Details

Time bar (total: 16.1s)

sample99.0ms

Algorithm
intervals
Results
22.0ms537×pre80true
16.0ms137×body160valid
15.0ms281×body80nan
10.0ms58×body320valid
3.0ms61×body80valid

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite198.0ms

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:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
55.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
84.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
120.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune258.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
99.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
209.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
218.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (516.0ms)

IterNodesCost
02475048
16124510
224994166
done50004166

prune589.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
30×add-cbrt-cube
18×times-frac
17×div-exp
14×add-sqr-sqrt *-un-lft-identity
12×cbrt-undiv associate-/l*
10×add-cube-cbrt prod-exp add-log-exp
6×associate-*r/ associate-/r/ cbrt-unprod
5×flip3-- flip--
4×pow1 div-inv
3×diff-log 1-exp associate-/l/
2×sub-neg frac-2neg clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in flip3-+ neg-log sqrt-prod flip-+
Counts
4 → 100
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series564.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
177.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
224.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.3s

Counts
112 → 112
Iterations

Useful iterations: 2 (454.0ms)

IterNodesCost
02253305
15562748
223882304
done50002304

prune382.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
0.3b
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c))))
0.3b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))

rewrite463.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
156×add-exp-log
114×add-sqr-sqrt *-un-lft-identity
80×div-exp
72×add-cbrt-cube
62×add-cube-cbrt
48×associate-/l*
43×prod-exp
34×cbrt-undiv
26×distribute-lft-out-- difference-of-squares
17×cbrt-unprod
15×div-inv
13×distribute-rgt-neg-in associate-/r* sqrt-prod
12×rec-exp 1-exp
8×add-log-exp
5×pow1
3×frac-2neg clear-num associate-/r/ associate-/l/
2×flip3-- diff-log flip--
1×associate--l- neg-sub0 sub-neg pow-flip div-sub neg-log inv-pow
Counts
4 → 252
Calls
4 calls:
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
159.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
124.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c))))
139.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
191.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))) (* 2.0 a))
252.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c))))
126.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 (* a c)))

simplify2.0s

Counts
264 → 264
Iterations

Useful iterations: 2 (640.0ms)

IterNodesCost
03838273
19907731
232796549
done50016549

prune590.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes184.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
12625
done2625

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s16422×pre80true
1.2s4894×body160valid
707.0ms8422×body80nan
325.0ms1329×body320valid
125.0ms1777×body80valid