Details

Time bar (total: 14.9s)

sample143.0ms

Algorithm
intervals
Results
38.0ms525×pre80true
29.0ms167×body160valid
24.0ms269×body80nan
9.0ms33×body320valid
5.0ms56×body80valid

simplify89.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
014365
124365
244325
378325
4102325
5111325
done111325

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
42.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite129.0ms

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-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
39.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series357.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
51.0ms
(- (* b b) (* (* 4.0 a) c))
134.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.5s

Counts
161 → 161
Iterations

Useful iterations: done (2.5s)

IterNodesCost
028087734
168982980
2307682299
done500182259

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.7b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune130.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 clear-num frac-2neg add-log-exp
1×associate-/l/
Counts
2 → 73
Calls
2 calls:
18.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
14.0ms
(/ (* a c) b)

series52.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
27.0ms
(/ (* a c) b)

simplify1.8s

Counts
79 → 79
Iterations

Useful iterations: done (1.8s)

IterNodesCost
016723274
146421513
2300821072
done500020952

prune618.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×*-un-lft-identity add-cube-cbrt
53×add-cbrt-cube add-exp-log
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×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 207
Calls
4 calls:
39.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
5.0ms
(/ c (sqrt b))
5.0ms
(/ a (sqrt b))
31.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
57.0ms
(/ c (sqrt b))
59.0ms
(/ a (sqrt b))
52.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.3s

Counts
219 → 219
Iterations

Useful iterations: done (1.3s)

IterNodesCost
035771900
1105264323
done500063636

prune1.2s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 5.6b

regimes970.0ms

Accuracy

0% (6.8b remaining)

Error of 12.0b against oracle of 5.2b and baseline of 12.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0583
1683
done683

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.3s4824×body160valid
1.1s16183×pre80true
613.0ms8183×body80nan
379.0ms1373×body320valid
126.0ms1803×body80valid