Details

Time bar (total: 14.9s)

sample56.0ms

Algorithm
intervals
Results
10.0ms197×body80valid
7.0ms28×body2560valid
7.0ms31×body1280valid
3.0ms77×body80nan
2.0ms11×body640valid
1.0ms7×body320valid
1.0ms5×body160valid

simplify106.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
132.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
138.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01671697
14331584
214861361
done50001347

prune426.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.4b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
90.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
222.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
357.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
170 → 170
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02625076
16444511
227154181
done50024179

prune769.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
11.7b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-exp-log
76×add-sqr-sqrt
75×*-un-lft-identity
63×div-exp
58×add-cbrt-cube
45×associate-/l*
43×add-cube-cbrt
34×prod-exp
27×cbrt-undiv
16×distribute-lft-out-- difference-of-squares
14×cbrt-unprod
11×sqrt-prod
10×div-inv
8×rec-exp distribute-rgt-neg-in 1-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div clear-num associate-/r* associate-/r/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff
Counts
4 → 195
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
136.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
189.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 4.0 a) c))
218.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
167.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
207 → 207
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03956061
110125676
235434774
done50004771

prune562.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.7b
(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c)))
11.7b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
22×add-sqr-sqrt
21×*-un-lft-identity prod-exp cbrt-unprod
14×times-frac
11×associate-*r*
10×pow1
9×cbrt-undiv add-cube-cbrt div-exp
7×associate-/l*
6×sqrt-prod distribute-lft-out-- add-log-exp difference-of-squares
4×expm1-log1p-u log1p-expm1-u
3×flip3-- distribute-rgt-neg-in pow-prod-down flip--
2×sqrt-div div-inv associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub associate-*r/ associate-*l* prod-diff clear-num associate-/r* *-commutative
Counts
4 → 110
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c)))
117.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
169.0ms
(* (* 2.0 a) (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c)))
145.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
123.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
122 → 122
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02153036
16062894
227502307
done50002305

prune447.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

regimes252.0ms

Accuracy

87.3% (3.5b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 32.7b

bsearch222.0ms

Steps
ItersRangePoint
8
1.9474646187349237e+36
8.662403776042349e+38
1.6056697633982866e+37
10
8.134666143579123e-130
4.886277919964174e-120
8.706117685651469e-130
5
-1.9941030622962047e+109
-5.928196142097795e+108
-1.8572382657132166e+109

simplify8.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03872
14669
done4669

end0.0ms

sample1.6s

Algorithm
intervals
Results
308.0ms1069×body2560valid
278.0ms5791×body80valid
216.0ms933×body1280valid
136.0ms2974×body80nan
80.0ms442×body640valid
41.0ms122×body5120valid
32.0ms244×body320valid
11.0ms126×body160valid