Details

Time bar (total: 15.6s)

sample63.0ms

Algorithm
intervals
Results
33.0ms270×body80valid
9.0ms100×body80nan

simplify212.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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 expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
25.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify878.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
0711146
11851058
2843952
done5000952

prune552.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.1b

localize138.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

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:
30.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
100 → 100
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01152639
12931655
212111574
done50011554

prune575.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.1b

localize151.0ms

Local error

Found 4 expressions with local error:

14.3b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div add-log-exp
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-diff
1×sub-neg fma-neg diff-log difference-of-squares
Counts
4 → 70
Calls
4 calls:
65.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01041631
12881150
212701073
done50001067

prune685.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.1b

localize202.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
152.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
76 → 76
Iterations

Useful iterations: done (3.3s)

IterNodesCost
0941248
12241156
27501052
339761040
done50001038

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.1b

regimes322.0ms

Accuracy

92.7% (0.9b remaining)

Error of 8.4b against oracle of 7.5b and baseline of 20.1b

bsearch281.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
4.713735678910177e+106
1.5438258933175616e+106
8
-2.1489000102508758e+104
-1.471055469501053e+100
-2.1102147844326466e+104

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
043130
148130
done48130

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.4s8674×body80valid
349.0ms2905×body80nan