Details

Time bar (total: 16.4s)

sample169.0ms

Algorithm
intervals
Results
16.0ms192×body80valid
14.0ms27×body2560valid
10.0ms23×body1280valid
9.0ms105×body80nan
4.0ms12×body640valid
4.0ms16×body320valid
2.0ms3×body5120valid
1.0ms4×body160valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize19.0ms

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))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite201.0ms

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:
124.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
48.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms
(- (* b_2 b_2) (* a c))
119.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
103 → 103
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01561821
13871727
215081613
done50011603

prune587.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.8b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite379.0ms

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:
84.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
130.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
127.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
239.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
288.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
199 → 199
Iterations

Useful iterations: 2 (778.0ms)

IterNodesCost
03045659
17654902
241264722
done50014722

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize33.0ms

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))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
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 → 177
Calls
4 calls:
64.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms
(- (* b_2 b_2) (* a c))
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
45.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
114.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
189 → 189
Iterations

Useful iterations: 2 (679.0ms)

IterNodesCost
02664484
16653936
235283786
done50023786

prune583.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

localize17.0ms

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))
1.3b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*l*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ div-exp cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 92
Calls
4 calls:
135.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
46.0ms
(- (* b_2 b_2) (* a c))
96.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01701774
14651645
224891411
done50001389

prune467.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.1b

regimes373.0ms

Accuracy

85.4% (3.9b remaining)

Error of 9.1b against oracle of 5.2b and baseline of 31.9b

bsearch160.0ms

Steps
ItersRangePoint
9
9.357224410271438e+98
8.450543925883448e+104
5.991199458469861e+103
7
-4.3103989639009063e-82
-2.5085206973204917e-83
-2.534983011264385e-83
3
-1.713609749393423e-29
-1.2239049760790121e-29
-1.6806111715441095e-29

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03561
14159
24259
done4259

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s5897×body80valid
481.0ms1057×body2560valid
349.0ms855×body1280valid
255.0ms476×body640valid
227.0ms2888×body80nan
61.0ms112×body5120valid
43.0ms218×body320valid
43.0ms117×body160valid