Details

Time bar (total: 17.9s)

sample73.0ms

Algorithm
intervals
Results
16.0ms41×body2560valid
12.0ms178×body80valid
8.0ms26×body1280valid
5.0ms75×body80nan
4.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify173.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite191.0ms

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:
135.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(- (* b b) (* 4.0 (* a c)))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
56.0ms
(- (* b b) (* 4.0 (* a c)))
115.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.4s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01571750
14021650
213171474
349661459
done50001459

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
3.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.1b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
21.0ms
(- (* b b) (* 4.0 (* a c)))
136.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
94.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series756.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* 4.0 (* a c)))
245.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
313.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
132.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: 2 (617.0ms)

IterNodesCost
02524460
16153954
224613652
done50013652

prune607.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* b b) (- (* (* 4.0 a) c)))
3.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b)) (* 2.0 a))
11.1b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b))
24.6b
(sqrt (+ (* b b) (- (* (* 4.0 a) c))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
8×add-log-exp
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/
5×pow1
4×div-inv
3×flip3-- flip3-+ flip-- flip-+ associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num sum-log cbrt-unprod
1×+-commutative neg-sub0 associate-+r- rem-sqrt-square sqrt-pow1 pow1/2 unsub-neg neg-log
Counts
4 → 141
Calls
4 calls:
18.0ms
(+ (* b b) (- (* (* 4.0 a) c)))
195.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b)) (* 2.0 a))
117.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b))
12.0ms
(sqrt (+ (* b b) (- (* (* 4.0 a) c))))

series1.1s

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (* b b) (- (* (* 4.0 a) c)))
228.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b)) (* 2.0 a))
698.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (+ (* b b) (- (* (* 4.0 a) c)))) b))
107.0ms
(sqrt (+ (* b b) (- (* (* 4.0 a) c))))

simplify1.7s

Counts
153 → 153
Iterations

Useful iterations: 2 (601.0ms)

IterNodesCost
02564673
16343993
225703657
done50003657

prune690.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize29.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (* c (* 4.0 a)))
15.5b
(cbrt (* c (* 4.0 a)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
2×cbrt-prod rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow1/3 flip--
Counts
4 → 48
Calls
4 calls:
21.0ms
(cbrt (* c (* 4.0 a)))
16.0ms
(cbrt (* c (* 4.0 a)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (* c (* 4.0 a)))
128.0ms
(cbrt (* c (* 4.0 a)))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
123.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
60 → 60
Iterations

Useful iterations: done (2.6s)

IterNodesCost
089804
1209734
2585668
31992654
done5000630

prune385.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

regimes345.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.4b against oracle of 5.5b and baseline of 32.8b

bsearch284.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
9.28238754477782e+92
7
-1.9051551317192057e-67
-2.58855871570434e-69
-1.1244234173654837e-68
8
-8.940247115892076e-48
-4.1534417895904633e-51
-2.8768523970510503e-50
6
-1.1735561027771561e+62
-8.164472492702187e+60
-9.913936217078672e+60

simplify21.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04375
15673
26773
done6773

end0.0ms

sample1.9s

Algorithm
intervals
Results
364.0ms1061×body2560valid
346.0ms5877×body80valid
235.0ms852×body1280valid
168.0ms2982×body80nan
106.0ms473×body640valid
51.0ms112×body5120valid
43.0ms243×body320valid
14.0ms123×body160valid