Details

Time bar (total: 14.1s)

sample53.0ms

Algorithm
intervals
Results
10.0ms196×body80valid
7.0ms31×body1280valid
7.0ms27×body2560valid
4.0ms92×body80nan
3.0ms16×body640valid
2.0ms5×body5120valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify136.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
76.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
92.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
56.0ms
(- (* b b) (* (* 3.0 a) c))
87.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
102 → 102
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01671697
14471590
220721363
done50001354

prune404.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.9b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
60.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
9.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 3.0 a) c)
106.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
52.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
106 → 106
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01611863
14131576
220891334
done50021267

prune315.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
0.9b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*r*
19×prod-diff sqrt-prod
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 fma-neg
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×sub-neg rec-exp sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 141
Calls
4 calls:
150.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
62.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
10.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
120.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
68.0ms
(- (* b b) (* (* 3.0 a) c))
92.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts
153 → 153
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02613336
17432946
242122502
done50002500

prune453.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.6b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (* b b) (* (* 3.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
14.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(- (* b b) (* (* 3.0 a) c))
119.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
115.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify697.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (133.0ms)

IterNodesCost
0711146
11851058
2843952
done5000952

prune339.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

regimes349.0ms

Accuracy

88.4% (3.3b remaining)

Error of 9.1b against oracle of 5.8b and baseline of 34.5b

bsearch235.0ms

Steps
ItersRangePoint
8
6412590.878131424
2116652649.122401
1213697253.0435753
8
8.5266395239053e-176
1.2801778449178496e-172
6.210794185865198e-173
8
-1.5489453231745737e+155
-2.021963087226922e+151
-2.2976245343188767e+152

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03971
14669
done4669

end0.0ms

sample2.8s

Algorithm
intervals
Results
857.0ms5752×body80valid
519.0ms1069×body2560valid
338.0ms918×body1280valid
248.0ms2909×body80nan
143.0ms489×body640valid
68.0ms243×body320valid
47.0ms109×body5120valid
11.0ms93×body160valid