Details

Time bar (total: 16.0s)

sample199.0ms

Algorithm
intervals
Results
21.0ms37×body2560valid
18.0ms191×body80valid
14.0ms30×body1280valid
12.0ms103×body80nan
6.0ms16×body640valid
2.0ms6×body320valid
1.0ms6×body160valid

simplify48.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 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 → 88
Calls
4 calls:
125.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms
(- (* b_2 b_2) (* a c))
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
100 → 100
Iterations
IterNodes
done5003
34058
21029
1378
0158

prune458.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
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 → 166
Calls
4 calls:
63.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
17.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
55.0ms
(- (* b_2 b_2) (* a c))
123.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
178 → 178
Iterations
IterNodes
done5000
21691
1626
0262

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize55.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
54.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5000
31579
2536
1185
080

prune510.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize53.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
76 → 76
Iterations
IterNodes
done5000
31579
2536
1185
080

prune463.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.8b

regimes379.0ms

Accuracy

81.1% (5.2b remaining)

Error of 10.8b against oracle of 5.6b and baseline of 33.1b

bsearch220.0ms

Steps
ItersRangePoint
7
3.2723221096518622e-21
8.349665184990521e-19
3.325219738594455e-21
7
5.034617224646791e-70
8.084342686052032e-69
1.0350377446088803e-69
1
1.8923753200636452e-106
2.0232344302868159e-106
1.990519652731023e-106
8
-5.8501169415505e+41
-1.816545290760657e+37
-2.782434836873191e+41

simplify14.0ms

Iterations
IterNodes
done50
150
038

end0.0ms

sample3.2s

Algorithm
intervals
Results
864.0ms837×body1280valid
633.0ms1071×body2560valid
594.0ms5919×body80valid
285.0ms3075×body80nan
233.0ms124×body5120valid
181.0ms461×body640valid
56.0ms241×body320valid
18.0ms121×body160valid