Details

Time bar (total: 20.3s)

sample169.0ms

Algorithm
intervals
Results
44.0ms195×body80valid
34.0ms19×body640valid
9.0ms34×body1280valid
9.0ms28×body2560valid
5.0ms97×body80nan
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify136.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
010283
115283
223243
330243
432243
534243
done34243

prune87.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 118
Calls
4 calls:
151.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms
(- (* b_2 b_2) (* a c))
132.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
58.0ms
(- (* b_2 b_2) (* a c))
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.1s)

IterNodesCost
019547423
149142559
2142038570
done500738520

prune695.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
19×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 119
Calls
4 calls:
129.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
54.0ms
(- (* b_2 b_2) (* a c))
124.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
131 → 131
Iterations

Useful iterations: done (1.9s)

IterNodesCost
021546759
155740007
2163334683
done500034498

prune746.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.8b
(- (* b_2 b_2) (* a c))
6.5b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
21.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
481×times-frac
378×add-sqr-sqrt
366×*-un-lft-identity
358×add-cube-cbrt
287×prod-diff
143×sqrt-prod
39×div-inv
23×fma-neg
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div log1p-expm1-u flip-- distribute-lft-out--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 411
Calls
4 calls:
26.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
13.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
49.0ms
(- (* b_2 b_2) (* a c))
107.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.6s

Counts
423 → 423
Iterations

Useful iterations: done (4.5s)

IterNodesCost
0499300343
11134269805
22652242573
done5000219209

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* -1/2 (/ c b_2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×expm1-log1p-u cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 34
Calls
1 calls:
21.0ms
(* -1/2 (/ c b_2))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(* -1/2 (/ c b_2))

simplify2.1s

Counts
37 → 37
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
0706080
11725466
25195304
317995304
done50025304

prune143.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.9b

regimes513.0ms

Accuracy

80.3% (5.6b remaining)

Error of 11.4b against oracle of 5.9b and baseline of 34.0b

bsearch154.0ms

Steps
ItersRangePoint
6
0.023031155523784402
0.1909160003853501
0.039411926192954486
9
-5.469119599515074e+54
-1.7131453104127492e+48
-1.918306653269124e+51

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
023723
126723
done26723

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s5864×body80valid
528.0ms1041×body2560valid
364.0ms919×body1280valid
230.0ms2928×body80nan
123.0ms465×body640valid
87.0ms109×body5120valid
38.0ms207×body320valid
14.0ms118×body160valid