Details

Time bar (total: 18.2s)

sample87.0ms

Algorithm
intervals
Results
18.0ms155×body160valid
15.0ms253×body80nan
13.0ms509×pre80true
6.0ms33×body320valid
4.0ms68×body80valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

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))
37.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite110.0ms

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)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(- (* b b) (* (* 4.0 a) c))
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14191461
219261245
done50011239

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

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)))))

rewrite232.0ms

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))
112.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
74.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(- (* b b) (* (* 4.0 a) c))
262.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
327.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts
163 → 163
Iterations

Useful iterations: 2 (638.0ms)

IterNodesCost
02475048
16594512
238214174
done50004174

prune561.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize23.0ms

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

rewrite219.0ms

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:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
102.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
198.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.9s

Counts
97 → 97
Iterations

Useful iterations: 2 (832.0ms)

IterNodesCost
01762262
15432068
243281760
done50011760

prune403.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite201.0ms

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:
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(/ (* (* 4.0 a) c) (* a 2.0))
16.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (/ (* (* 4.0 a) c) (* a 2.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(/ (* (* 4.0 a) c) (* a 2.0))
64.0ms
(- (* b b) (* (* 4.0 a) c))
175.0ms
(/ (/ (* (* 4.0 a) c) (* a 2.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.7s

Counts
141 → 141
Iterations

Useful iterations: 2 (766.0ms)

IterNodesCost
02253880
16653713
246063029
done50013029

prune408.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes187.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01823
12323
done2323

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.2s1316×body320valid
841.0ms4898×body160valid
788.0ms16243×pre80true
752.0ms8243×body80nan
131.0ms1786×body80valid