Details

Time bar (total: 18.4s)

sample52.0ms

Algorithm
intervals
Results
10.0ms32×body2560valid
10.0ms184×body80valid
7.0ms31×body1280valid
4.0ms84×body80nan
3.0ms17×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify75.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
0.2b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
1.4b
(- (* b b) (* (* 4.0 c) a))
24.6b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 118
Calls
4 calls:
92.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
50.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
12.0ms
(- (* b b) (* (* 4.0 c) a))
9.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
123.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
71.0ms
(- (* b b) (* (* 4.0 c) a))
97.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.2s

Counts
130 → 130
Iterations
IterNodes
done5000
22147
1509
0198

prune804.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
0.2b
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 118
Calls
4 calls:
93.0ms
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
65.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
14.0ms
(- (* b b) (* a (* c 4.0)))
17.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
94.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
60.0ms
(- (* b b) (* a (* c 4.0)))
100.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.6s

Counts
130 → 130
Iterations
IterNodes
done5002
22220
1510
0199

prune700.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
0.2b
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 196
Calls
4 calls:
63.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
82.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
7.0ms
(- (* b b) (* a (* c 4.0)))
9.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
104.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
68.0ms
(- (* b b) (* a (* c 4.0)))
131.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.5s

Counts
208 → 208
Iterations
IterNodes
done5001
23555
1763
0303

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize92.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 67
Calls
4 calls:
8.0ms
(- (* b b) (* a (* c 4.0)))
8.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
9.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
9.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* b b) (* a (* c 4.0)))
111.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
127.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
134.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify1.2s

Counts
79 → 79
Iterations
IterNodes
done5000
2864
1190
071

prune704.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes408.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.6b against oracle of 6.1b and baseline of 34.4b

bsearch219.0ms

Steps
ItersRangePoint
8
2.8373581988670566e-35
2.2677514638291856e-31
2.8983489306952693e-35
8
-2.748004767191833e+152
-7.260401024913698e+147
-2.221067196710922e+149

simplify7.0ms

Iterations
IterNodes
done32
132
028

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s1040×body2560valid
594.0ms5835×body80valid
355.0ms906×body1280valid
317.0ms2881×body80nan
121.0ms456×body640valid
95.0ms232×body320valid
94.0ms102×body5120valid
16.0ms116×body160valid