Details

Time bar (total: 17.1s)

sample70.0ms

Algorithm
intervals
Results
34.0ms290×body80valid
9.0ms89×body80nan

simplify144.0ms

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize144.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
1.5b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite50.0ms

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:
18.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
9.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
3.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (- b) (sqrt (fma (* 4.0 a) (- c) (* b b))))
160.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
109.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
131.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify2.2s

Counts
173 → 173
Iterations
IterNodes
done5001
21828
1430
0194

prune992.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.1b

localize268.0ms

Local error

Found 4 expressions with local error:

20.3b
(cbrt (fma 4.0 (* a (- c)) (* b b)))
20.3b
(cbrt (fma 4.0 (* a (- c)) (* b b)))
20.3b
(cbrt (fma 4.0 (* a (- c)) (* b b)))
20.7b
(fma (- (fabs (cbrt (fma 4.0 (* a (- c)) (* b b))))) (sqrt (cbrt (fma 4.0 (* a (- c)) (* b b)))) (- b))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
1.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
1.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
0.0ms
(fma (- (fabs (cbrt (fma 4.0 (* a (- c)) (* b b))))) (sqrt (cbrt (fma 4.0 (* a (- c)) (* b b)))) (- b))

series1.6s

Counts
4 → 12
Calls
4 calls:
311.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
310.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
369.0ms
(cbrt (fma 4.0 (* a (- c)) (* b b)))
608.0ms
(fma (- (fabs (cbrt (fma 4.0 (* a (- c)) (* b b))))) (sqrt (cbrt (fma 4.0 (* a (- c)) (* b b)))) (- b))

simplify1.3s

Counts
61 → 61
Iterations
IterNodes
done5002
32657
2644
1211
098

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.1b

localize171.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))
19.6b
(fma (* (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b))))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))

rewrite9.0ms

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:
2.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
2.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
2.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
1.0ms
(fma (* (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b))))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
107.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
93.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
88.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))
899.0ms
(fma (* (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b))))) (cbrt (sqrt (fma (* 4.0 a) (- c) (* b b)))) (- b))

simplify558.0ms

Counts
67 → 67
Iterations
IterNodes
done5001
31010
2263
1122
070

prune649.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.7b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (- b) b) (* 2.0 a))
0.3b
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
1.5b
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
19.5b
(sqrt (fma (* 4.0 a) (- c) (* b b)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
43×*-un-lft-identity
31×add-cube-cbrt
18×times-frac prod-diff sqrt-prod
14×add-cbrt-cube add-exp-log
13×associate-/l*
11×distribute-lft-out--
8×distribute-rgt-out-- difference-of-squares
7×associate-/r*
6×distribute-lft-neg-in distribute-rgt-neg-in fma-neg add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u
3×flip3-- flip--
2×clear-num neg-mul-1 frac-2neg prod-exp associate-/r/ cbrt-unprod div-inv associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 131
Calls
4 calls:
61.0ms
(/ (- (- b) b) (* 2.0 a))
20.0ms
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
9.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
1.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (- (- b) b) (* 2.0 a))
329.0ms
(/ (* 2.0 c) (- (sqrt (fma (* 4.0 a) (- c) (* b b))) b))
129.0ms
(- (sqrt (fma (* 4.0 a) (- c) (* b b))) b)
133.0ms
(sqrt (fma (* 4.0 a) (- c) (* b b)))

simplify1.4s

Counts
143 → 143
Iterations
IterNodes
done5002
22736
1565
0226

prune945.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.6b

regimes886.0ms

Accuracy

87.6% (1.0b remaining)

Error of 12.7b against oracle of 11.7b and baseline of 19.9b

bsearch143.0ms

Steps
ItersRangePoint
8
2.072994944964499e+129
8.571507078369983e+131
2.4837615969358526e+130

simplify17.0ms

Iterations
IterNodes
done58
358
257
153
045

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.2s8727×body80valid
300.0ms2877×body80nan