Details

Time bar (total: 17.5s)

sample61.0ms

Algorithm
intervals
Results
23.0ms285×body80valid
8.0ms106×body80nan

simplify178.0ms

Counts
1 → 1
Iterations
IterNodes
done176
6176
5174
4161
3122
266
136
020

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize169.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2 distribute-lft-out
1×neg-sub0 +-commutative neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log associate-+l- flip-+
Counts
4 → 77
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* (* 4.0 a) c))
116.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
89 → 89
Iterations
IterNodes
done5000
21331
1278
0104

prune828.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.2b

localize154.0ms

Local error

Found 4 expressions with local error:

8.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
25.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series824.0ms

Counts
4 → 12
Calls
4 calls:
496.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
100 → 100
Iterations
IterNodes
done5001
21219
1293
0115

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.9b

localize239.0ms

Local error

Found 4 expressions with local error:

9.6b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
8×add-log-exp
6×cbrt-prod
5×pow1
4×expm1-log1p-u cbrt-div add-cbrt-cube add-exp-log log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-- sqrt-prod flip--
2×sum-log pow1/3 sqrt-div
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ pow1/2 neg-log associate-+l- flip-+
Counts
4 → 72
Calls
4 calls:
16.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
84 → 84
Iterations
IterNodes
done5000
21706
1402
0152

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.9b

localize177.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u flip-- add-log-exp
Counts
4 → 68
Calls
4 calls:
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
80 → 80
Iterations
IterNodes
done5000
33708
2585
1147
054

prune783.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.9b

regimes475.0ms

Accuracy

94.1% (0.8b remaining)

Error of 7.6b against oracle of 6.8b and baseline of 20.1b

bsearch266.0ms

Steps
ItersRangePoint
8
1.0335802065380817e+152
4.346839969020365e+154
1.042426094136288e+152
9
-2.466971418500489e+156
-4.2382065616346e+150
-3.0962139685642337e+153

simplify15.0ms

Iterations
IterNodes
done49
149
043

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s8718×body80valid
747.0ms2875×body80nan