Details

Time bar (total: 8.3s)

sample42.0ms

Algorithm
intervals
Results
9.0ms40×body2560valid
8.0ms187×body80valid
4.0ms23×body1280valid
3.0ms86×body80nan
2.0ms16×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37916
49216
510016
done10016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite71.0ms

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-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
36.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
48.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify735.0ms

Counts
161 → 161
Iterations

Useful iterations: done (729.0ms)

IterNodesCost
02784083
16683911
224453753
done50003752

prune448.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
0.8b
(- (pow b 2) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite133.0ms

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-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
71.0ms
(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
7.0ms
(- (pow b 2) (* 4.0 (* a c)))
40.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
8.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0) a)
43.0ms
(- (pow b 2) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify703.0ms

Counts
161 → 161
Iterations

Useful iterations: done (698.0ms)

IterNodesCost
02774083
16633903
223993757
done50013756

prune600.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
0.8b
(- (pow b 2) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite184.0ms

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 associate-*r/ pow-prod-down *-commutative
Counts
4 → 117
Calls
4 calls:
125.0ms
(* (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
9.0ms
(- (pow b 2) (* 4.0 (* a c)))
38.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
7.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) (/ (/ 1 2.0) a))
47.0ms
(- (pow b 2) (* 4.0 (* a c)))
77.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
69.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.1s

Counts
129 → 129
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02622757
17022478
226992214
done50002205

prune335.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0)))
0.8b
(- (pow b 2) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
438×add-sqr-sqrt
363×*-un-lft-identity
289×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
40×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
6×pow1 cbrt-undiv
5×associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 354
Calls
4 calls:
51.0ms
(/ 1 (/ a (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0)))
7.0ms
(- (pow b 2) (* 4.0 (* a c)))
39.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
7.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ 1 (/ a (/ (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b) 2.0)))
42.0ms
(- (pow b 2) (* 4.0 (* a c)))
76.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
71.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify532.0ms

Counts
366 → 366
Iterations

Useful iterations: done (518.0ms)

IterNodesCost
056811964
1135210911
done500010211

prune522.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes182.0ms

Accuracy

83.5% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch93.0ms

Steps
ItersRangePoint
8
1.3679096689958957e-81
5.608239720335765e-77
3.84613441880261e-81
7
-3.550313394724354e+57
-2.3888623512096697e+55
-3.124283374205192e+57

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02738
13138
done3138

end0.0ms

sample1.2s

Algorithm
intervals
Results
251.0ms1074×body2560valid
228.0ms5844×body80valid
172.0ms907×body1280valid
108.0ms2890×body80nan
66.0ms452×body640valid
28.0ms102×body5120valid
25.0ms234×body320valid
9.0ms119×body160valid