Details

Time bar (total: 8.9s)

sample42.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
7.0ms183×body80valid
5.0ms84×body80nan
4.0ms24×body1280valid
2.0ms14×body640valid
1.0ms13×body320valid
1.0ms3×body5120valid
0.0ms1×body160valid

simplify73.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26317
311417
413117
513717
614017
done14017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
32.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify431.0ms

Counts
89 → 89
Iterations

Useful iterations: done (429.0ms)

IterNodesCost
01571750
14121650
213981474
done50001465

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
16×sqrt-prod
13×distribute-rgt-neg-in
10×add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
3×cbrt-undiv flip3-- diff-log div-exp associate-/r* flip--
2×sub-neg sqrt-div div-sub
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 164
Calls
4 calls:
39.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
48.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify746.0ms

Counts
176 → 176
Iterations

Useful iterations: done (740.0ms)

IterNodesCost
02834621
16904441
225484265
done50004264

prune407.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
3701×times-frac
1907×add-sqr-sqrt
1906×*-un-lft-identity
1398×add-cube-cbrt
254×distribute-lft-out-- difference-of-squares
138×div-inv
130×sqrt-prod
127×distribute-rgt-neg-in
80×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
10×add-log-exp
6×rec-exp
5×pow1
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 1217
Calls
4 calls:
57.0ms
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
47.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
1229 → 1229
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0148954153
1447845496
done500043162

prune619.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*l*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ div-exp cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 92
Calls
4 calls:
49.0ms
(* (/ 1 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (/ 1 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify626.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
01722042
14491847
216081635
done50001635

prune250.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes172.0ms

Accuracy

82.4% (5.0b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 33.6b

bsearch70.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
1.3316184968738608e+61
2
-4.223797038045246e-104
-3.7861133082378615e-104
-4.1690865718193236e-104

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02737
13137
done3137

end0.0ms

sample1.1s

Algorithm
intervals
Results
248.0ms1069×body2560valid
233.0ms5865×body80valid
161.0ms828×body1280valid
111.0ms2882×body80nan
70.0ms477×body640valid
32.0ms110×body5120valid
27.0ms248×body320valid
8.0ms113×body160valid