Details

Time bar (total: 18.9s)

sample75.0ms

Algorithm
intervals
Results
41.0ms276×body80valid
8.0ms80×body80nan

simplify193.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
020616
136616
266616
3122616
4161616
5174616
6176616
done176616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize168.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 151
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
163 → 163
Iterations

Useful iterations: done (2.4s)

IterNodesCost
017985356
144174970
2181766601
done500153231

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize181.0ms

Local error

Found 4 expressions with local error:

12.5b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 76
Calls
4 calls:
14.0ms
(+ (- 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)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
09026587
126022220
2110621540
done500021275

prune816.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize199.0ms

Local error

Found 4 expressions with local error:

21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
80 → 80
Iterations

Useful iterations: done (2.9s)

IterNodesCost
05424556
114721664
258521504
3370821504
done500021404

prune885.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize282.0ms

Local error

Found 4 expressions with local error:

21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
85.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
80 → 80
Iterations

Useful iterations: done (2.7s)

IterNodesCost
05424556
114721664
258521504
3370821504
done500021404

prune882.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

regimes312.0ms

Accuracy

93.1% (0.9b remaining)

Error of 8.2b against oracle of 7.3b and baseline of 19.8b

bsearch170.0ms

Steps
ItersRangePoint
7
3.193559613742934e+82
9.45571118856315e+83
8.991400549328154e+83
3
-1.280729871585891e+137
-9.51166686841298e+136
-1.177741376353206e+137

simplify12.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0391424
1471424
done471424

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8708×body80valid
345.0ms2874×body80nan