Details

Time bar (total: 17.8s)

sample219.0ms

Algorithm
intervals
Results
73.0ms205×body80valid
16.0ms31×body2560valid
12.0ms31×body1280valid
7.0ms89×body80nan
4.0ms12×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify48.0ms

Counts
1 → 1
Iterations
IterNodes
done44
444
341
232
118
010

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize74.0ms

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)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- 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 → 91
Calls
4 calls:
14.0ms
(- (* b_2 b_2) (* a c))
120.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b_2 b_2) (* a c))
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
97.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
103 → 103
Iterations
IterNodes
done5000
21530
1393
0158

prune557.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize24.0ms

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)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in 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 → 89
Calls
4 calls:
6.0ms
(- (* b_2 b_2) (* a c))
129.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b_2 b_2) (* a c))
146.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
127.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts
101 → 101
Iterations
IterNodes
done5000
22879
1462
0177

prune582.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize37.0ms

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)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- 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 → 91
Calls
4 calls:
6.0ms
(- (* b_2 b_2) (* a c))
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b_2 b_2) (* a c))
147.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
122.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
103 → 103
Iterations
IterNodes
done5000
21530
1393
0158

prune503.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* a c)) a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.5b
(/ (+ 0 (* a c)) a)
19.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
129×*-un-lft-identity
128×times-frac
70×add-sqr-sqrt
69×add-cube-cbrt
30×distribute-lft-out
16×associate-/l*
15×distribute-rgt-neg-in
11×add-cbrt-cube add-exp-log
8×associate-/r* div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×flip3-+ sqrt-prod flip-+ associate-/l/
2×clear-num sum-log frac-2neg sqrt-div associate-/r/
1×neg-sub0 +-commutative rem-sqrt-square sqrt-pow1 flip3-- pow1/2 neg-log associate-+l- flip--
Counts
4 → 159
Calls
4 calls:
72.0ms
(/ (/ (+ 0 (* a c)) a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
29.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(/ (+ 0 (* a c)) a)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(/ (/ (+ 0 (* a c)) a) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
109.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(/ (+ 0 (* a c)) a)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
171 → 171
Iterations
IterNodes
done5002
23456
1648
0252

prune942.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

regimes506.0ms

Accuracy

97.3% (0.8b remaining)

Error of 5.9b against oracle of 5.2b and baseline of 34.1b

bsearch189.0ms

Steps
ItersRangePoint
8
2.072994944964499e+129
8.571507078369983e+131
3.873872856767695e+129
8
-4.7565405277843116e-290
-8.04405113032372e-293
-8.315573719317122e-293
7
-5.856362438573669e+138
-1.280729871585891e+137
-2.3037792410978802e+138

simplify29.0ms

Iterations
IterNodes
done31
131
027

end0.0ms

sample2.8s

Algorithm
intervals
Results
845.0ms1029×body2560valid
421.0ms922×body1280valid
412.0ms5835×body80valid
235.0ms2877×body80nan
141.0ms455×body640valid
104.0ms122×body5120valid
93.0ms242×body320valid
15.0ms123×body160valid