Details

Time bar (total: 16.9s)

sample52.0ms

Algorithm
intervals
Results
23.0ms276×body80valid
6.0ms79×body80nan

simplify175.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize159.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
1.2b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite51.0ms

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:
23.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
19.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
118.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
114.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
131.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify2.4s

Counts
173 → 173
Iterations
IterNodes
done5001
21828
1430
0194

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize173.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma 4.0 (* a (- c)) (* b b))
1.2b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
22.6b
(sqrt (fma 4.0 (* a (- c)) (* b b)))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×sqrt-prod
18×prod-diff
6×pow1 fma-neg add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares
1×sub-neg flip3-- diff-log fma-udef flip-- distribute-lft-out--
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma 4.0 (* a (- c)) (* b b))
11.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
2.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma 4.0 (* a (- c)) (* b b))
121.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
147.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
115.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify1.5s

Counts
93 → 93
Iterations
IterNodes
done5000
33140
2623
1221
0112

prune790.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.4b

localize158.0ms

Local error

Found 4 expressions with local error:

13.6b
(- (- b) (* (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b)))) (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b))))))
22.6b
(sqrt (fma 4.0 (* a (- c)) (* b b)))
22.6b
(sqrt (fma 4.0 (* a (- c)) (* b b)))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite33.0ms

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
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 82
Calls
4 calls:
25.0ms
(- (- b) (* (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b)))) (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b))))))
1.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
1.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (* (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b)))) (sqrt (sqrt (fma 4.0 (* a (- c)) (* b b))))))
123.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
97.0ms
(sqrt (fma 4.0 (* a (- c)) (* b b)))
128.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify2.4s

Counts
94 → 94
Iterations
IterNodes
done5000
33805
2697
1234
0113

prune801.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.4b

localize154.0ms

Local error

Found 4 expressions with local error:

18.2b
(fma (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
22.6b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 55
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))
1.0ms
(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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
649.0ms
(fma (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (sqrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))
121.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
131.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
114.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify585.0ms

Counts
67 → 67
Iterations
IterNodes
done5001
31055
2282
1112
065

prune673.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.9b

regimes483.0ms

Accuracy

85.5% (1.1b remaining)

Error of 13.5b against oracle of 12.4b and baseline of 20.1b

bsearch136.0ms

Steps
ItersRangePoint
9
3.768382185355077e+69
1.107955803311012e+78
7.756215947175277e+77

simplify9.0ms

Iterations
IterNodes
done43
343
242
138
032

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.7s8719×body80valid
349.0ms2811×body80nan