Details

Time bar (total: 16.7s)

sample90.0ms

Algorithm
intervals
Results
31.0ms273×body80valid
11.0ms103×body80nan

simplify142.0ms

Counts
1 → 1
Iterations
IterNodes
done193
6193
5189
4179
3143
279
139
020

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize125.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
2.0b
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
22.7b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
22.7b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 161
Calls
4 calls:
19.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
38.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
2.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
120.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
125.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
137.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify2.3s

Counts
173 → 173
Iterations
IterNodes
done5000
21758
1430
0194

prune786.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize124.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
1.3b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
22.7b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff sqrt-prod
8×add-cbrt-cube add-exp-log
6×associate-/r* times-frac fma-neg difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u log1p-expm1-u distribute-lft-out--
2×cbrt-undiv flip3-- div-exp associate-/r/ flip--
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv associate-/l*
Counts
3 → 87
Calls
3 calls:
24.0ms
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
10.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
2.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series634.0ms

Counts
3 → 9
Calls
3 calls:
366.0ms
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
149.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
119.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify876.0ms

Counts
96 → 96
Iterations
IterNodes
done5001
21365
1346
0146

prune1000.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.1b

localize136.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b))
0.2b
(* (* 2.0 c) (/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b)))
1.3b
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
22.7b
(sqrt (fma (- c) (* a 4.0) (* b b)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
56×*-un-lft-identity
40×add-cube-cbrt
36×times-frac
30×add-exp-log
24×associate-*r*
23×sqrt-prod
18×add-cbrt-cube prod-diff
16×difference-of-squares
12×prod-exp
11×pow1
8×distribute-lft-out--
6×associate-/r* fma-neg div-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×cbrt-undiv rec-exp flip3-- 1-exp pow-prod-down flip-- associate-/l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 154
Calls
4 calls:
14.0ms
(/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b))
47.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b)))
9.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
1.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))

series819.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b))
308.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (fma (- c) (* a 4.0) (* b b))) b)))
119.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
115.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))

simplify1.6s

Counts
166 → 166
Iterations
IterNodes
done5001
22808
1563
0214

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.1b

localize159.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
1.3b
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
22.7b
(sqrt (fma (- c) (* a 4.0) (* b b)))
22.7b
(sqrt (fma (- c) (* a 4.0) (* b b)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 112
Calls
4 calls:
25.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
17.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
2.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))
3.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
123.0ms
(- (sqrt (fma (- c) (* a 4.0) (* b b))) b)
108.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))
145.0ms
(sqrt (fma (- c) (* a 4.0) (* b b)))

simplify1.6s

Counts
124 → 124
Iterations
IterNodes
done5000
31948
2420
1168
084

prune753.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.1b

regimes406.0ms

Accuracy

93.1% (0.6b remaining)

Error of 13.2b against oracle of 12.6b and baseline of 21.3b

bsearch263.0ms

Steps
ItersRangePoint
8
1.9371672431899034e+133
9.06569062969358e+135
1.4786955103698794e+135
8
1.8451777477141087e-282
1.805639974384451e-278
1.8895905412153287e-282

simplify11.0ms

Iterations
IterNodes
done49
249
147
041

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s8730×body80valid
286.0ms2931×body80nan