Details

Time bar (total: 16.4s)

sample122.0ms

Algorithm
intervals
Results
9.0ms29×body2560valid
9.0ms202×body80valid
7.0ms31×body1280valid
5.0ms106×body80nan
1.0ms9×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify27.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite535.0ms

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:
89.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms
(- (* b_2 b_2) (* a c))
412.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
130 → 130
Iterations
IterNodes
done5007
21420
1491
0195

prune729.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 119
Calls
4 calls:
183.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
13.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
62.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
131 → 131
Iterations
IterNodes
done5000
21633
1557
0215

prune647.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

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:
86.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
6.0ms
(- (* b_2 b_2) (* a c))
44.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms
(- (* b_2 b_2) (* a c))
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
130 → 130
Iterations
IterNodes
done5007
21420
1491
0195

prune629.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite153.0ms

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 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
64.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
112.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts
128 → 128
Iterations
IterNodes
done5007
33200
2875
1285
0110

prune706.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

regimes434.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.4b

bsearch157.0ms

Steps
ItersRangePoint
8
1.5119020269574885e-23
1.8921341643334238e-20
9.136492990928292e-23
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify8.0ms

Iterations
IterNodes
done27
127
024

end0.0ms

sample2.7s

Algorithm
intervals
Results
892.0ms1059×body2560valid
390.0ms5860×body80valid
375.0ms2871×body80nan
335.0ms902×body1280valid
175.0ms434×body640valid
94.0ms124×body5120valid
39.0ms224×body320valid
14.0ms115×body160valid