Details

Time bar (total: 15.5s)

sample108.0ms

Algorithm
intervals
Results
20.0ms192×body80valid
17.0ms27×body2560valid
12.0ms23×body1280valid
11.0ms105×body80nan
5.0ms16×body320valid
5.0ms12×body640valid
2.0ms3×body5120valid
1.0ms4×body160valid

simplify181.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize41.0ms

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)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite131.0ms

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:
68.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
35.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
71.0ms
(- (* b b) (* 4.0 (* a c)))
123.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
89 → 89
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01571750
14181650
216441474
done50001466

prune586.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize51.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×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 → 141
Calls
4 calls:
59.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
122.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
118.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
250.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
298.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
120.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
153 → 153
Iterations

Useful iterations: 2 (700.0ms)

IterNodesCost
02504579
16494063
236203761
done50013761

prune740.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize37.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.3b
(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
9.7b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
137×times-frac
122×add-exp-log
78×add-sqr-sqrt
63×div-exp
59×*-un-lft-identity
58×add-cbrt-cube
41×add-cube-cbrt associate-/l*
34×prod-exp
27×cbrt-undiv
18×difference-of-squares
14×cbrt-unprod
12×sqrt-prod
10×div-inv
9×distribute-lft-out--
8×rec-exp 1-exp
6×add-log-exp
5×pow1
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div clear-num associate-/r* associate-/r/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 180
Calls
4 calls:
69.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
143.0ms
(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
110.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
154.0ms
(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
193.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify621.0ms

Counts
192 → 192
Iterations

Useful iterations: done (610.0ms)

IterNodesCost
03805645
111135265
done50004578

prune789.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
78.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms
(- (* b b) (* 4.0 (* a c)))
28.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
87.0ms
(- (* b b) (* 4.0 (* a c)))
100.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
137 → 137
Iterations

Useful iterations: 2 (391.0ms)

IterNodesCost
02263421
15883066
225932852
done50012852

prune547.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes386.0ms

Accuracy

86.6% (3.6b remaining)

Error of 8.8b against oracle of 5.2b and baseline of 32.0b

bsearch297.0ms

Steps
ItersRangePoint
9
9.357224410271438e+98
8.450543925883448e+104
5.4751892066510406e+101
8
-8.192702314535924e-168
-6.224077830324573e-171
-8.106344882435715e-168
3
-1.713609749393423e-29
-1.2239049760790121e-29
-1.6806111715441095e-29

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03669
14369
done4369

end0.0ms

sample3.5s

Algorithm
intervals
Results
845.0ms2885×body80nan
673.0ms1054×body2560valid
621.0ms5897×body80valid
370.0ms855×body1280valid
188.0ms477×body640valid
111.0ms112×body5120valid
49.0ms219×body320valid
21.0ms115×body160valid