Details

Time bar (total: 17.3s)

sample102.0ms

Algorithm
intervals
Results
23.0ms41×body2560valid
17.0ms178×body80valid
14.0ms29×body1280valid
9.0ms93×body80nan
6.0ms17×body640valid
1.0ms5×body160valid
1.0ms1×body5120valid
1.0ms2×body320valid

simplify108.0ms

Counts
1 → 1
Iterations
IterNodes
done96
796
695
593
485
370
242
124
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
111.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a) 2.0)
97.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
60.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
161 → 161
Iterations
IterNodes
done5038
21964
1669
0279

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
62×add-sqr-sqrt
46×*-un-lft-identity
43×associate-*r*
41×add-cube-cbrt
19×add-exp-log
13×add-cbrt-cube
8×add-log-exp
7×pow1
6×div-exp associate-*l*
5×flip3-- prod-exp sqrt-prod flip--
4×div-inv difference-of-squares unswap-sqr
3×cbrt-undiv cbrt-unprod
2×frac-times sub-neg sqrt-div diff-log associate-*l/ distribute-lft-out--
1×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 117
Calls
4 calls:
166.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
58.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ (/ 1 a) 2.0))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
129 → 129
Iterations
IterNodes
done5002
22295
1716
0265

prune888.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 a) (sqrt 2.0))
1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
87×add-sqr-sqrt
84×*-un-lft-identity
82×add-cube-cbrt
46×sqrt-prod
13×add-exp-log associate-/l*
9×add-cbrt-cube
8×div-inv add-log-exp
6×associate-/r* div-exp
5×pow1
3×cbrt-undiv flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp distribute-lft-out-- associate-/l/
Counts
4 → 156
Calls
4 calls:
20.0ms
(/ (/ 1 a) (sqrt 2.0))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (/ 1 a) (sqrt 2.0))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
168 → 168
Iterations
IterNodes
done5000
21427
1611
0273

prune938.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt (sqrt 2.0)))
1.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
29×*-un-lft-identity
27×times-frac add-cube-cbrt
9×associate-/r*
8×pow1 add-exp-log add-log-exp
6×add-cbrt-cube
5×sqrt-pow1 pow-flip
3×flip3-- pow1/2 flip-- associate-/l*
2×sub-neg sqrt-div diff-log div-exp difference-of-squares
1×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp div-inv distribute-lft-out-- inv-pow
Counts
4 → 101
Calls
4 calls:
9.0ms
(/ 1 (sqrt (sqrt 2.0)))
56.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
114.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
58.0ms
(- (* b b) (* (* 4.0 a) c))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
111 → 111
Iterations
IterNodes
done5001
33271
2985
1367
0178

prune604.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.1b

regimes362.0ms

Accuracy

85.5% (4.2b remaining)

Error of 10.1b against oracle of 5.9b and baseline of 34.9b

bsearch244.0ms

Steps
ItersRangePoint
10
8.767897341253802e-114
4.657027509742155e-104
4.6129908231112306e-104
9
-6.117539429929052e+154
-3.6285784997486435e+148
-3.6803290429888884e+148

simplify7.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s2954×body80nan
617.0ms1115×body2560valid
601.0ms5809×body80valid
372.0ms902×body1280valid
205.0ms454×body640valid
117.0ms210×body320valid
56.0ms105×body5120valid
18.0ms126×body160valid