Details

Time bar (total: 16.3s)

sample73.0ms

Algorithm
intervals
Results
14.0ms197×body80valid
12.0ms28×body2560valid
11.0ms31×body1280valid
5.0ms77×body80nan
3.0ms11×body640valid
1.0ms7×body320valid
1.0ms5×body160valid

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
177.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
54.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(- (* b b) (* (* 4.0 a) c))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
117.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
77.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
118 → 118
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01952476
14802169
214411861
done50001789

prune433.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
70.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
97.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series619.0ms

Counts
4 → 12
Calls
4 calls:
297.0ms
(/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
128.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
117 → 117
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01862435
14402126
213331820
done50001750

prune377.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

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:
20.0ms
(* (* 4.0 a) c)
50.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
8.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 4.0 a) c)
99.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
55.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts
106 → 106
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01611863
13671562
211281333
345011245
done50001245

prune356.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
78 → 78
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0711146
11681050
2574952
32407952
done5000936

prune414.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.1b

regimes417.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 34.5b

bsearch94.0ms

Steps
ItersRangePoint
5
8.424566153134112e-50
2.125375155764958e-49
9.146553797812777e-50
5
-1.9941030622962047e+109
-5.928196142097795e+108
-1.8572382657132166e+109

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02840
13540
done3540

end0.0ms

sample2.0s

Algorithm
intervals
Results
390.0ms1069×body2560valid
352.0ms5791×body80valid
273.0ms933×body1280valid
174.0ms2974×body80nan
99.0ms442×body640valid
55.0ms122×body5120valid
41.0ms244×body320valid
14.0ms126×body160valid