Details

Time bar (total: 18.7s)

sample113.0ms

Algorithm
intervals
Results
22.0ms137×body160valid
22.0ms281×body80nan
20.0ms537×pre80true
13.0ms58×body320valid
5.0ms61×body80valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize34.0ms

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))))

rewrite183.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(- (* b b) (* (* 4.0 a) c))
160.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
125.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune289.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)))))

rewrite254.0ms

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:
13.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
75.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series627.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
132.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
216.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
226.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (565.0ms)

IterNodesCost
02475048
16124510
224994166
done50004166

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))
0.5b
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

rewrite720.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
305.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
205.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c))))))
51.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))
135.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

series838.0ms

Counts
4 → 12
Calls
4 calls:
314.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
335.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c))))))
128.0ms
(/ (- (pow b 4) (* (* (* 4.0 a) c) (* (* 4.0 a) c))) (+ (* b b) (* (* 4.0 a) c)))
61.0ms
(* (* (* 4.0 a) c) (* (* 4.0 a) c))

simplify2.4s

Counts
247 → 247
Iterations

Useful iterations: done (2.4s)

IterNodesCost
037510404
19389558
240278740
done50008733

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* b b) (* (* 4.0 a) c))) (cbrt (+ (* b b) (* (* 4.0 a) c))))
0.5b
(cbrt (+ (* b b) (* (* 4.0 a) c)))
0.5b
(cbrt (+ (* b b) (* (* 4.0 a) c)))
0.5b
(cbrt (+ (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
56.0ms
(* (cbrt (+ (* b b) (* (* 4.0 a) c))) (cbrt (+ (* b b) (* (* 4.0 a) c))))
5.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))
16.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))

series579.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (cbrt (+ (* b b) (* (* 4.0 a) c))) (cbrt (+ (* b b) (* (* 4.0 a) c))))
132.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))
157.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))
145.0ms
(cbrt (+ (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
99 → 99
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01192388
12632221
27491997
322251796
done50011734

prune671.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02241
12739
done2739

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.3s4894×body160valid
1.3s8422×body80nan
711.0ms16422×pre80true
389.0ms1329×body320valid
135.0ms1777×body80valid