Details

Time bar (total: 9.0s)

sample60.0ms

Algorithm
intervals
Results
12.0ms111×body320valid
10.0ms513×pre80true
9.0ms257×body80nan
7.0ms103×body160valid
2.0ms13×body640valid
1.0ms29×body80valid

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
29.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify766.0ms

Counts
82 → 82
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
01541565
14061461
213611245
done50001235

prune195.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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

rewrite107.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
35.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
165.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.0s

Counts
163 → 163
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02545790
16705273
223884513
done50004511

prune447.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize18.0ms

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))))
0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite85.0ms

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:
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
125.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.1s

Counts
97 → 97
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01842432
15462259
223251818
done50001817

prune268.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
0.4b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*l*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-lft-neg-out distribute-rgt-out
4×associate-/r*
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*l/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg diff-log div-exp associate-*r* unsub-neg clear-num sum-log *-commutative div-inv
Counts
4 → 96
Calls
4 calls:
23.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
24.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
132.0ms
(+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))
190.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (+ (* (- b) (* 2.0 a)) (* (- (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))

simplify947.0ms

Counts
108 → 108
Iterations

Useful iterations: done (944.0ms)

IterNodesCost
02133197
16072705
222482325
done50002320

prune356.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02026
12923
23023
done3023

end0.0ms

sample1.7s

Algorithm
intervals
Results
391.0ms3587×body320valid
304.0ms16016×pre80true
282.0ms8016×body80nan
226.0ms2960×body160valid
74.0ms518×body640valid
35.0ms935×body80valid