Details

Time bar (total: 20.5s)

sample242.0ms

Algorithm
intervals
Results
70.0ms517×pre80true
27.0ms120×body320valid
20.0ms261×body80nan
16.0ms94×body160valid
5.0ms14×body640valid
2.0ms28×body80valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.4b

localize34.0ms

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))
25.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite206.0ms

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:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
57.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms
(- (* b b) (* (* 4.0 a) c))
170.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
129.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune328.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))))

rewrite331.0ms

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:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
167.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
108.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series739.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
61.0ms
(- (* b b) (* (* 4.0 a) c))
237.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
305.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.4s

Counts
163 → 163
Iterations

Useful iterations: 2 (582.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune750.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
0.3b
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
0.7b
(pow (* (* a c) 4.0) 3)

rewrite525.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
58×*-un-lft-identity times-frac
36×difference-of-squares
34×add-cube-cbrt
23×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
13×associate-/l*
12×distribute-lft-out--
11×associate-/r*
9×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
8×sqrt-prod
4×distribute-rgt-neg-in associate-/r/ associate-/l/ add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg associate-*r/ div-exp clear-num flip-- div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 161
Calls
4 calls:
77.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
141.0ms
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
255.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
37.0ms
(pow (* (* a c) 4.0) 3)

series833.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
92.0ms
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
468.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
95.0ms
(pow (* (* a c) 4.0) 3)

simplify3.3s

Counts
173 → 173
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
03377440
18326981
244006599
done50016599

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite322.0ms

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:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
122.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(- (* b b) (* (* 4.0 a) c))
176.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
260.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.2s

Counts
97 → 97
Iterations

Useful iterations: 2 (550.0ms)

IterNodesCost
01762262
14932066
225551750
done50011750

prune397.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes157.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01725
12223
done2223

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.3s16269×pre80true
979.0ms3625×body320valid
760.0ms8269×body80nan
582.0ms2929×body160valid
287.0ms528×body640valid
71.0ms918×body80valid