Details

Time bar (total: 20.0s)

sample55.0ms

Algorithm
intervals
Results
10.0ms32×body2560valid
10.0ms184×body80valid
8.0ms31×body1280valid
4.0ms84×body80nan
3.0ms17×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify132.0ms

Counts
1 → 1
Iterations
IterNodes
done129
5129
4120
387
246
125
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
0.2b
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
1.4b
(- (* b b) (* a (* 4.0 c)))
24.6b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite142.0ms

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:
69.0ms
(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
38.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
19.0ms
(- (* b b) (* a (* 4.0 c)))
13.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) a)
109.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
69.0ms
(- (* b b) (* a (* 4.0 c)))
90.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify2.8s

Counts
130 → 130
Iterations
IterNodes
done5001
22197
1512
0199

prune788.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (- (* a (* 4.0 c))))) b) a)
0.2b
(- (sqrt (fma b b (- (* a (* 4.0 c))))) b)
1.8b
(fma b b (- (* a (* 4.0 c))))
24.6b
(sqrt (fma b b (- (* a (* 4.0 c)))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 110
Calls
4 calls:
40.0ms
(/ (- (sqrt (fma b b (- (* a (* 4.0 c))))) b) a)
18.0ms
(- (sqrt (fma b b (- (* a (* 4.0 c))))) b)
0.0ms
(fma b b (- (* a (* 4.0 c))))
2.0ms
(sqrt (fma b b (- (* a (* 4.0 c)))))

series448.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (sqrt (fma b b (- (* a (* 4.0 c))))) b) a)
105.0ms
(- (sqrt (fma b b (- (* a (* 4.0 c))))) b)
64.0ms
(fma b b (- (* a (* 4.0 c))))
129.0ms
(sqrt (fma b b (- (* a (* 4.0 c)))))

simplify1.5s

Counts
122 → 122
Iterations
IterNodes
done5001
21395
1421
0177

prune700.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
0.2b
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
1.4b
(- (* b b) (* (* a c) 4.0))
24.6b
(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite201.0ms

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 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 → 196
Calls
4 calls:
86.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
76.0ms
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
13.0ms
(- (* b b) (* (* a c) 4.0))
17.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
142.0ms
(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
66.0ms
(- (* b b) (* (* a c) 4.0))
117.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.2s

Counts
208 → 208
Iterations
IterNodes
done5000
23948
1755
0301

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize44.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* a c) 4.0))
1.4b
(- (* b b) (* (* a c) 4.0))
24.6b
(sqrt (- (* b b) (* (* a c) 4.0)))
24.6b
(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
10.0ms
(- (* b b) (* (* a c) 4.0))
6.0ms
(- (* b b) (* (* a c) 4.0))
16.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))
18.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* b b) (* (* a c) 4.0))
61.0ms
(- (* b b) (* (* a c) 4.0))
119.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))
109.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

simplify3.4s

Counts
78 → 78
Iterations
IterNodes
done5000
34853
2797
1180
069

prune637.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.8b

regimes507.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.6b against oracle of 6.1b and baseline of 34.4b

bsearch176.0ms

Steps
ItersRangePoint
8
2.8373581988670566e-35
2.2677514638291856e-31
2.8983489306952693e-35
8
-2.748004767191833e+152
-7.260401024913698e+147
-2.221067196710922e+149

simplify40.0ms

Iterations
IterNodes
done46
246
138
030

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s5835×body80valid
989.0ms1040×body2560valid
379.0ms906×body1280valid
305.0ms2881×body80nan
186.0ms456×body640valid
61.0ms102×body5120valid
56.0ms232×body320valid
18.0ms116×body160valid