Details

Time bar (total: 5.9s)

sample41.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
7.0ms187×body80valid
5.0ms26×body1280valid
3.0ms19×body640valid
3.0ms73×body80nan
1.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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:
67.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
110.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0405779
11563685
25001674
done5001674

prune273.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
158.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06512692
131392439
250022426
done50022426

prune428.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
7.8b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
41×add-sqr-sqrt
34×*-un-lft-identity
30×add-cbrt-cube
27×associate-*r*
24×times-frac
17×add-cube-cbrt prod-exp
16×div-exp
9×cbrt-undiv cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×associate-/l/
4×frac-times distribute-rgt-neg-in flip3-+ associate-*l/ flip-+
3×rec-exp flip3-- 1-exp associate-*l* flip-- unswap-sqr
2×sqrt-div diff-log associate-*r/ associate-/r/ un-div-inv div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
90.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
184.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify201.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
07351779
146581453
250011437
done50011437

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
8.0b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
54×add-cbrt-cube
40×div-exp
30×prod-exp
22×cbrt-undiv
20×add-sqr-sqrt
19×*-un-lft-identity
16×cbrt-unprod
8×times-frac 1-exp associate-/l* add-log-exp
7×add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 107
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
63.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms
(/ (* 1 (/ 4.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
105.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Counts
119 → 119
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07781661
140101312
250021300
done50021300

prune238.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes276.0ms

Accuracy

89.6% (2.7b remaining)

Error of 8.2b against oracle of 5.5b and baseline of 31.7b

bsearch206.0ms

Steps
ItersRangePoint
10
1.8478564550364503e-23
1.1395487446675666e-13
3.3294485045805704e-14
9
-3.8269450675186263e-243
-3.0624496234880425e-249
-3.106669992168921e-249
10
-4.9909276054097234e+78
-4.785667473127655e+65
-3.974595954042362e+78

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05030
15230
25230
done5230

end0.0ms

sample1.2s

Algorithm
intervals
Results
243.0ms1107×body2560valid
218.0ms5758×body80valid
170.0ms913×body1280valid
98.0ms2871×body80nan
67.0ms488×body640valid
30.0ms105×body5120valid
23.0ms222×body320valid
8.0ms110×body160valid