Details

Time bar (total: 18.5s)

sample47.0ms

Algorithm
intervals
Results
20.0ms283×body80valid
6.0ms106×body80nan

simplify263.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize125.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
75 → 75
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01061330
12411181
27481110
326611090
done50001085

prune548.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize117.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv div-exp sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in 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 → 80
Calls
4 calls:
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
63.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
10.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
234.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
32.0ms
(/ (* a c) b)
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
92 → 92
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01781468
14331368
216081212
done50001182

prune564.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize155.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×associate-/r* add-log-exp unswap-sqr
5×distribute-lft-out--
4×sqrt-prod difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in 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 → 118
Calls
4 calls:
61.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
79.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
272.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02622573
17102440
227771940
done50021753

prune849.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize152.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
3.8b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
44×add-cbrt-cube
33×prod-exp cbrt-unprod
25×add-sqr-sqrt
24×cbrt-undiv div-exp
20×*-un-lft-identity
14×times-frac
10×add-cube-cbrt
7×pow1 associate-*l*
6×associate-/r* add-log-exp
5×associate-*r* distribute-lft-out--
4×sqrt-prod difference-of-squares unswap-sqr
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in 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 → 117
Calls
4 calls:
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
120.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
61.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))))))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series789.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
321.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
259.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))))))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
129 → 129
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02803999
17813835
233523070
done50002560

prune950.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

regimes532.0ms

Accuracy

90.8% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 21.5b

bsearch390.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
1.7754385347718217e+40
8
-4.810799056667626e+157
-8.81647488783933e+153
-1.367002129773412e+154

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
054149
164149
done64149

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.2s8744×body80valid
251.0ms3010×body80nan