Details

Time bar (total: 5.5s)

sample39.0ms

Algorithm
intervals
Results
7.0ms197×body80valid
6.0ms28×body2560valid
5.0ms31×body1280valid
3.0ms77×body80nan
2.0ms11×body640valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

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:
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
23.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0403779
11514685
25002674
done5002674

prune230.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
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 → 148
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
82.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Counts
160 → 160
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06282579
129542333
250012320
done50012320

prune393.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.8b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
11.7b
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
256×add-sqr-sqrt
255×*-un-lft-identity
159×add-cube-cbrt
154×add-exp-log
117×associate-/l*
94×div-exp
72×add-cbrt-cube
48×distribute-lft-out-- difference-of-squares
40×cbrt-undiv
30×prod-exp
27×sqrt-prod
24×distribute-rgt-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp 1-exp
6×add-log-exp
5×pow1
2×flip3-- frac-2neg sqrt-div div-sub clear-num associate-/r* associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 338
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
99.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
68.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* a c)))
131.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))) (* 2.0 a))
112.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 4.0) (* a c))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify84.0ms

Counts
350 → 350
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
017286034
150025412
done50025412

prune746.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
14.5b
(/ (* a c) a)
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×flip3-- times-frac diff-log associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 66
Calls
4 calls:
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(/ (* a c) a)
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series215.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(/ (* a c) a)
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0319529
11417484
25001463
done5001463

prune202.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.7b

regimes220.0ms

Accuracy

96.2% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.6b

bsearch174.0ms

Steps
ItersRangePoint
8
1.4961070689597945e+139
4.5158951869773294e+141
1.668280145404844e+139
9
4.3776406734974095e-271
1.1159862536287976e-265
5.433188992089221e-271
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-8.889080831912834e+153

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04426
14426
done4426

end0.0ms

sample1.2s

Algorithm
intervals
Results
235.0ms1069×body2560valid
212.0ms5791×body80valid
173.0ms933×body1280valid
105.0ms2974×body80nan
70.0ms442×body640valid
35.0ms122×body5120valid
25.0ms244×body320valid
9.0ms126×body160valid