Details

Time bar (total: 21.3s)

sample80.0ms

Algorithm
intervals
Results
32.0ms205×body80valid
9.0ms31×body2560valid
8.0ms31×body1280valid
4.0ms89×body80nan
2.0ms12×body640valid
1.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010283
119283
233283
346283
449283
done49283

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite211.0ms

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-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 171
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
119.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b_2 b_2) (* a c))
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
93.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts
183 → 183
Iterations

Useful iterations: done (2.5s)

IterNodesCost
024492638
158482243
2215874304
done500062879

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×associate-*r* add-exp-log
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg sqrt-div div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 169
Calls
4 calls:
14.0ms
(- (* b_2 b_2) (* a c))
130.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* b_2 b_2) (* a c))
108.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
77.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.1s

Counts
181 → 181
Iterations

Useful iterations: done (4.1s)

IterNodesCost
026390561
165377918
2375068788
done500068663

prune714.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite136.0ms

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-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 171
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
86.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
104.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
183 → 183
Iterations

Useful iterations: done (2.3s)

IterNodesCost
024492638
158482243
2215874304
done500062879

prune745.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
5.3b
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
19.5b
(sqrt (- (* b_2 b_2) (* a c)))
20.8b
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
90×prod-diff
85×*-un-lft-identity
76×add-cube-cbrt
70×log-prod exp-sum
38×sqrt-prod
32×distribute-rgt-neg-in
30×distribute-lft-neg-in
13×associate-*r* add-exp-log
11×times-frac
10×neg-mul-1 fma-neg
9×pow1 add-cbrt-cube
8×associate-*l* add-log-exp
6×exp-prod difference-of-squares
5×flip3-- flip--
4×expm1-log1p-u sqrt-div prod-exp log1p-expm1-u distribute-lft-out--
3×log-pow unswap-sqr
2×frac-times log-div sqrt-pow1 pow1/2 exp-diff diff-log div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sub-neg 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv rem-exp-log
Counts
4 → 209
Calls
4 calls:
96.0ms
(* (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
10.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
36.0ms
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

series403.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) (/ 1 a))
94.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))
95.0ms
(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))

simplify3.5s

Counts
221 → 221
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0327170140
1774104694
2374491208
done500189138

prune933.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes501.0ms

Accuracy

85.7% (4.1b remaining)

Error of 9.3b against oracle of 5.2b and baseline of 34.1b

bsearch133.0ms

Steps
ItersRangePoint
8
2.072994944964499e+129
8.571507078369983e+131
3.087668654677018e+130
8
-8.904680992578465e-52
-2.849527055171251e-56
-4.356959927988237e-56

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
024763
127763
done27763

end0.0ms

sample2.2s

Algorithm
intervals
Results
503.0ms5835×body80valid
409.0ms455×body640valid
392.0ms1029×body2560valid
263.0ms922×body1280valid
171.0ms2877×body80nan
48.0ms122×body5120valid
45.0ms123×body160valid
35.0ms242×body320valid