Details

Time bar (total: 18.0s)

sample78.0ms

Algorithm
intervals
Results
34.0ms275×body80valid
10.0ms90×body80nan

simplify263.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02038
13838
27837
313637
416337
517537
617937
done17937

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize191.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify990.0ms

Counts
75 → 75
Iterations

Useful iterations: done (986.0ms)

IterNodesCost
01001330
12541186
210291089
done50011074

prune750.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.3b

localize182.0ms

Local error

Found 4 expressions with local error:

8.8b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls
4 calls:
27.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify930.0ms

Counts
70 → 70
Iterations

Useful iterations: done (926.0ms)

IterNodesCost
0861428
12421014
21033938
done5001930

prune785.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.3b

localize190.0ms

Local error

Found 4 expressions with local error:

8.9b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite549.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
3×sqrt-prod
2×pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
26.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
497.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
182.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
193.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
67 → 67
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01491566
13791475
216261275
done50001259

prune939.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.3b

localize223.0ms

Local error

Found 4 expressions with local error:

23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
131.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
136.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
72 → 72
Iterations

Useful iterations: 2 (125.0ms)

IterNodesCost
0521140
11371008
2531928
33095928
done5002928

prune893.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.3b

regimes443.0ms

Accuracy

92.1% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 20.1b

bsearch342.0ms

Steps
ItersRangePoint
8
4.049254448328916e+76
2.3057443967677173e+80
2.2766902918844874e+80
9
-4.894566258717386e+103
-4.829208015252428e+98
-3.907007642335128e+103

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
041133
150133
done50133

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s8789×body80valid
457.0ms3015×body80nan