e+155	-2.875458900305947e+147	-8.593339349284274e+151

Iters

Range

Point

9.012561940608131e+125

1.467599966670541e+126

1.0763848226380752e+126

-4.532619757041417e-294

-8.312848984102269e-296

-1.3101258183672603e-294

-7.230061550164269e+155

-2.875458900305947e+147

-8.593339349284274e+151

simplify5.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

615.0ms	900×	body	1280	valid
424.0ms	5790×	body	80	valid
355.0ms	1114×	body	2560	valid
226.0ms	2911×	body	80	nan
78.0ms	460×	body	640	valid
36.0ms	104×	body	5120	valid
29.0ms	234×	body	320	valid
11.0ms	106×	body	160	valid