Details

Time bar (total: 7.0s)

sample196.0ms

Algorithm
intervals
Results
150.0ms120×body320valid
9.0ms494×pre80true
8.0ms238×body80nan
7.0ms97×body160valid
2.0ms17×body640valid
1.0ms22×body80valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune5.0ms

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)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
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 → 183
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series308.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify984.0ms

Counts
195 → 195
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
03214967
17514592
221864283
done50004264

prune472.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize4.0ms

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

prune25.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
3.0ms
(/ (* a c) b)
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series39.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (* a c) b)
20.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify679.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
01711200
14441154
21797992
done5001992

prune192.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.3b

localize14.0ms

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)))

rewrite66.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 215
Calls
4 calls:
3.0ms
(/ a (sqrt b))
3.0ms
(/ c (sqrt b))
25.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
23.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series158.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ a (sqrt b))
45.0ms
(/ c (sqrt b))
34.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
37.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.3s

Counts
227 → 227
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03653367
110123145
239622529
done50012513

prune509.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 2.3b

regimes240.0ms

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

sample1.7s

Algorithm
intervals
Results
389.0ms3615×body320valid
310.0ms16135×pre80true
282.0ms8135×body80nan
220.0ms2978×body160valid
72.0ms495×body640valid
33.0ms912×body80valid