Details

Time bar (total: 9.7s)

sample36.0ms

Algorithm
intervals
Results
8.0ms40×body2560valid
7.0ms194×body80valid
5.0ms28×body1280valid
2.0ms76×body80nan
1.0ms10×body640valid
0.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12117
24116
37516
48716
59516
done9516

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.4b
(* (* 3.0 a) c)
0.4b
(- (* b b) (* (* 3.0 a) c))
24.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×*-un-lft-identity
10×pow1
8×add-cube-cbrt
6×times-frac associate-/l* add-log-exp
5×sqrt-prod
4×prod-exp cbrt-unprod difference-of-squares
3×flip3-- associate-*r* pow-prod-down flip--
2×cbrt-undiv sqrt-div div-exp associate-/l/ distribute-lft-out--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*l* clear-num associate-/r* *-commutative div-inv
Counts
4 → 75
Calls
4 calls:
35.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
6.0ms
(* (* 3.0 a) c)
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
23.0ms
(* (* 3.0 a) c)
41.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify583.0ms

Counts
87 → 87
Iterations

Useful iterations: done (581.0ms)

IterNodesCost
01571410
13961336
215231170
done50001169

prune218.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.4b
(* (* 3.0 a) c)
0.4b
(- (* b b) (* (* 3.0 a) c))
24.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
17.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
6.0ms
(* (* 3.0 a) c)
2.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
23.0ms
(* (* 3.0 a) c)
42.0ms
(- (* b b) (* (* 3.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts
72 → 72
Iterations

Useful iterations: 3 (761.0ms)

IterNodesCost
01201001
1279903
2998825
34312821
done5000821

prune171.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.4b
(* (* 3.0 a) c)
0.4b
(- (* b b) (* (* 3.0 a) c))
24.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×*-un-lft-identity
10×pow1
8×add-cube-cbrt
6×times-frac associate-/r* add-log-exp
5×sqrt-prod
4×prod-exp cbrt-unprod difference-of-squares
3×flip3-- associate-*r* pow-prod-down flip--
2×cbrt-undiv sqrt-div div-exp associate-/r/ distribute-lft-out--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
20.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
6.0ms
(* (* 3.0 a) c)
2.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
19.0ms
(* (* 3.0 a) c)
45.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify831.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
01481369
13611275
214871127
done50001127

prune218.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.4b
(* (* 3.0 a) c)
0.4b
(- (* b b) (* (* 3.0 a) c))
24.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
18.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
6.0ms
(* (* 3.0 a) c)
2.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
20.0ms
(* (* 3.0 a) c)
41.0ms
(- (* b b) (* (* 3.0 a) c))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (765.0ms)

IterNodesCost
01201001
1279903
2998825
34312821
done5000821

prune157.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.7b

regimes430.0ms

Accuracy

82.9% (4.9b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 34.3b

bsearch115.0ms

Steps
ItersRangePoint
8
10920358539895.18
4.2009936632527795e+17
11181767625882.13
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02842
13542
done3542

end0.0ms

sample1.1s

Algorithm
intervals
Results
241.0ms1105×body2560valid
214.0ms5867×body80valid
156.0ms909×body1280valid
99.0ms2861×body80nan
57.0ms422×body640valid
27.0ms96×body5120valid
25.0ms214×body320valid
8.0ms119×body160valid