Details

Time bar (total: 6.7s)

sample59.0ms

Algorithm
intervals
Results
15.0ms120×body320valid
9.0ms494×pre80true
8.0ms238×body80nan
7.0ms97×body160valid
2.0ms17×body640valid
1.0ms22×body80valid

simplify52.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
27.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
19.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series307.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify987.0ms

Counts
161 → 161
Iterations

Useful iterations: done (981.0ms)

IterNodesCost
02804083
16653911
219753753
done50003752

prune447.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune21.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 frac-2neg clear-num add-log-exp
1×associate-/l/
Counts
2 → 73
Calls
2 calls:
3.0ms
(/ (* a c) b)
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series40.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (* a c) b)
21.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify688.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
01671164
14401118
21795956
done5001956

prune178.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ a (sqrt b))
0.3b
(/ c (sqrt b))
0.3b
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
0.4b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt *-un-lft-identity
53×add-exp-log add-cbrt-cube
48×sqrt-prod
23×cbrt-undiv div-exp
22×associate-*r* associate-*l*
15×associate-/r*
13×prod-exp cbrt-unprod associate-/l*
9×div-inv unswap-sqr
6×pow1
4×add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 207
Calls
4 calls:
3.0ms
(/ a (sqrt b))
3.0ms
(/ c (sqrt b))
26.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
27.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series167.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ a (sqrt b))
46.0ms
(/ c (sqrt b))
35.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
42.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.3s

Counts
219 → 219
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03573295
19913073
239122473
done50002465

prune482.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.3b

regimes208.0ms

Accuracy

0% (3.6b remaining)

Error of 6.2b against oracle of 2.6b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
165
done65

end0.0ms

sample1.6s

Algorithm
intervals
Results
388.0ms3615×body320valid
304.0ms16135×pre80true
272.0ms8135×body80nan
211.0ms2978×body160valid
70.0ms495×body640valid
33.0ms912×body80valid