Details

Time bar (total: 17.9s)

sample115.0ms

Algorithm
intervals
Results
11.0ms188×body80valid
10.0ms35×body2560valid
6.0ms28×body1280valid
4.0ms85×body80nan
2.0ms14×body640valid
2.0ms10×body320valid
2.0ms5×body5120valid
0.0ms4×body160valid

simplify64.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite238.0ms

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:
138.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
10.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
63.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
131.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
134 → 134
Iterations
IterNodes
done5002
21393
1494
0199

prune608.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite333.0ms

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 insert-posit16 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 → 123
Calls
4 calls:
196.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
18.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
49.0ms
(- (* b_2 b_2) (* a c))
82.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
135 → 135
Iterations
IterNodes
done5000
21630
1559
0219

prune720.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

localize26.0ms

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)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))
21.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

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:
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
85.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
134.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
132 → 132
Iterations
IterNodes
done5001
33200
2878
1287
0112

prune672.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize64.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
21.2b
(sqrt (- (* b_2 b_2) (* a c)))
22.0b
(cbrt (- (* b_2 b_2) (* a c)))
22.0b
(cbrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×expm1-log1p-u cbrt-div flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×prod-diff sqrt-prod
2×pow1/3 sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log
Counts
4 → 69
Calls
4 calls:
33.0ms
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))
6.0ms
(cbrt (- (* b_2 b_2) (* a c)))
6.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))
115.0ms
(cbrt (- (* b_2 b_2) (* a c)))
127.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
81 → 81
Iterations
IterNodes
done5000
34809
21314
1417
0158

prune527.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

regimes434.0ms

Accuracy

83.8% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 34.0b

bsearch100.0ms

Steps
ItersRangePoint
6
1.5727591416233446e-143
1.789606490082599e-142
1.744031351412433e-142
8
-1.3198903247987554e+155
-1.1250773400730914e+152
-1.2705286994550075e+152

simplify5.0ms

Iterations
IterNodes
done27
127
024

end0.0ms

sample3.1s

Algorithm
intervals
Results
710.0ms2985×body80nan
654.0ms1082×body2560valid
613.0ms5804×body80valid
426.0ms933×body1280valid
144.0ms492×body640valid
77.0ms120×body160valid
60.0ms108×body5120valid
49.0ms245×body320valid