Details

Time bar (total: 16.1s)

sample76.0ms

Algorithm
intervals
Results
14.0ms296×body80nan
14.0ms143×body160valid
12.0ms552×pre80true
8.0ms55×body320valid
3.0ms58×body80valid

simplify171.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize30.0ms

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite161.0ms

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:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
121.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune304.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))))
0.2b
(/ (/ (+ 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)))))

rewrite249.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
83.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
184.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
259.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Counts
163 → 163
Iterations

Useful iterations: 2 (556.0ms)

IterNodesCost
02475048
16124510
224994166
done50004166

prune641.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize38.0ms

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

rewrite234.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
109.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
87.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series630.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (* b b) (* (* 4.0 a) c))
125.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
175.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
241.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.9s

Counts
97 → 97
Iterations

Useful iterations: 2 (584.0ms)

IterNodesCost
01762262
14932066
225551750
done50001750

prune415.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
46×add-sqr-sqrt *-un-lft-identity
44×times-frac
19×cbrt-undiv div-exp
18×add-cube-cbrt prod-exp cbrt-unprod
14×distribute-lft-out-- difference-of-squares
10×div-inv add-log-exp
8×associate-/r*
7×distribute-rgt-neg-in sqrt-prod
6×associate-/l*
4×pow1
3×flip3-- diff-log flip--
2×sub-neg frac-2neg clear-num associate-/r/
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 129
Calls
4 calls:
103.0ms
(/ (/ (* (* 4.0 a) c) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))

series474.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(/ (/ (* (* 4.0 a) c) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms
(- (* b b) (* (* 4.0 a) c))
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))

simplify2.0s

Counts
141 → 141
Iterations

Useful iterations: 2 (728.0ms)

IterNodesCost
02253880
16143713
230903199
done50013199

prune357.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes103.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
11717
done1717

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.3s4842×body160valid
669.0ms8186×body80nan
666.0ms16186×pre80true
379.0ms1362×body320valid
201.0ms1796×body80valid