Details

Time bar (total: 16.5s)

sample194.0ms

Algorithm
intervals
Results
20.0ms37×body2560valid
17.0ms191×body80valid
13.0ms30×body1280valid
10.0ms103×body80nan
5.0ms16×body640valid
2.0ms6×body160valid
1.0ms6×body320valid

simplify56.0ms

Counts
1 → 1
Iterations
IterNodes
done34
534
432
330
223
115
010

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize40.0ms

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)))

rewrite225.0ms

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-- insert-posit16 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 → 122
Calls
4 calls:
112.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
10.0ms
(- (* b_2 b_2) (* a c))
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
62.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
134 → 134
Iterations
IterNodes
done5002
21393
1494
0199

prune514.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize43.0ms

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)))

rewrite204.0ms

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 insert-posit16 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 → 200
Calls
4 calls:
87.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
18.0ms
(- (* b_2 b_2) (* a c))
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
29.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
47.0ms
(- (* b_2 b_2) (* a c))
95.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
212 → 212
Iterations
IterNodes
done5001
22129
1742
0303

prune756.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize38.0ms

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)))

rewrite177.0ms

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 insert-posit16 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 → 200
Calls
4 calls:
77.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
64.0ms
(- (* b_2 b_2) (* a c))
133.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
212 → 212
Iterations
IterNodes
done5001
22129
1742
0303

prune741.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize24.0ms

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)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 120
Calls
4 calls:
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
114.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
132 → 132
Iterations
IterNodes
done5001
33200
2878
1287
0112

prune682.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

regimes471.0ms

Accuracy

81.1% (5.2b remaining)

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

bsearch205.0ms

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

simplify8.0ms

Iterations
IterNodes
done49
149
038

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.0s5919×body80valid
592.0ms1071×body2560valid
372.0ms837×body1280valid
330.0ms3075×body80nan
204.0ms461×body640valid
70.0ms124×body5120valid
48.0ms241×body320valid
16.0ms121×body160valid