Details

Time bar (total: 17.2s)

sample84.0ms

Algorithm
intervals
Results
14.0ms38×body2560valid
11.0ms178×body80valid
7.0ms24×body1280valid
6.0ms104×body80nan
4.0ms16×body640valid
2.0ms5×body5120valid
1.0ms7×body320valid
1.0ms6×body160valid

simplify101.0ms

Counts
1 → 1
Iterations
IterNodes
done94
794
693
591
483
368
239
121
012

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.4b
(- (* b b) (* (* 3.0 a) c))
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
82.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
6.0ms
(- (* b b) (* (* 3.0 a) c))
58.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
81.0ms
(- (* b b) (* (* 3.0 a) c))
100.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
84 → 84
Iterations
IterNodes
done5001
21254
1392
0154

prune632.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.4b
(- (* b b) (* (* 3.0 a) c))
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
99.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
12.0ms
(- (* b b) (* (* 3.0 a) c))
72.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
69.0ms
(- (* b b) (* (* 3.0 a) c))
126.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
124.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts
161 → 161
Iterations
IterNodes
done5004
22080
1667
0281

prune1000.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
0.4b
(- (* b b) (* (* 3.0 a) c))
1.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
26×add-exp-log
22×associate-*r* add-cube-cbrt
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×flip3-- flip--
2×rec-exp sub-neg sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 107
Calls
4 calls:
129.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
9.0ms
(- (* b b) (* (* 3.0 a) c))
40.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
65.0ms
(- (* b b) (* (* 3.0 a) c))
145.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
119 → 119
Iterations
IterNodes
done5001
22026
1610
0220

prune754.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
0.4b
(- (* b b) (* 3.0 (* a c)))
1.5b
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.4b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
15.0ms
(* 3.0 (* a c))
6.0ms
(- (* b b) (* 3.0 (* a c)))
49.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
7.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 3.0 (* a c))
71.0ms
(- (* b b) (* 3.0 (* a c)))
105.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
119.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.2s

Counts
72 → 72
Iterations
IterNodes
done5001
32927
2802
1276
0117

prune423.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.2b

regimes938.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.1b

bsearch234.0ms

Steps
ItersRangePoint
10
2.044647849876085e-45
1.359053137570048e-33
6.407662420749315e-35
10
-8.897020078895062e+156
-1.101416214509623e+146
-1.0061247252330729e+153

simplify6.0ms

Iterations
IterNodes
done37
137
029

end0.0ms

sample3.0s

Algorithm
intervals
Results
947.0ms1026×body2560valid
533.0ms5811×body80valid
406.0ms885×body1280valid
342.0ms2885×body80nan
137.0ms506×body640valid
108.0ms118×body5120valid
43.0ms216×body320valid
16.0ms121×body160valid