Details

Time bar (total: 16.3s)

sample75.0ms

Algorithm
intervals
Results
14.0ms187×body80valid
12.0ms29×body2560valid
8.0ms25×body1280valid
8.0ms103×body80nan
4.0ms16×body640valid
2.0msbody5120valid
1.0msbody320valid
1.0msbody160valid

simplify125.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
01417
12417
24416
37816
410216
511116
done11116

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize40.0ms

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)))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
add-exp-log add-cbrt-cube
add-sqr-sqrt
add-cube-cbrt
distribute-lft-out
pow1 times-frac associate-/l*
distribute-rgt-neg-in sqrt-prod
cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
+-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:
94.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
57.0ms
(- (* b b) (* 4.0 (* a c)))
126.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
93.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify960.0ms

Counts
82 → 82
Iterations

Useful iterations: done (958.0ms)

IterNodesCost
01521565
14191461
217251245
done50011239

prune477.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite281.0ms

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
associate-/r* add-log-exp
cbrt-undiv div-exp
associate-/r/
pow1 flip3-- flip--
div-inv
associate-/l/
frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
78.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series779.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
234.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
314.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
115.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts
166 → 166
Iterations

Useful iterations: 2 (623.0ms)

IterNodesCost
02535113
16594543
237234219
done50004219

prune854.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

9.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
9.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×times-frac
add-log-exp
pow1 add-exp-log sqrt-prod add-cbrt-cube
difference-of-squares
flip3-- sqrt-div associate-/r* flip--
associate-/l*
rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 80
Calls
4 calls:
72.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
12.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series630.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
127.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
108.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
92 → 92
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01593048
14101909
221421785
done50011763

prune692.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.2b
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
152×times-frac
121×add-sqr-sqrt
109×*-un-lft-identity
94×add-exp-log
85×associate-*r*
68×add-cube-cbrt
58×add-cbrt-cube
39×div-exp
35×prod-exp
21×cbrt-undiv cbrt-unprod
20×distribute-lft-out-- difference-of-squares
13×sqrt-prod
10×distribute-rgt-neg-in add-log-exp
pow1 associate-*l*
flip3-- associate-/r/ flip--
div-inv
rec-exp 1-exp unswap-sqr
diff-log
sub-neg sqrt-div
associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 185
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
42.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
244.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* 4.0 (* a c)))
133.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
241.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
129.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify635.0ms

Counts
197 → 197
Iterations

Useful iterations: done (623.0ms)

IterNodesCost
03545470
112324974
done50014278

prune683.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes461.0ms

Accuracy

86.7% (3.5b remaining)

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

bsearch376.0ms

Steps
ItersRangePoint
9
5.2308229534737164e+20
4.4914796769937245e+27
3.3627913932282257e+22
10
2.3120063448528447e-114
6.389619675209379e-102
2.3448135958717817e-114
9
-1.6867412280479856e+126
-2.8600599763572115e+119
-1.6733539759872003e+120

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03982
14680
24780
done4780

end0.0ms

sample3.7s

Algorithm
intervals
Results
925.0ms5854×body80valid
834.0ms918×body1280valid
587.0ms1075×body2560valid
336.0ms2889×body80nan
281.0ms457×body640valid
60.0ms110×body5120valid
54.0ms210×body320valid
15.0ms108×body160valid