Details

Time bar (total: 27.3s)

sample102.0ms

Algorithm
intervals
Results
52.0ms275×body80valid
11.0ms90×body80nan

simplify254.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02038
13938
27937
314337
417937
518937
619337
done19337

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize179.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite215.0ms

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×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
97.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
62.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
146.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
146.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts
177 → 177
Iterations

Useful iterations: 2 (748.0ms)

IterNodesCost
02086992
15084619
226663570
done50003570

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.3b

localize199.0ms

Local error

Found 4 expressions with local error:

17.3b
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
1×fma-udef
Counts
4 → 61
Calls
4 calls:
1.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
142.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
139.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts
73 → 73
Iterations

Useful iterations: done (4.1s)

IterNodesCost
0711269
11741005
2677906
33809906
done5000903

prune944.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.3b

localize240.0ms

Local error

Found 4 expressions with local error:

24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
183.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
188.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
176.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.3b

localize235.0ms

Local error

Found 4 expressions with local error:

23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
32.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts
80 → 80
Iterations

Useful iterations: done (4.6s)

IterNodesCost
0541228
11471088
25711004
334401004
done50001000

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.3b

regimes398.0ms

Accuracy

92.1% (1.1b remaining)

Error of 7.7b against oracle of 6.6b and baseline of 20.1b

bsearch347.0ms

Steps
ItersRangePoint
8
4.049254448328916e+76
2.3057443967677173e+80
2.2766902918844874e+80
10
-6.623625638726693e+82
-6.4709084601913214e+72
-4.6218828469248316e+82

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
040122
147122
done47122

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.3s8789×body80valid
377.0ms3015×body80nan