Details

Time bar (total: 5.3s)

sample336.0ms

Algorithm
intervals
Results
7.0ms41×body2560valid
7.0ms178×body80valid
4.0ms26×body1280valid
2.0ms75×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1337
2467
3497
4497
done497

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

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:
79.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05493055
118262150
250022063
done50022063

prune341.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

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:
47.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms
(- (* b_2 b_2) (* a c))
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Counts
269 → 269
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07704550
132153424
250023236
done50023236

prune360.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
5.5b
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
21.9b
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
91×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
68×add-cube-cbrt log-prod exp-sum
37×sqrt-prod
31×distribute-rgt-neg-in
30×distribute-lft-neg-in
11×fma-neg
10×neg-mul-1 add-log-exp
7×pow1
6×exp-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log log-pow difference-of-squares
2×sub-neg log-div sqrt-pow1 pow1/2 exp-diff distribute-lft-out--
1×associate--l- neg-sub0 rem-sqrt-square neg-log rem-exp-log
Counts
4 → 178
Calls
4 calls:
10.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
36.0ms
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
74.0ms
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Counts
190 → 190
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05354477
114732268
250022146
done50022146

prune299.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
3.2b
(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
10.9b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
30×associate-/r*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log associate-/r/ add-cbrt-cube
7×flip3-- flip--
6×div-inv associate-/l* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×frac-2neg sqrt-div clear-num associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 194
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
59.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
78.0ms
(/ a (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
194.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify123.0ms

Counts
206 → 206
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
07192966
136232772
250012767
done50012767

prune504.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

regimes205.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.9b

bsearch128.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
5.416822515930612e+93
8
-1.4649997057013753e-301
-1.9636081948043714e-305
-1.992191814191663e-305
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-6.5409487627245864e+153

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03821
13821
done3821

end0.0ms

sample1.0s

Algorithm
intervals
Results
192.0ms1061×body2560valid
185.0ms5876×body80valid
119.0ms854×body1280valid
82.0ms2976×body80nan
54.0ms471×body640valid
25.0ms113×body5120valid
20.0ms242×body320valid
7.0ms125×body160valid