Details

Time bar (total: 26.9s)

sample332.0ms

Algorithm
intervals
Results
34.0ms121×body320valid
22.0ms244×body80nan
21.0ms500×pre80true
19.0ms93×body160valid
6.0ms12×body640valid
3.0ms30×body80valid

simplify160.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
26.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite250.0ms

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:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
158.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series611.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
216.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(- (* b b) (* (* 4.0 a) c))
188.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01541565
14191461
219061245
done50001239

prune603.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

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

rewrite377.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
116.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
185.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series880.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(- (* b b) (* (* 4.0 a) c))
360.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
291.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify3.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02475048
16584512
237774174
done50014174

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize57.0ms

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

rewrite341.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
116.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series754.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
212.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
94.0ms
(- (* b b) (* (* 4.0 a) c))
290.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify3.5s

Counts
97 → 97
Iterations

Useful iterations: 2 (983.0ms)

IterNodesCost
01762262
15432068
242111750
done50001750

prune774.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize105.0ms

Local error

Found 4 expressions with local error:

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) (+ (* (* a c) 4.0) (* b b)))))))) (* 2.0 a))
0.3b
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))))
0.4b
(* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))
0.8b
(pow (* (* a c) 4.0) 3)

rewrite909.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
114×times-frac
77×*-un-lft-identity
45×add-cube-cbrt
42×difference-of-squares
40×associate-/l*
33×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
16×distribute-lft-out--
12×sqrt-prod
11×prod-exp cbrt-unprod
9×unpow-prod-down pow-prod-down
7×cbrt-undiv div-exp
6×distribute-rgt-neg-in associate-/r/
4×associate-/r* div-inv add-log-exp
3×pow-unpow flip3-- pow-pow associate-*r* pow-exp flip-- associate-/l/ rem-cube-cbrt
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 190
Calls
4 calls:
538.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))))))) (* 2.0 a))
118.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))))
198.0ms
(* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))
33.0ms
(pow (* (* a c) 4.0) 3)

series980.0ms

Counts
4 → 12
Calls
4 calls:
453.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))))))) (* 2.0 a))
268.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))))
146.0ms
(* (* (* a c) 4.0) (+ (* (* a c) 4.0) (* b b)))
114.0ms
(pow (* (* a c) 4.0) 3)

simplify921.0ms

Counts
202 → 202
Iterations

Useful iterations: done (904.0ms)

IterNodesCost
04129693
111239086
done50008466

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes412.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01725
12223
22323
done2323

end0.0ms

sample6.4s

Algorithm
intervals
Results
1.7s2937×body160valid
1.4s3688×body320valid
916.0ms8221×body80nan
857.0ms16221×pre80true
345.0ms493×body640valid
137.0ms882×body80valid