Details

Time bar (total: 8.6s)

sample40.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
7.0ms183×body80valid
4.0ms24×body1280valid
3.0ms84×body80nan
2.0ms14×body640valid
1.0ms13×body320valid
1.0ms3×body5120valid
0.0ms1×body160valid

simplify85.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312017
414417
515017
615317
done15317

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×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 → 157
Calls
4 calls:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify738.0ms

Counts
169 → 169
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
02436690
16074755
219903760
done50003759

prune355.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
41.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
6.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
43.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify773.0ms

Counts
183 → 183
Iterations

Useful iterations: done (762.0ms)

IterNodesCost
02467041
15845094
218384140
done50004139

prune375.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
165×times-frac
118×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 257
Calls
4 calls:
30.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
269 → 269
Iterations

Useful iterations: 2 (298.0ms)

IterNodesCost
03539970
18097637
228166393
done50006393

prune614.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
56.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
177 → 177
Iterations

Useful iterations: done (998.0ms)

IterNodesCost
02696947
16774904
224533851
done50013850

prune333.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.3b

regimes184.0ms

Accuracy

82.5% (4.9b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 33.7b

bsearch65.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
1.3316184968738608e+61
2
-4.223797038045246e-104
-3.7861133082378615e-104
-4.1690865718193236e-104

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03043
13843
done3843

end0.0ms

sample1.1s

Algorithm
intervals
Results
243.0ms1069×body2560valid
223.0ms5865×body80valid
153.0ms828×body1280valid
103.0ms2882×body80nan
73.0ms477×body640valid
30.0ms110×body5120valid
29.0ms248×body320valid
8.0ms113×body160valid