Details

Time bar (total: 20.9s)

sample80.0ms

Algorithm
intervals
Results
26.0ms271×body80valid
7.0ms79×body80nan

simplify222.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize127.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (* b b) (* (* 4.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

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:
17.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(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

prune376.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize149.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
162.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
186.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
66 → 66
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0901170
12041110
25721000
31928985
done5001952

prune505.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

localize162.0ms

Local error

Found 4 expressions with local error:

8.8b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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 add-cbrt-cube
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 54
Calls
4 calls:
12.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series567.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
174.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
139.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts
66 → 66
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01461516
13671425
212061215
345291185
done50011155

prune526.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

localize119.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

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:
13.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series956.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
161.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
547.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts
67 → 67
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01491566
13631475
211721275
344571245
done50011215

prune607.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.8b

regimes439.0ms

Accuracy

91.8% (1.0b remaining)

Error of 8.7b against oracle of 7.7b and baseline of 20.3b

bsearch225.0ms

Steps
ItersRangePoint
0
2.0836136179885362e+135
2.1675125417143413e+135
2.1255630798514387e+135
10
-7.092886765712621e+82
-3.4482088762076956e+69
-3.2734862173190983e+79

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043143
153143
done53143

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s8745×body80valid
420.0ms2922×body80nan