Details

Time bar (total: 8.6s)

sample41.0ms

Algorithm
intervals
Results
10.0ms194×body80valid
9.0ms40×body2560valid
5.0ms28×body1280valid
3.0ms76×body80nan
1.0ms10×body640valid
1.0ms2×body5120valid
0.0ms3×body320valid
0.0ms1×body160valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

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
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify646.0ms

Counts
82 → 82
Iterations

Useful iterations: done (643.0ms)

IterNodesCost
01521565
14041461
213251245
done50001231

prune234.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
0.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
24×*-un-lft-identity associate-*l*
19×times-frac
16×add-cube-cbrt
9×add-exp-log add-cbrt-cube
8×add-log-exp difference-of-squares
7×pow1 sqrt-prod
4×flip3-- flip-- distribute-lft-out--
3×associate-*r*
2×sub-neg sqrt-div diff-log prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 85
Calls
4 calls:
50.0ms
(* (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
49.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01721773
14111667
212431509
339641501
done50011500

prune259.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
0.4b
(- (* b b) (* 4.0 (* a c)))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series242.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify923.0ms

Counts
66 → 66
Iterations

Useful iterations: done (922.0ms)

IterNodesCost
0601010
1146930
2488834
31938834
done5000832

prune241.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series678.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
377.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify740.0ms

Counts
166 → 166
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
02535113
16384541
224634211
done50014209

prune397.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.7b

regimes273.0ms

Accuracy

89.8% (2.9b remaining)

Error of 8.6b against oracle of 5.7b and baseline of 34.2b

bsearch194.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
7.053924884551729e+44
9
5.147670875442886e-182
5.782915581029284e-176
2.2133129180520688e-178
11
-1.829086240692416e+154
-2.187052964502477e+134
-8.555281377770497e+140

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03568
14266
done4266

end0.0ms

sample1.1s

Algorithm
intervals
Results
252.0ms1104×body2560valid
228.0ms5868×body80valid
177.0ms910×body1280valid
113.0ms2861×body80nan
63.0ms422×body640valid
27.0ms96×body5120valid
23.0ms212×body320valid
9.0ms120×body160valid