Details

Time bar (total: 18.7s)

sample82.0ms

Algorithm
intervals
Results
37.0ms282×body80valid
10.0ms80×body80nan

simplify208.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize114.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (* b b) (* (* 4.0 a) c))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
60.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune417.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize118.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

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:
82.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
70 → 70
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune527.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize154.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

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:
100.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
161.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
158.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
101 → 101
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01893740
13463338
27172673
320352622
done50002541

prune613.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize162.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b
(sqrt (* (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite411.0ms

Algorithm
rewrite-expression-head
Rules
220×cbrt-div
190×sqrt-div
136×frac-times
111×flip3-- flip--
68×associate-*l/
26×associate-*r/
15×pow1
9×pow-prod-down
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod sqrt-pow1 pow1/3
4×add-exp-log sqrt-prod add-cbrt-cube add-log-exp
2×pow1/2
1×rem-sqrt-square
Counts
4 → 135
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
361.0ms
(sqrt (* (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* 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)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (* (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
150.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
147 → 147
Iterations

Useful iterations: done (2.9s)

IterNodesCost
039211273
177510441
216209243
333148685
done50018457

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.9b

regimes648.0ms

Accuracy

92.8% (0.9b remaining)

Error of 8.6b against oracle of 7.7b and baseline of 20.3b

bsearch122.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
9
-1.489991982892314e+158
-2.0545059602165346e+153
-1.3596485852230119e+154

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043140
150140
done50140

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8687×body80valid
394.0ms2888×body80nan