Details

Time bar (total: 16.8s)

sample70.0ms

Algorithm
intervals
Results
30.0ms279×body80valid
7.0ms77×body80nan

simplify223.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize101.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* b b) (* (* 4.0 a) c))
54.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
66 → 66
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune804.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.0b

localize129.0ms

Local error

Found 4 expressions with local error:

12.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
11×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 flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
21.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0901506
12251066
27261000
32540988
done5000984

prune510.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.0b

localize123.0ms

Local error

Found 4 expressions with local error:

7.8b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
94.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
70 → 70
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune448.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.0b

localize133.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
23.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
132.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
126.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
101 → 101
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01893740
13463338
27172673
320352622
done50002541

prune580.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.0b

regimes252.0ms

Accuracy

92.5% (0.9b remaining)

Error of 8.6b against oracle of 7.7b and baseline of 19.8b

bsearch189.0ms

Steps
ItersRangePoint
8
5.30600492772346e+88
1.193256888551369e+92
1.8685092199711007e+90
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-1.3283483556924014e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043143
149143
done49143

end0.0ms

sample1.3s

Algorithm
intervals
Results
629.0ms8727×body80valid
192.0ms2974×body80nan