Details

Time bar (total: 19.6s)

sample69.0ms

Algorithm
intervals
Results
19.0ms178×body80valid
12.0ms40×body2560valid
9.0ms36×body1280valid
4.0ms88×body80nan
3.0ms15×body640valid
1.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify81.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
0.2b
(- (* b b) (* (* 4.0 c) a))
0.7b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite174.0ms

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:
82.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
7.0ms
(- (* b b) (* (* 4.0 c) a))
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
68.0ms
(- (* b b) (* (* 4.0 c) a))
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
100.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.5s

Counts
130 → 130
Iterations
IterNodes
done5001
22112
1509
0198

prune838.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
0.2b
(- (* b b) (* (* 4.0 c) a))
0.7b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite162.0ms

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:
71.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
7.0ms
(- (* b b) (* (* 4.0 c) a))
59.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4.0 c) a))) b)))
83.0ms
(- (* b b) (* (* 4.0 c) a))
125.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
113.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.4s

Counts
208 → 208
Iterations
IterNodes
done5001
23970
1761
0303

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 c) a))
0.2b
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))
0.7b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
56×*-un-lft-identity
55×prod-diff
51×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
13×associate-*l* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg prod-exp log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sqrt-div diff-log div-exp associate-*r/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 158
Calls
4 calls:
7.0ms
(- (* b b) (* (* 4.0 c) a))
132.0ms
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))
45.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 c) a))
223.0ms
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4.0 c) a))) b))
140.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
83.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.1s

Counts
170 → 170
Iterations
IterNodes
done5000
23868
1694
0243

prune883.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
0.7b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))
24.4b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite178.0ms

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:
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
72.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
114.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))
96.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify1.6s

Counts
128 → 128
Iterations
IterNodes
done5001
21229
1295
0113

prune986.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.4b

regimes603.0ms

Accuracy

82.9% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 33.9b

bsearch194.0ms

Steps
ItersRangePoint
7
4.7547400806771625e-82
1.9034131584556183e-80
6.088267304256603e-81
9
-6.8759269530282916e+131
-3.539957239594031e+126
-8.213216247196925e+129

simplify8.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s1052×body2560valid
755.0ms898×body1280valid
664.0ms5902×body80valid
202.0ms2839×body80nan
128.0ms451×body640valid
98.0ms239×body320valid
87.0ms111×body5120valid
15.0ms105×body160valid