Details

Time bar (total: 17.1s)

sample95.0ms

Algorithm
intervals
Results
48.0ms266×body80valid
10.0ms79×body80nan

simplify205.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize124.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
23.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
72 → 72
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0971211
12261091
27561009
32904998
done5001996

prune456.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize164.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
107.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune464.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize134.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.4b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.0b
(/ (* a c) b)
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 71
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
11.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
36.0ms
(/ (* a c) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
83 → 83
Iterations

Useful iterations: 2 (305.0ms)

IterNodesCost
01551221
13931165
21501997
done5000997

prune456.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize124.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.7b
(* (/ a (sqrt b)) (/ c (sqrt b)))
1.0b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
51×times-frac
33×add-cube-cbrt *-un-lft-identity
27×sqrt-prod
22×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp add-log-exp
5×prod-exp cbrt-unprod
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 123
Calls
4 calls:
13.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
98.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
195.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 b)))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
135 → 135
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02592237
17282118
226631706
done50001676

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

regimes236.0ms

Accuracy

93.4% (1.0b remaining)

Error of 7.5b against oracle of 6.6b and baseline of 21.1b

bsearch503.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.2875942964765074e+78
10
-3.579862835853504e-259
-1.0472779812871276e-269
-4.452231346955638e-267
9
-4.4874797001979404e+160
-1.588602326591779e+153
-1.3506760573432116e+154

simplify19.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
066197
183146
291146
399146
done99146

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s8712×body80valid
466.0ms2994×body80nan