Details

Time bar (total: 17.2s)

sample88.0ms

Algorithm
intervals
Results
17.0ms35×body2560valid
15.0ms179×body80valid
11.0ms30×body1280valid
7.0ms76×body80nan
5.0ms8×body5120valid
3.0ms9×body640valid
2.0ms10×body320valid
0.0ms2×body160valid

simplify130.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*l* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 76
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
131.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series402.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* 4.0 (* a c))
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
111.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01691499
14461389
214601181
done50001169

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.9b
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite304.0ms

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:
47.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
135.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
98.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
218.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
284.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
134.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
166 → 166
Iterations

Useful iterations: 2 (608.0ms)

IterNodesCost
02565113
16354571
223534211
done50014211

prune609.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 1) (* (/ (* 2.0 a) (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.3b
(/ (* 2.0 a) (* a (* 4.0 c)))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
283×add-exp-log
136×div-exp
121×prod-exp
109×add-cbrt-cube
42×cbrt-undiv
41×cbrt-unprod
40×1-exp
32×times-frac
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
16×rec-exp
14×associate-/l*
8×add-log-exp
5×pow1 associate-/r/
4×flip3-- sqrt-prod flip-- div-inv
2×frac-times frac-2neg sqrt-div diff-log associate-*r/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log associate-*l/ associate-/l/
Counts
4 → 173
Calls
4 calls:
139.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
41.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(/ (* 2.0 a) (* a (* 4.0 c)))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series484.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (/ 1 1) (* (/ (* 2.0 a) (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
94.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(/ (* 2.0 a) (* a (* 4.0 c)))
138.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
185 → 185
Iterations

Useful iterations: 2 (754.0ms)

IterNodesCost
03405571
18354818
231873505
done50013505

prune316.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 2.0) (/ (* 4.0 c) 1))
0.3b
(/ (* (/ 1 2.0) (/ (* 4.0 c) 1)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
148×add-exp-log
73×div-exp
56×prod-exp
54×add-cbrt-cube
36×add-sqr-sqrt
29×*-un-lft-identity
26×1-exp
21×cbrt-undiv times-frac
16×add-cube-cbrt cbrt-unprod
13×associate-*l*
10×rec-exp
8×add-log-exp
7×pow1 associate-*r* associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
3×flip3-- distribute-rgt-neg-in flip-- div-inv associate-/l/ unswap-sqr
2×frac-times sqrt-div diff-log associate-*r/ associate-*l/ associate-/r/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num *-commutative associate-/l*
Counts
4 → 152
Calls
4 calls:
39.0ms
(* (/ 1 2.0) (/ (* 4.0 c) 1))
87.0ms
(/ (* (/ 1 2.0) (/ (* 4.0 c) 1)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (/ 1 2.0) (/ (* 4.0 c) 1))
283.0ms
(/ (* (/ 1 2.0) (/ (* 4.0 c) 1)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
103.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
164 → 164
Iterations

Useful iterations: 2 (543.0ms)

IterNodesCost
02673419
16452705
224372227
done50002227

prune384.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

regimes187.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.8b

bsearch291.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
6.326287366549383e+74
9
-7.006116511457938e-281
-2.476656944921405e-289
-3.3203606567416007e-289
6
-3.779251410483496e+105
-5.080294099506613e+104
-1.361733299857302e+105

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03760
14660
done4660

end0.0ms

sample3.7s

Algorithm
intervals
Results
999.0ms5866×body80valid
778.0ms906×body1280valid
722.0ms1023×body2560valid
299.0ms2914×body80nan
173.0ms442×body640valid
79.0ms127×body5120valid
54.0ms244×body320valid
16.0ms109×body160valid