Details

Time bar (total: 18.2s)

sample70.0ms

Algorithm
intervals
Results
36.0ms283×body80valid
8.0ms69×body80nan

simplify193.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize123.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

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:
14.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series772.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
526.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
66 → 66
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune394.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize119.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

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:
79.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
70 → 70
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune516.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize178.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

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:
26.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
72 → 72
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0901506
12251066
27261000
32540988
done5000984

prune496.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize127.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite168.0ms

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)))))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series585.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
134.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
185.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
101 → 101
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01893740
13463338
27172673
320352622
done50002541

prune643.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

regimes201.0ms

Accuracy

89.9% (1.2b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 19.9b

bsearch277.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
10
-2.386196042261592e+160
-1.0923850232644114e+143
-1.3255191511081353e+154

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043140
150140
done50140

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.7s8735×body80valid
360.0ms2941×body80nan