Details

Time bar (total: 15.4s)

sample139.0ms

Algorithm
intervals
Results
30.0ms106×body80valid
24.0ms307×body80nan
24.0ms150×body160valid
18.0ms563×pre80true

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite165.0ms

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:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(- (* b b) (* (* 4.0 a) c))
98.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(- (* b b) (* (* 4.0 a) c))
143.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune275.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* 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)))))

rewrite229.0ms

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:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
122.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
69.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series588.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
212.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
233.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.2s

Counts
163 → 163
Iterations

Useful iterations: 2 (476.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune531.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(- (* b b) (* (* 4.0 a) c))
119.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(- (* b b) (* (* 4.0 a) c))
125.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
231.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (478.0ms)

IterNodesCost
01762262
14932066
225551750
done50011750

prune407.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (/ (* 4.0 (* a c)) (* a 2.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
47×*-un-lft-identity
43×times-frac
33×add-exp-log add-cbrt-cube
19×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
13×cbrt-undiv div-exp
10×sqrt-prod add-log-exp
9×prod-exp cbrt-unprod div-inv
7×distribute-rgt-neg-in associate-/r*
5×pow1 associate-/l*
4×flip3-- flip--
3×diff-log
2×sub-neg sqrt-div associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 119
Calls
4 calls:
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(/ (/ (* 4.0 (* a c)) (* a 2.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))

series503.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
212.0ms
(/ (/ (* 4.0 (* a c)) (* a 2.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
109.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(- (* b b) (* (* 4.0 a) c))

simplify1.9s

Counts
131 → 131
Iterations

Useful iterations: 2 (572.0ms)

IterNodesCost
02373765
16333592
233273170
done50003170

prune442.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes266.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01723
12223
done2223

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.6s16589×pre80true
910.0ms4475×body160valid
725.0ms8589×body80nan
349.0ms3525×body80valid