Details

Time bar (total: 18.2s)

sample171.0ms

Algorithm
intervals
Results
57.0ms152×body160valid
26.0ms278×body80nan
21.0ms534×pre80true
13.0ms39×body320valid
6.0ms65×body80valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize14.0ms

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.8b
(+ (- 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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms
(- (* b b) (* (* 4.0 a) c))
149.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
123.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune281.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))))

rewrite313.0ms

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))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
109.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(- (* b b) (* (* 4.0 a) c))
244.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
257.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.5s

Counts
163 → 163
Iterations

Useful iterations: 2 (594.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune718.0ms

Pruning

8 alts after pruning (8 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
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite289.0ms

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:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series627.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
202.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms
(- (* b b) (* (* 4.0 a) c))
220.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.7s

Counts
97 → 97
Iterations

Useful iterations: 2 (673.0ms)

IterNodesCost
01762262
14932066
225611750
done50021750

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
719×times-frac
330×add-exp-log
257×add-sqr-sqrt *-un-lft-identity
214×div-exp
185×add-cube-cbrt
138×add-cbrt-cube
83×prod-exp
72×cbrt-undiv
52×div-inv
50×associate-/r/
45×1-exp
38×associate-/r*
36×distribute-lft-out-- difference-of-squares
33×cbrt-unprod
18×rec-exp flip3-- distribute-rgt-neg-in sqrt-prod flip--
15×associate-/l*
6×add-log-exp
4×pow1
3×frac-2neg clear-num
1×sub-neg diff-log associate-/l/
Counts
4 → 457
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
91.0ms
(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
97.0ms
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series764.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
239.0ms
(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
307.0ms
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify3.2s

Counts
469 → 469
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
069219688
1175216552
2468014802
done500014802

prune883.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01725
12223
done2223

end0.0ms

sample4.1s

Algorithm
intervals
Results
851.0ms4874×body160valid
792.0ms16128×pre80true
764.0ms1334×body320valid
717.0ms8128×body80nan
211.0ms1792×body80valid