Details

Time bar (total: 12.3s)

sample72.0ms

Algorithm
intervals
Results
13.0ms196×body80valid
10.0ms31×body1280valid
10.0ms27×body2560valid
6.0ms92×body80nan
4.0ms16×body640valid
3.0ms5×body5120valid
1.0ms4×body160valid
1.0ms3×body320valid

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.9b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
26.0ms
(* (* 3.0 a) c)
60.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms
(- (* b b) (* (* 3.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* 3.0 a) c)
121.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
51.0ms
(- (* b b) (* (* 3.0 a) c))
95.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1000.0ms

Counts
72 → 72
Iterations

Useful iterations: 2 (255.0ms)

IterNodesCost
01201001
1302911
21541825
done5000825

prune268.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
98.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.0ms
(- (* b b) (* (* 3.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
98.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
60.0ms
(- (* b b) (* (* 3.0 a) c))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14141463
218861247
done50001241

prune346.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.9b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
17.0ms
(* (* 3.0 a) c)
66.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 3.0 a) c)
123.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
58.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
72 → 72
Iterations

Useful iterations: 2 (256.0ms)

IterNodesCost
01201001
1302911
21541825
done5000825

prune227.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
0.9b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
26×add-exp-log
22×add-cube-cbrt associate-*r*
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×flip3-- flip--
2×sub-neg rec-exp sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 107
Calls
4 calls:
105.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
55.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series390.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
103.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
66.0ms
(- (* b b) (* (* 3.0 a) c))
97.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts
119 → 119
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02202448
16322259
234111967
done50011959

prune379.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.6b

regimes477.0ms

Accuracy

88.6% (3.3b remaining)

Error of 9.0b against oracle of 5.8b and baseline of 34.5b

bsearch231.0ms

Steps
ItersRangePoint
8
6412590.878131424
2116652649.122401
1002079476.3917758
9
8.721259829163707e-156
9.718125079054439e-147
2.7708701278796453e-155
8
-1.5489453231745737e+155
-2.021963087226922e+151
-7.161497278645233e+152

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03669
14267
24367
done4367

end0.0ms

sample3.0s

Algorithm
intervals
Results
857.0ms5752×body80valid
468.0ms918×body1280valid
453.0ms1069×body2560valid
309.0ms2909×body80nan
124.0ms489×body640valid
101.0ms243×body320valid
53.0ms109×body5120valid
12.0ms93×body160valid