Details

Time bar (total: 20.2s)

sample70.0ms

Algorithm
intervals
Results
31.0ms281×body80valid
9.0ms92×body80nan

simplify298.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize162.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite167.0ms

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:
56.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
142.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
177 → 177
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune739.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize159.0ms

Local error

Found 4 expressions with local error:

9.4b
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×prod-diff sqrt-prod
2×pow1/3 sqrt-div
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log
Counts
4 → 65
Calls
4 calls:
46.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
123.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
77 → 77
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01641691
13901578
211211356
340391320
done50001319

prune700.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize169.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 66
Calls
4 calls:
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
31.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
168.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
78 → 78
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0941238
12161114
26171028
321591022
done50011004

prune679.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize137.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 66
Calls
4 calls:
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
78 → 78
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0941238
12161114
26171028
321591022
done50011004

prune740.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

regimes274.0ms

Accuracy

93% (0.9b remaining)

Error of 8.3b against oracle of 7.4b and baseline of 20.1b

bsearch291.0ms

Steps
ItersRangePoint
8
4.61796087672408e+142
8.313972478035852e+145
5.1397209577748005e+144
7
-6.338089291324522e+142
-9.408663701389454e+140
-5.105369019268964e+141

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
054180
164180
done64180

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s8715×body80valid
376.0ms2915×body80nan