Details

Time bar (total: 18.6s)

sample81.0ms

Algorithm
intervals
Results
38.0ms283×body80valid
8.0ms69×body80nan

simplify248.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize105.0ms

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)))

rewrite50.0ms

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))
17.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (* b b) (* (* 4.0 a) c))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
66 → 66
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune791.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize106.0ms

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)))

rewrite126.0ms

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:
90.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
70 → 70
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune518.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize153.0ms

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)))

rewrite55.0ms

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:
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
72 → 72
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0901506
12251066
27261000
32540988
done5000984

prune507.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize119.0ms

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)))

rewrite207.0ms

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:
174.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
123.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
185.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
207.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
101 → 101
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01893740
13463338
27172673
320352622
done50002541

prune599.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

regimes217.0ms

Accuracy

89.9% (1.2b remaining)

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

bsearch282.0ms

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

sample2.7s

Algorithm
intervals
Results
1.7s8735×body80valid
380.0ms2941×body80nan