Details

Time bar (total: 20.6s)

sample155.0ms

Algorithm
intervals
Results
34.0ms195×body80valid
31.0ms29×body2560valid
29.0ms28×body1280valid
15.0ms97×body80nan
14.0ms18×body640valid
4.0ms8×body320valid
4.0ms3×body5120valid
0.0ms1×body160valid

simplify194.0ms

Counts
1 → 1
Iterations
IterNodes
done142
7142
6140
5135
4130
3110
263
129
014

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.4b
(- (* b b) (* 4 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
17.0ms
(- (* b b) (* 4 (* a c)))
42.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
82.0ms
(- (* b b) (* 4 (* a c)))
111.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
124.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts
173 → 173
Iterations
IterNodes
done2005
32005
21867
1599
0239

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
0.5b
(fma b b (* -4 (* a c)))
0.8b
(- (- b) (sqrt (fma b b (* -4 (* a c)))))
20.6b
(sqrt (fma b b (* -4 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
25×add-exp-log
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
10×fma-neg
9×div-exp
8×pow1 add-log-exp
7×neg-mul-1
6×prod-exp
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u
3×rec-exp times-frac 1-exp associate-/l*
2×diff-log cbrt-unprod pow-flip distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 pow-prod-down neg-log associate-*l/ associate-/r/ fma-udef div-inv flip-- inv-pow
Counts
4 → 154
Calls
4 calls:
23.0ms
(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
0.0ms
(fma b b (* -4 (* a c)))
10.0ms
(- (- b) (sqrt (fma b b (* -4 (* a c)))))
1.0ms
(sqrt (fma b b (* -4 (* a c))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ 1 (* (/ 2 (- (- b) (sqrt (fma b b (* -4 (* a c)))))) a))
64.0ms
(fma b b (* -4 (* a c)))
126.0ms
(- (- b) (sqrt (fma b b (* -4 (* a c)))))
120.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify1.6s

Counts
166 → 166
Iterations
IterNodes
done2002
32002
21356
1534
0233

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize90.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
6×sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 145
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4 (* a c))))
19.0ms
(sqrt (- (* b b) (* 4 (* a c))))
19.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
126.0ms
(sqrt (- (* b b) (* 4 (* a c))))
135.0ms
(sqrt (- (* b b) (* 4 (* a c))))
127.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts
157 → 157
Iterations
IterNodes
done2000
32000
21011
1392
0164

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.5b

localize76.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))
20.6b
(sqrt (- (* b b) (* 4 (* a c))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
6×sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 145
Calls
4 calls:
34.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms
(sqrt (- (* b b) (* 4 (* a c))))
16.0ms
(sqrt (- (* b b) (* 4 (* a c))))
26.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
117.0ms
(sqrt (- (* b b) (* 4 (* a c))))
105.0ms
(sqrt (- (* b b) (* 4 (* a c))))
113.0ms
(sqrt (- (* b b) (* 4 (* a c))))

simplify1.3s

Counts
157 → 157
Iterations
IterNodes
done2000
32000
21011
1392
0164

prune1.2s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 5.5b

regimes895.0ms

Accuracy

81.6% (5.2b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 33.4b

bsearch183.0ms

Steps
ItersRangePoint
4
2.0351360940656854e+23
4.0047314049975276e+23
3.912332224813067e+23
8
-9.258644314597195e-129
-3.187950860214187e-133
-8.424937854855119e-129

simplify10.0ms

Iterations
IterNodes
done32
132
026

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.7s5815×body80valid
1.3s1110×body2560valid
841.0ms906×body1280valid
560.0ms2984×body80nan
293.0ms443×body640valid
169.0ms210×body320valid
129.0ms107×body5120valid
35.0ms107×body160valid