Details

Time bar (total: 20.6s)

sample54.0ms

Algorithm
intervals
Results
26.0ms281×body80valid
7.0ms92×body80nan

simplify222.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize122.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.6s

Counts
163 → 163
Iterations

Useful iterations: 3 (2.2s)

IterNodesCost
01796238
14174208
211683343
347922690
done50002690

prune751.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize157.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
8×add-log-exp
6×cbrt-prod
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- distribute-rgt-neg-in sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 72
Calls
4 calls:
13.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
84 → 84
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01521636
13891532
213071322
done50001289

prune705.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize171.0ms

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)))

rewrite95.0ms

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:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
78 → 78
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0941238
12161114
26171028
321591022
done50011004

prune765.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize160.0ms

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)))

rewrite73.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
149.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
78 → 78
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0941238
12161114
26171028
321591022
done50011004

prune850.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

regimes226.0ms

Accuracy

93% (0.9b remaining)

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

bsearch346.0ms

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
049180
161180
done61180

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.2s8715×body80valid
368.0ms2915×body80nan