Details

Time bar (total: 9.9s)

sample33.0ms

Algorithm
intervals
Results
14.0ms285×body80valid
4.0ms87×body80nan

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13938
27937
314337
416937
517837
618137
done18137

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize110.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.9b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff sqrt-prod
8×add-log-exp
7×fma-neg
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 91
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
103 → 103
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01302001
12901668
28841450
336481362
done50011361

prune345.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize114.0ms

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))))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
100 → 100
Iterations

Useful iterations: 3 (877.0ms)

IterNodesCost
01152639
12811649
28751574
336841538
done50011538

prune401.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize115.0ms

Local error

Found 4 expressions with local error:

6.1b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
8.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify673.0ms

Counts
95 → 95
Iterations

Useful iterations: done (666.0ms)

IterNodesCost
01782699
14272590
213592248
done50002236

prune462.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize120.0ms

Local error

Found 4 expressions with local error:

21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
92.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
72 → 72
Iterations

Useful iterations: 3 (249.0ms)

IterNodesCost
0671268
11621216
25091100
319851076
done50001076

prune430.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes163.0ms

Accuracy

88.9% (1.3b remaining)

Error of 8.9b against oracle of 7.6b and baseline of 19.6b

bsearch204.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
7.989761210864844e+108
10
-2.1502820188078274e+175
-2.227381996671495e+165
-2.2572095326645574e+165

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046155
154155
done54155

end0.0ms

sample821.0ms

Algorithm
intervals
Results
435.0ms8712×body80valid
138.0ms2998×body80nan